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##### Past 2006 Seminars

 2006 Seminars Time and Date: 2:00 p.m., Wednesday, January 4, 2006 Event: Mathematical Biology Seminar Speaker: Yoichiro Mori, NYU Subject:A Three Dimensional Model of Cellular Electrical Activity'' Location: WMAX 216 Abstract:After a brief discussion of the motivations for developing the model, I will formulate the system of PDEs that govern 3D cellular electrical activity. The relationship between our 3D model and traditional cable models will be explained, thereby illustrating the different time scales that are present in the equations. I will then present an existence analysis for a particular simplification of the model, which will further illuminate the behavior of the system. A numerical method to solve these equations will be presented. This will be followed by simulation results for a particular physiological phenomenon for which our model has provided novel insight: cardiac action potential propagation without gap junctions. I will end with a discussion of future directions. Time and Date: 3:00-4:00 p.m., Thursday, January 5, 2006 Event: PDE and Analysis Seminar Speaker: Andrej Zlatos, University of Wisconsin-Madison Subject:Reaction and Diffusion in the Presence of Fluid Flow'' Location: WMAX 110 Abstract:In this talk I will review some recent developments in the area of reaction-diffusion-advection equations. I will concentrate on the phenomenon of quenching (extinction) of flames by a strong flow. These questions naturally lead to the related problem of estimating the relaxation speed for the solution of a corresponding passive scalar equation, which will also be discussed. Time and Date: 3:00--4:00 p.m., Friday, January 6, 2006 Event: Mathematics Colloquium Speaker: Andrej Zlatos, University of Wisconsin-Madison Subject: Spectral Theory and the Sum Rules for Jacobi Matrices and Orthogonal Polynomials'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, January 9, 2006 Event: IAM Seminar Series Speaker: Mark Jellinek, Department of Earth and Ocean Sciences, UBC Subject:How Continents influence the way in which the Earth cools: An Example of 'Self-Optimization' in a Convecting System'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: It is generally assumed that continents, which act as thermal insulation above the convecting mantle of the Earth, inhibit the Earth's internal heat loss. We test the validity of this intuitive picture using a combination of laboratory experiments and numerical simulations that are understood with scaling theory. We find that the partial insulation of the Earth's mantle due to continents does not generally reduce global heat flow and can actually enhance the rate at which the planet cools. A theory is presented that predicts the surface area at which heat flow is maximized. Remarkably, it appears that the surface area of continents through geological time has remained close to that which maximizes global cooling. Time and Date: 4:00 p.m., Monday, January 9, 2006 Event: Mathematics Colloquium Speaker: Malabika Pramanik, Caltech Subject: Optimal Sobolev regularity of a class of Fourier integral operators'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30 p.m., Tuesday, January 10, 2006 Event: DG-MP-PDE Seminar Speaker: Malabika Pramanik, Caltech Subject:Geometry of linear and monomial polyhedra and their applications'' Location: WMAX 110 Abstract: We define "balls" given by a large number of monomial inequalities, and obtain structure theorems for such sets. In the real setting, this leads to L^p boundedness of maximal averages associated to a family of such balls. In the complex case, these balls play an important role in obtaining Bergman kernel estimates on the diagonal for certain weakly pseudoconvex domains in \mathbb C^n. This is joint work with Alexander Nagel. Time and Date: 2:00 p.m., Wednesday, January 11, 2006 Event: Mathematical Biology Seminar Speaker: Sasha Jilkine, UBC Subject:Cytoskeletal dynamics during cleavage of the C. elegans embryo'' Location: WMAX 216 Abstract: Understanding how cells cleave has been an important problem in cell biology for the last 50 years. In animal cells a contractile ring of actin and myosin assembles beneath the plasma membrane and constricts the cell in two. We visualize the dynamics of GFP-labeled myosin and filamentous actin in live embryos to understand how these two proteins are recruited to the cleavage furrow. We use RNA interference to suppress expression of genes essential for cytokinesis, as well as mechanical perturbations of the mitotic apparatus to investigate how the microtubule-based mitotic apparatus interacts with the actomyosin cortex to determine cleavage furrow position in C. elegans. This work was done in Gene Network Dynamics and Cellular Behavior course at the University of Washington Friday Harbor Laboratories. Time and Date: 3:00 p.m., Thursday, January 12, 2006 Event: DG-MP-PDE Seminar Speaker: David Damanik, Caltech Subject:Dominated Schrodinger cocycles'' Location: WMAX 216 Abstract: We consider ergodic Schrodinger operators over uniformly hyperbolic base transformations and show that at moderately small coupling, the Lyapunov exponent is positive away from a finite set of exceptional energies. This is joint work with Artur Avila. Time and Date: 3:30 p.m., Thursday, January 12, 2006 Event: Algebraic Geometry Seminar Speaker: Patrick Brosnan, UBC Subject:Jumps in the height of the biextension normal function'' Location: WMAX 110 Abstract: I continue the talk given at the end of last semester on my joint work with Greg Pearstein on the height of the Ceresa cycle. At the beginning of the talk there will also be an organizational meeting to decide a final date and time for the seminar. Time and Date: 4:00 p.m., Thursday, January 12, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Traian Pirvu, Department of Mathematics, UBC Subject:Maximizing Portfolio Growth Rate under Risk Constraints'' Location: WMAX 216 Abstract: This work studies the problem of optimal investment subject to risk constraints: Value-at-Risk, Tail Value-at-Risk and Limited Expected Loss. We get closed-form solutions for this problem, and find that the optimal policy is a projection of the optimal portfolio of an unconstrained log agent (the Merton proportion) onto the constraint set, with respect to the inner product induced by the variance-covariance volatilities matrix of the risky assets. In the more complicated situation of constraint sets depending on the current wealth level, we maximize the growth rate of portfolio subject to these risk constraints. We extend the analysis to a market with random coefficients, which is not necessarily complete. We also perform a robust control analysis. We find that a trader subject to Value-at-Risk and Tail Value-at-Risk is allowed to incur some risk. A trader faced with the Limited Expected Loss constraint behaves more conservatively and does not exhibit the above behavior. This is a joint work with Steven Shreve and Gordan Zitkovic. Notes: Coffee and cookies will be served at 3:45 in the PIMS lounge. Please bring your own mug to allow PIMS to be more environmentally friendly. Time and Date: 4:00 p.m., Thursday, January 12, 2006 Event: Complex Fluids Seminar Speaker: Stefan Storey, Dept. of Mechanical Engineering, UBC Subject:Displacing yield-stress fluids in eccentric annuli'' Location: MATH 204 Abstract: Eccentric annular displacement flows of yield stress fluids are of interest principally as a model for the primary cementing of oil wells, in which drilling mud is displaced by a cement slurry. Here we address the issue of laminar displacement fluid mechanics. In vertical displacements, large eccentricities can cause incomplete purging of drilling muds which in turn can lead to poor zonal isolation. Our experimental and numerical work investigates the role of fluid rheology and flow rate in predicting the efficiency of displacement. In general, three modes of displacement are possible; steady, unsteady, and static. These modes refer to the interface dynamics; a steady case represents an efficient displacement where the interface shape is unchanging, and an unsteady case represents a poor displacement with an elongating interface. For yield stress fluids, a static case is possible where the interface on the narrow side of the annulus is stationary. For our experiments, we use Xanthan to displace Carbopol solutions in a lab-scale pilot flow loop. The interface shape is controlled by varying the fluid rheologies, annulus eccentricity and fluid flow rate. We experimentally test all three modes of displacement, and locate the leading and trailing edges of the interface using optical techniques. We show our initial experimental results and make qualitative comparisons to the numerical simulations based on models derived in [1,2,3]. [1] S. Bittleston, J. Ferguson & I.A. Frigaard,  Mud removal and cement placement in primary cementing of an oil well. J. Engineering Mathematics, 43, pp. 229-253 (2002). [2] S. Pelipenko and I.A. Frigaard,  On steady state displacements in primary cementing of an oil well. Journal of Engineering Mathematics, 48(1), pp. 1-26, (2004). [3] S. Pelipenko and I.A. Frigaard, "Visco-plastic fluid displacements in near-vertical eccentric annuli: lubrication modelling." J. Fluid Mech. 520, pp. 343-377, (2004). Time and Date: 3:00 p.m., Friday, January 13, 2006 Event: Mathematics Colloquium Speaker: David Damanik, Caltech Subject: Structures of intermediate complexity and quantum dynamics'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, January 16, 2006 Event: IAM-PIMS-MITACS 2006 Distinguished Colloquium Series Speaker: Lakshminarayanan Mahadevan, Gordon McKay Professor of Applied Mathematics and Mechanics, Division of Engineering and Applied Sciences, Harvard University Subject:Geometry and Elasticity in Physical Packing Problems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Mathematical packing problems, which have a venerable history, typically deal with the arrangements of rigid spheres in unbounded domains. Physical packing (and unpacking) problems have a much shorter history and deal with the relatively large deformations of soft extended objects such as strings and membranes. Examples include the exquisitely orchestrated packing of a long thin strand of DNA into a cell nucleus or in a virus, the aesthetic drapes of a textile, the intricate folds in origami, the wrinkles in a drying raisin and the violent crumpling of a sheet of paper. I will discuss some of the general and specific features of the statics and dynamics of packing and their role in the evolution of structures on many different length scales in the material world. Time and Date: 3:00 p.m., Monday, January 16, 2006 Event: Algebraic Geometry Seminar Speaker: Joel Friedman, UBC Subject:Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity'' Location: WMAX 110 (PIMS) Abstract: Counting connected components and Betti numbers was a known technique in algebraic complexity theory in the late 1970's and early 1980's. Speculation arose as to whether such methods could attack lower bounds in Boolean complexity theory (e.g., P vs. NP). This approach via cohomology (or, in particular, Betti numbers) is appealing due to a vast array of tools developed to study cohomology and its interplay with combinatorics. To our knowledge no essential progress has been made in this approach to date. We shall show that if one generalizes the setting to Grothendieck topologies and uses the machinery of the Grothendieck school (actually a very small part of this machinery), it is possible to circumvent two obstacles to connecting Boolean depth complexity lower bounds to cohomology. We describe ongoing research to look for models of Grothendieck topologies that yield, via these techniques, interesting lower bounds. Time and Date: 4:00 p.m., Monday, January 16, 2006 Event: Mathematics Colloquium Speaker: Ryan O'Donnell, Microsoft Subject: Noise stability, in elections and elsewhere'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Tuesday, January 17, 2006 Event: Discrete Mathematics Seminar Speaker: Ryan O'Donnell, Microsoft Subject:An invariance theorem for functions with small influences'' Location: WMAX 216 Abstract: In this talk I will discuss functions with small "influences" on product probability spaces. These are functions f : Omega_1 x ... x Omega_n -> R such that E[Var_{Omega_i}[f]] is small compared to Var[f] for every each i. The analysis of boolean functions f : {-1,1}^n -> {-1,1} with small influences has become a central problem in discrete harmonic analysis. It is motivated by fundamental questions arising in areas such as theoretical computer science, economics, combinatorics, and statistical physics. I will prove an invariance theorem for multilinear polynomials with small influences and bounded degree, showing that under mild conditions the distribution of such polynomials is essentially invariant for all product spaces. The proof is relatively simple, and provides a non-linear extension of Lindeberg's classical proof of the Central Limit Theorem. Applications of this theorem include the resolution of the "Majority Is Stablest" conjecture from theoretical computer science, and the "It Ain't Over Till It's Over" conjecture from social choice theory. This talk is based on joint work with Elchanan Mossel (Berkeley) and Krzysztof Oleszkiewicz (Warsaw). Time and Date: 3:30 p.m., Tuesday, January 17, 2006 Event: DG-MP-PDE Seminar Speaker: Daniele Cassani, UBC Subject:Nonlinear elliptic systems with critical growth'' Location: WMAX 110 Time and Date: 2:00 p.m., Wednesday, January 18, 2006 Event: Mathematical Biology Seminar Speaker: Dejan Milutinovic, University of Utrecht Subject:Stochastic Model of a Micro-Agent population'' Location: WMAX 216 Abstract: This presentation concerns one of the emergent hot topics in biological research. At the micro level, the immune system acts as a discrete event multi agent system. Most of the reactions (i.e. events) among particles within the immune system are well known, but it is not clear what kind of macro behavior they result in due to the complex interaction among particles in the population. A similar problem appears in Robotics when the control of population of micro-robots is considered. To study such a complex system, we propose the Micro-Agent model of individuals and the Stochastic Micro-Agent population model. They are defined in the Hybrid Systems framework. These models are general enough to describe biological, as well as, robotic agents. Using them, we develop a theory, which is based on the probability density function of the Micro-Agent state. This function connects the state of each Micro-Agent to the state of population within a probabilistic framework. This work is motivated by the modeling of T-cell receptors down-regulation dynamics of the T-cell population mixed with antigen presenting cells. The work includes the numerical examples related to both this application and to the optimal control of a large-size robotic population. Time and Date: 3:30 p.m., Wednesday, January 18, 2006 Event: Probability Seminar Speaker: Frank den Hollander, U Leiden and EURANDOM, The Netherlands Subject:Phase Transitions for Interacting Diffusions'' Location: WMAX 216 Abstract: In this talk we consider the following system of interacting diffusions: dX_i(t)=\sum_{j\in bbb Z^d}a(i,j)[X_j(t)-X_i(t)] dt+\sqrt{bX_i^2(t)} dW_i(t),\quad i\in bbb Z^d,t\geq 0. Here, a(\cdot ,\cdot) is an irreducible random walk transition kernel on bbb Z^d, b\in (0,\infty) is a diffusion parameter, and {W_i}_{i\in bbb Z^d} is a collection of independent standard Brownian motions on bbb R. The initial condition is chosen such that {X_i(0)}_{i\in bbb Z^d} is a shift-invariant and shift-ergodic random field on [0,\infty) with finite mean. We show that the long-time behaviour of this system is the result of a delicate interplay between a(\cdot ,\cdot) and b, in contrast to systems where the diffusion function is subquadratic. In particular, we show that if a(\cdot,\cdot) is transient and symmetric, then the system has an infinite sequence of critical points b_*\geq b_2\geq b_3\geq b_4\geq ...\downarrow 0 at which the successive moments of the distribution of the single components in equilibrium change from infinite to finite. In some cases strict inequality between these critical points can be established. The proof is based on a Feynman-Kac formula, through which the moments of the single components are related to exponential moments of the intersection local time of random walks. Via large deviation theory, the latter lead to variational expressions for the critical points, from which sharp bounds are deduced. This is joint work with Andreas Greven (Erlangen, Germany). Time and Date: 3:00 p.m., Thursday, January 19, 2006 Event: DG-MP-PDE Seminar Speaker: Zhiwu Lin, Courant Institute, NYU Subject:Stability of collisionless plasmas'' Location: WMAX 110 Abstract: A plasma is a completed ionized gas. In many applications such as in nuclear fusion or astrophysical phenomena, the plasma has high temperature or low density, and collisions can be ignored. The standard kinetic models for a collisionless plasma are the Vlasov-Maxwell and Vlasov-Poisson systems. The Vlasov-Poisson system is also used to model galaxy dynamics, where a star plays the role of a particle. There exists infinitely many equilibria for Vlasov models and their stability is of central importance in physics. I will describe my recent works on stability and instability of various Vlasov equilibria. I will focus primarily on some methods and techniques which has been developed recently. One of these utilizes the geometric properties of the dynamical system that describes the particle paths. Time and Date: 4:00--4:50 p.m., Thursday, January 19, 2006 Event: Graduate Student Seminar Speaker: Ben Young, Department of Mathematics, UBC Subject:Everything I know about LaTeX'' Location: MATX 1102 Abstract: LaTeX is a large, open-source computer program for typesetting scientific documents. It is used to create almost all math papers and math graduate theses, as well as many textbooks, presentations, love letters, and so forth. I use LaTeX for three slightly weird purposes: * to take notes in math classes * to organize my research * to produce pretty output from my own computer programs There's lots of good reasons to do all three of these things. I will tell you how and why. Large sections of my talk will be applicable to those who "just want to graduate", as well. If you have a laptop, please install LaTeX on it and bring it to my talk. You may also find it helpful to practice typing backslashes, brackets, and punctuation as quickly as possible. Time and Date: 4:00 p.m., Thursday, January 19, 2006 Event: Complex Fluids Seminar Speaker: Ian Frigaard, UBC Subject:Visco-plastic lubrication, a nonlinearly stable multilayer shear flow'' Location: MATH 204 Abstract: A common problem in multi-layer shear flows, especially from the perspective of process engineering, is the occurrence of interfacial instabilities. For purely viscous fluids these occur at both long and short wavelengths, and at low Reynolds numbers. However, multi-layer duct flows can be stabilised by using a suitable yield stress fluid as the lubricant [1,2]. We focus on the simplest practically interesting case of visco-plastically lubricated viscous shear flow: a core-annular pipe flow consisting of a central core of Newtonian fluid surrounded by a Bingham fluid. First we show how interfacial instabilities may be eliminated through the introduction of a yield-stress fluid as the lubricant and by preserving an unyielded layer adjacent to the interface. Second, we show that nonlinear stability of this type of two-layer flow can also be achieved, at significant Reynolds numbers. Finally we show the results of our recent experimental study of these flows. This is a joint work with C.K. Huen, D.M. Martinez and M.A. Moyers-Gonzalez. [1] Frigaard, I.A., "Super-stable parallel flows of multiple visco-plastic fluids." J. Non-Newtonian Fluid Mech. 100, pp. 49-76, (2001). [2] Moyers-Gonzalez, M., Frigaard, I.A. and Nouar, C., "Nonlinear stability of a visco-plastically lubricated shear flow." J. Fluid Mech. 506, pp.117-146, (2004). Time and Date: 3:00 p.m., Friday, January 20, 2006 Event: Mathematics Colloquium Speaker: Zhiwu Lin, Courant Institute, NYU Subject: Stability of ideal plane flows'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Abstract: Ideal plane flows are incompressible inviscid two dimensional fluids, described mathematically by the Euler equations. Infinitely many steady states exist. The stability of these steady states is a very classical problem initiated by Rayleigh in 1880. It is also physically very important since instability is believed to cause the onset of turbulence of a fluid. Nevertheless, progress in its understanding has been very slow. I will discuss several concepts of stability and some linear stability and instability criteria. In some cases nonlinear stability and instability can be showed to follow from linear results. I will also briefly describe some ideas in the proof of these results. Time and Date: 3:00--4:00 p.m., Monday, January 23, 2006 Event: IAM Seminar Speaker: Roderick Edwards, Department of Mathematics and Statistics, University of Victoria Subject:Gene regulatory networks and dynamical systems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Recent advances in genomics have begun to allow particular gene regulation pathways to be worked out but it has been realized since the 1960's that gene regulatory networks could in principle have arbitrarily complicated interaction structures and behaviour. One framework for the study of such systems in full generality has been to concentrate on structural classes and activation/repression switching dynamics by means of a hard switching' limit. The equations are continuous in time but the interactions between variables (protein concentrations) depend only on whether they are above or below a threshold, i.e. active' or inactive'. This simplified framework has been successfully applied to the analysis of dynamics in several real gene regulatory networks. This class of networks (Glass networks'), though not smooth, is mathematically tractable due to its piecewise-linear nature. Even in quite small (e.g. 4-gene) networks, there is a rich variety of stable dynamics, including multistability (crucial to cell differentiation, for example), periodic orbits (e.g. the cell cycle, circadian rhythms) and chaos. An analytic framework has been developed, involving reduction to explicitly calculated discrete maps on Poincar\'e sections. This allows proof of existence and stability of fixed point, periodic and, remarkably, even chaotic attractors. Some interesting mathematics arises, mainly in dynamical systems and linear algebra. Most of this work was originally done under some restrictive (and unrealistic) assumptions, such as equal decay rates and a single threshold per gene. The removal of these restrictions is an area of current research. Time and Date: 3:00 p.m., Monday, January 23, 2006 Event: Algebraic Geometry Seminar Speaker: Joel Friedman, UBC Subject:Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity, II'' Location: WMAX 110 (PIMS) Abstract: Counting connected components and Betti numbers was a known technique in algebraic complexity theory in the late 1970's and early 1980's. Speculation arose as to whether such methods could attack lower bounds in Boolean complexity theory (e.g., P vs. NP). This approach via cohomology (or, in particular, Betti numbers) is appealing due to a vast array of tools developed to study cohomology and its interplay with combinatorics. To our knowledge no essential progress has been made in this approach to date. We shall show that if one generalizes the setting to Grothendieck topologies and uses the machinery of the Grothendieck school (actually a very small part of this machinery), it is possible to circumvent two obstacles to connecting Boolean depth complexity lower bounds to cohomology. We describe ongoing research to look for models of Grothendieck topologies that yield, via these techniques, interesting lower bounds. Time and Date: 4:00 p.m., Monday, January 23, 2006 Event: Mathematics Colloquium Speaker: Antoine Mellet, University of Texas, Austin Subject: On the homogenization of some free boundary problems'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:20 p.m., Tuesday, January 24, 2006 Event: Joint SFU/UBC Discrete Math Seminar Speaker: Maria Chudnovsky, Princeton University Subject:The Structure of bull-free graphs'' Location: SFU Campus, ASB 10900 (IRMACS Lecture Theatre) Abstract: A {\em bull} is a graph consisting of a triangle and two pendant edges. A graph is said to be {\em bullfree} if it contains no induced subgraph isomorphic to a bull. An obvious example of a bull free graph is a graph with no triangle, or a graph with no stable set of size three; but there are others. It turns out, however, that all bullfree graphs can be built starting from graphs that belong to a few basic classes, and gluing them together by certain operations; and this is the main topic of this talk. Using this structure theorem, in joint work with S. Safra, we prove that every bullfree graph has either a stable set or a clique containing at least |V(G)|^(1/4) vertices, thus settling the Erdos-Hajnal conjecture for the bull. Time and Date: 3:30 p.m., Tuesday, January 24, 2006 Event: DG-MP-PDE Seminar Speaker: Antoine Mellet, University of Texas, Austin Subject:Weak solutions for isentropic compressible Navier-Stokes equations'' Location: WMAX 110 Abstract: The existence and stability of weak solutions for compressible Navier-Stokes equations is an important and challenging problem in fluid mechanics. The case of constant (positive) viscosity coefficients has been adressed, in particular, by P. L. Lions (in the 90's) and E. Feireisl (more recently). In this talk, I will discuss some recent results concerning the case of viscosity coefficients that vanish with the density. Time and Date: 2:00 p.m., Wednesday, January 25, 2006 Event: Mathematical Biology Seminar Speaker: Joe Mahaffy, San Diego State University Subject:Modeling Marine Phage Ecology'' Location: WMAX 216 Abstract: Marine phage are virus that infect bacteria in the ocean. There are about 1.2x1030 phage in the oceans, yet little is known about phage ecology and population dynamics. Each day they destroy about 25% of the marine bacteria, playing an important role in the carbon cycle of the oceans, which is a significant part of the global CO2 cycle. Our studies have used shotgun sequencing and mathematical models based on a Lander-Waterman algorithm to learn about species diversity and abundance. Studies show that the ratio of bacteria to phage remains fairly constant (about 1:10) through a variety of habitats. We develop a two compartment model and fit a number of parameters to explain how this ratio can be maintained. A modified model with delays using quorum sensing of the bacterial population by the phage shows how adaptations of phage between lysogenic and lytic life cycles can produce oscillations in the phage and its host populations, while the ratio of bacteria to phage still remains fairly constant. Time and Date: 3:30 p.m., Wednesday, January 25, 2006 Event: Probability Seminar Speaker: Michiel van den Berg, U Bristol, UK Subject:Heat flow, Brownian motion and Newtonian capacity: a refinement of theorems by F. Spitzer and S.C. Port'' Location: WMAX 216 Abstract: We obtain estimates for the probability that a Brownian motion in R^m, m > 2 hits a non-polar compact set before (a large) time t. Time and Date: 3:30--3:50 p.m., Thursday, January 26, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Andrew Odlyzko, Digital Technology Center, University of Minnesota Subject:Zeros of the Riemann zeta function: Computations and implications'' Location: SFU Campus, Room ASB 10900 Time and Date: 4:00 p.m., Thursday, January 26, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Traian Pirvu, Department of Mathematics, UBC Subject:Portfolio optimization under Value-at-Risk constraint'' Location: WMAX 216 Abstract: In this paper, we analyze the effects arising from imposing a Value-at-Risk constraint in an agent's consumption and portfolio selection problem. The market consists of m risky assets (stocks) plus a risk free asset. The stocks are modelled as exponential Brownian motions with random drift and volatility. The risk of the trading portfolio and consumption is reevaluated dynamically and hence the agent must satisfy the Value-at-Risk constraint continuously. We derive the optimal consumption and portfolio allocation policy in closed form for the case of logarithmic utility. The problem for general power utility is reduced to a deterministic control one, which is analyzed and solved numerically. The VaR constraint remains active once it becomes active and reduces the consumption and investment in the risky assets. The optimal policies are projections of the optimal unconstrained ones onto the constraint set. Time and Date: 4:00 p.m., Thursday, January 26, 2006 Event: Complex Fluids Seminar Speaker: Christian Schoof, Department of Earth and Ocean Sciences, UBC Subject:Sliding under ice sheets'' Location: MATH 204 Abstract: Continental ice sheets, such as those covering Greenland and Antarctica, behave as thin viscous films, and standard lubrication models are capable of describing many aspects of their dynamics. One respect in which ice sheets differ from most other thin-film flows is their ability to slide at the contact between the ice and its substrate (the glacier bed'). Here we review the basic mechanisms of glacier sliding, and investigate the form of friction laws appropriate to glacier sliding. The talk will focus mostly on the effect of cavity formation on glacier sliding, and explore similarities between models for glacier sliding and Signorini-type elastic contact problems. Our results show that friction laws appropriate for glacier sliding are essentially regularized Coulomb friction laws, and we briefly touch on the challenges presented by incorporating a Coulomb friction law into a thin-film model for ice sheet flow. Time and Date: 4:10--5:00 p.m., Thursday, January 26, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Stephen Choi, SFU Subject:On the maximum modulus of multivariate polynomials: Preliminary report'' Location: SFU Campus, Room ASB 10900 Time and Date: 11:00 a.m., Friday, January 27, 2006 Event: Mathematical Biology Seminar Speaker: Yangjin Kim, University of Minnesota Subject:Mathematical modeling of tumor spheroid growth'' Location: WMAX 110 Abstract: Multicellular tumor spheroids (MCTS) have been used as a model system because of their remarkable ability of reproducing the properties of tumors in vivo. MCTS are made of three layers with different mechanical properties, i.e. proliferating outer layer, quiescent middle zone, and necrotic zone. Helmlinger et al (1997) were able to measure the residual stress generated by tumor growth in agarose gel. These results showed that tumor growth can be regulated by stress and that mechanical properties of extracellular matrix (ECM), such as stiffness, can inhibit the tumor growth in vitro. These authors also found that MCTS grew in ellipsoidal shape rather than spherical shape when grown in a long cylinder, which indicates that stress was a controling factor in MCTS growth. The residual stress caused by uncontrolled cell proliferation is believed as possible cause of localized blood vessel collapse in the tumor, thereby causing malfunction of vital organs. For the proliferating zone, I consider force balance equation to get the evolution of cell movement where each cell is considered as a growing viscoelastic ellipse with two major axes. The discretely modeled cells can divide, push each other, and find the right path to move. These cells keep dividing as long as they get the necessary nutrients. As cells proliferate, cells in the center do not have enough nutrient and start to die, a process called necrosis. Cells in outer part of spheroid continue to proliferate, which produces residual stresses. Increased stresses surrounding the spheroid then inhibit MCTS growth and increase the cell density in the proliferating zone. By considering that the gel, quiescent zone, and necrotic region are viscoelastic materials, I use continuum model in these regions and couple the continuum model to the discrete cell model. Reaction-diffusion equations for nutrients are considered to describe the evolution of concentration of nutrients. I discuss the stress effect on tumor growth and growth behavior of active tumor cells. I will also discuss a possible mechanism for reduction of cell volume. My future work includes the incorporation of a shedding effect, which is when tumor cells detach from the primary tumor and shed into the suspension medium. I will discuss how I plan to incorporate this effect, which is an important issue in cancer such as certain brain cancers. Another aspect of my future work is the inclusion of internal cell dynamics. I will discuss this as well. Time and Date: 3:00 p.m., Friday, January 27, 2006 Event: Mathematics Colloquium Speaker: Joe Mahaffy, San Diego State University Subject: Mathematical Models for Red Blood Cell Production'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, January 30, 2006 Event: IAM Seminar Speaker: Wayne Nagata, Department of Mathematics, UBC Subject:Bifurcations of Gyroscopic Systems near a 0:1 Resonance'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We study the local and global bifurcation behavior of gyroscopic dynamical systems near a 0:1 resonance. As an example, we study a rotating shaft under axial load, which occurs in many mechanical applications. Another example of a gyroscopic system is a supported pipe conveying a pulsating fluid. Local bifurcation analysis shows how energy may be transferred from a high frequency vibration mode to a low frequency mode as parameters are varied. Global bifurcation analysis detects the presence of orbits which are homoclinic to certain invariant sets, and this implies chaotic dynamics nearby. Time and Date: 3:00 p.m., Monday, January 30, 2006 Event: Algebraic Geometry Seminar Speaker: Zinovy Reichstein, UBC Subject:A lower bound on the essential dimension'' Location: WMAX 110 (PIMS) Abstract: Let K/k be a field extension. The essential dimension of an object (e.g., a quadratic form, a finite-dimensional algebra, an algebraic variety, a group action, etc.) defined over K is the minimal value of trdeg_k(K_0) such that our object descends to K_0. Here K_0 ranges over the intermediate fields k subset K_0 subset K. In this talk, based on joint work with Boris Youssin, I will discuss a lower bound on certain essential dimensions. The proof of this bound is based on a resolution theorem for algebraic group actions which is of independent interest. Time and Date: 2:00 p.m., Wednesday, February 1, 2006 Event: Mathematical Biology Seminar Speaker: Eldon Emberly, SFU Subject:Synchronizing Mechanisms in Circadian Oscillators'' Location: WMAX 216 Abstract: Many organisms possess internal biochemical clocks, known as circadian oscillators, which allow them to regulate their biological activity with a 24-hour period. It was recently discovered that the circadian oscillator of photosynthetic cyanobacteria is able to function in a test tube with only three proteins, KaiA, KaiB, and KaiC, and ATP. Biochemical events are intrinsically stochastic, and this tends to desynchronize oscillating protein populations. In this talk I will present a model that predicts that the stability of the Kai-protein oscillator relies on active synchronization by (i) monomer exchange between KaiC hexamers during the day, and (ii) formation of clusters of KaiC hexamers at night. The results highlight the importance of collective assembly/disassembly of proteins in biochemical networks. Stochastic effects will also be discussed and will be shown to occasionally enhance oscillatory behavior. Time and Date: 3:30 p.m., Wednesday, February 1, 2006 Event: Algebra Topology Seminar Speaker: Dale Rolfsen, UBC Subject:Foliations of orbifolds and manifolds'' Location: WMAX 110 Abstract: This will be an introduction to foliations on manifolds, with emphasis on codimension one examples in dimensions 2, 3, 4. It will be elementary, beginning from the beginning, but will end with some new results and examples. We will define and illustrate issues such as transverse orientation, liftings under covering maps, invariance under orbifold actions and R-covered foliations. In dimension 2, only two closed manifolds enjoy codimension one foliations at all -- the torus and Klein bottle which have zero Euler characteristic. These already illustrate interesting foliation examples. By contrast, we will see that ALL closed orientable 3-manifolds support codimension one foliations (they all have zero Euler characteristic, too). On the other hand, there are obstructions to supporting certain nice kinds of foliations. I'll conclude with a family of examples of 3-manifolds which have nice R-covered foliations, invariant under an infinite dihedral group. On the other hand, I will argue that they do not support transversely oriented R-covered foliations, by careful inspection of the fundamental group. Time and Date: 3:30 p.m., Wednesday, February 1, 2006 Event: Probability Seminar Speaker: Anthony Quas, Department of Mathematics and Statistics, U. Victoria Subject:Non-monotonicity in (BC)STV'' Location: WMAX 216 Abstract: We study non-monotonicity of outcomes in Instant Runoff Voting (STV with a single winner). This system is used in Australian Senate Elections as well as in Mayoral/Gubernatorial Elections. The system is known to fail to be monotonic. We study the probability of non-monotonic outcomes of the election. Time and Date: 4:00--4:50 p.m., Thursday, February 2, 2006 Event: Graduate Student Seminar Speaker: Alex Duncan, Department of Mathematics, UBC Subject:An Overview of Groebner Bases'' Location: MATX 1102 Abstract: A Groebner basis is a special kind of generating set for an ideal in a polynomial ring. They are a staple of most computer algebra systems and can be used to determine if two ideals are equal, decide whether a polynomial is contained in a given ideal and do computations in quotient spaces. Perhaps their most exciting application is in solving systems of simultaneous polynomial equations. I will give an overview of the theory of Groebner bases including monomial orderings, general multivariate polynomial division and Buchberger's algorithm. The talk should be accessible to anyone who knows basic ring theory. Time and Date: 4:00 p.m., Thursday, February 2, 2006 Event: Complex Fluids Seminar Speaker: Teodor Burghelea, Department of Mathematics, UBC Subject:When a strong nonlinearity has smooth consequences: Scaling and Universality in Elastic Turbulence'' Location: MATH 204 Abstract: After briefly introducing the elastic turbulence as a new type of random flow in a dilute polymer solution, I will review the existing theoretical work [1,2]. Next, I present an experimental flow investigation in a regime of elastic turbulence, with a particular focus on the applicability of Taylor frozen flow hypothesis [3,4]. I will show how a strong hydrodynamic nonlinearity (related to the elastic stresses present in the flow) surprisingly generates a spatially smooth flow at all scales. For such flows, the Taylor hypothesis generally fails, unless a proper choice of the advection velocity is made. Finally, in order to connect our experimental results with the theory, I focus on the role of elastic stresses in statistical and scaling properties of elastic turbulence. Analogy with a small scale fast dynamo in magnetohydrodynamics and with a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, flow structure, and scaling of elastic turbulence. The experimental results will be compared with the existing theoretical predictions. [1] M. Chertkov, Phys. Rev. Lett. *84*, 4761 (2000). [2] A. Fouxon, V. Lebedev, Phys. Fluids *15*, 2060 (2003). [3] T. Burghelea, E. Segre and V. Steinberg, Phys. Fluids *17*, 103101 (2005). [4] T. Burghelea, PhD thesis, The Weizmann Institute of Science,(2005). Time and Date: 3:00 p.m., Friday, February 3, 2006 Event: Mathematics Colloquium Speaker: Frank den Hollander, University of Leiden, EURANDOM Subject: Random walk in random scenery'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m.(MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, February 6, 2006 Event: IAM Seminar Series Speaker: Martin Snajdr, Department of Physics and Astronomy, UBC Subject:Applications of High Resolution Shock Capturing Methods in Relativistic Hydrodynamics'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: It is a well known fact that the solutions of Euler's equations admit discontinuities (shocks, contact discontinuities). Therefore it is not possible to use standard finite difference techniques to numerically advance solutions in time. One way to circumvent the problem is to introduce artificial viscosity that smoothes the discontinuities. Another possibility is to take advantage of the conservative formulation of the Euler's equations and use Godunov type finite volume methods. In this talk I will explain the latter approach and present several astrophysical applications. For certain type of calculations adaptive mesh refinment (AMR) is a necessity, and part of my talk will be devoted to the issue of incorporating AMR into the numerical scheme. Time and Date: 3:00 p.m., Monday, February 6, 2006 Event: Algebraic Geometry Seminar Speaker: Julia Pevtsova, University of Washington, Seattle Subject:Support varieties for some non-cocommutative Hopf algebras and quantum shifted subgroups'' Location: WMAX 110 (PIMS) Abstract: The theory of support varieties for modules was originated in groundbreaking work of Quillen who introduced geometry into the study of cohomological properties of a finite group. Recently, Buan, Krause and Solberg, inspired by the work of Balmer, developed an axiomatic approach to the theory of support varieties starting with any tensor triangulated category. Despite the general nature of the theory, the two known concrete settings to which the theory applies are the derived category of bounded perfect complexes on a Noetherian scheme and the stable module category of a finite group scheme. Both categories share the property of being symmetric tensor categories. One of the goals of the work I'll describe is to present a new, "non-symmetric" setting to which the theory applies as well. In this talk I'll construct the rank and support varieties for the Borel part of a "small" quantum group: namely, b_q(sl_2^n), which can be viewed as a quantum analogue of an elementary abelian p-group. The main challenge, and the major difference from the known cases, arises from the fact that the coproduct, which gives rise to the tensor structure on the module category, is not cocommutative. Yet, we find analogues of Carlson's shifted cyclic subgroups for b_q(sl_2^n), and prove that the support variety of a b_q(sl_2^n)-module defined in terms of cohomology and the rank variety defined in terms of representation theory coincide. As an application, we generalize the result of Erdmann and Holloway who establish a similar "rank=support" theorem for the modules of truncated polynomial algebras of the form k[t_1, ... t_n]/(t^2_i). This is joint work with Sarah Witherspoon. Time and Date: 11:00 a.m., Tuesday, February 7, 2006 Event: Mathematical Biology Seminar Speaker: Rafael Meza Rodriguez, University of Washington Subject:Gestational Mutations and Carcinogenesis'' Location: WMAX 110 Abstract: The risk of getting most cancers increases as a power of age. This terrible fact remained unexplained until 1954, when Armitage and Doll used a simple mathematical model to show that the power of age in cancer risk may be related to the number of genetic events required to produce a malignant cell. Several years later, Knudson used another mathematical model (now widely known as the Moolgavkar-Venzon-Knudson model) to postulate the existence of specific tumor suppressor genes. A few years later, experimentalists corroborated Knudson's hypothesis, revolutionizing cancer research. These two examples are proof that mathematical modeling can contribute significantly to the progress of biological research, and in particular to the study of human diseases. During this talk I will introduce some of the mathematical ideas behind the theory of multistage carcinogenesis. In addition, I will present a mathematical formulation designed to evaluate the effects of gestational mutations on cancer risk. Models for the accumulation of critical mutations during gestation (Luria-Delbruk type) are used in tandem with multistage models of carcinogenesis to derive hazard and survival functions for cancer in specific tissues. To illustrate the use of the methodology, I will present estimations of the proportion of colorectal cancers in the US population that could be attributed to gestational mutations, and discuss the possible effects of in utero X-Ray exposures on colorectal cancer risk. Time and Date: 3:30 p.m., Tuesday, February 7, 2006 Event: DG-MP-PDE Seminar Speaker: Yujin Guo, Department of Mathematics, UBC Subject:On the partial differential equations arising from electrostatic MEMS'' Location: WMAX 110 Abstract: We analyze the nonlinear parabolic problem u_t=\Delta u - \frac{\lambda f(x)}{(1+u)^2} on a bounded domain \Omega of R^N with Dirichlet boundary conditions. This equation models the dynamic deflection of a simple electrostatic Micro-Electromechanical System (MEMS) device, consisting of a thin dielectric elastic membrane with boundary supported at 0 above a rigid ground plate located at -1. Here f(x) \geq 0 characterizes the varying dielectric permittivity profile. When a voltage --represented here by \lambda-- is applied, the membrane deflects towards the ground plate and a snap-through (touchdown) may occur when it exceeds a certain critical value \lambda ^*. Applying analytical and numerical techniques, the existence of \lambda ^* is established together with rigorous bounds. We show the existence of at least one steady-state when \lambda < \lambda ^* (and when \lambda =\lambda ^* in dimension N < 8), while none is possible for \lambda >\lambda ^*. More refined properties of steady states, such as regularity, stability, uniqueness, multiplicity, energy estimates and compactness results, are shown to depend on the dimension of the ambient space and on the permittivity profile. For the dynamic case, the membrane globally converges to its unique maximal steady-state when \lambda \leq \lambda ^*; on the other hand, if \lambda > \lambda ^* the membrane must touchdown at finite time, and touchdown can not take place at the location where the permittivity profile vanishes. Refined description of MEMS touchdown behavior is also given, including touchdown rate, touchdown time, touchdown points, etc. This is joint work with Nassif Ghoussoub at UBC. Time and Date: 2:00 p.m., Wednesday, February 8, 2006 Event: Mathematical Biology Seminar Speaker: Meredith Greer, Applied Mathematics, Bates College, Lewiston, Maine Subject:Modeling Protein Population Interactions in Prion Diseases'' Location: WMAX 216 Abstract: A prion is an infectious form of protein that differs from a naturally produced protein only in its folding. Prions are thought to cause several diseases, with Bovine Spongiform Encephalopathy (BSE) perhaps the most widely known example. Diseases associated with prions have very long incubation periods, are difficult to detect in all but the latest stages, and are highly fatal. These characteristics alone make study of prions interesting, but even more so, there is the question of prion replication. Proteins do not possess any nucleic acid. Without DNA or RNA, how does the structure copy itself and spread? There is evidence that prions form polymers or aggregates, most likely with additional stability. Some or all of these polymers attach to the similar naturally produced protein and convert it to the infectious variety. Polymers also split. Altogether, both the overall quantity of infectious proteins, and the number of polymer strands, increase. To model these phenomena, we represent prion polymer length as a continuous structure variable. We obtain a system of two partial differential equations modeling interaction of the infectious and non-infectious conformations of prion protein within an infected individual. We use this system to create numerical simulations of disease progress within such an individual. Under some circumstances, we can simplify to a system of three ordinary differential equations. In the ODE case, we discuss steady states, their stability, and relative parameter changes that affect their viability. Time and Date: 3:30 p.m., Wednesday, February 8, 2006 Event: Algebra Topology Seminar Speaker: Kee Y. Lam, UBC Subject:Truncated Projective spaces and the Kervaire Invariant problem'' Location: WMAX 110 Abstract: The Kervaire Invariant problem is currently the most outstanding problem in the homotopy theory of spheres. In this talk I will begin by providing some background to this problem, and then argue that from a bundle-theorectic view point, it is really a profound analogue of the classical problem of sphere parallelisability. I will then conclude by outlining a strategy by which this problem can hopefully be resolved. Time and Date: 3:30 p.m., Wednesday, February 8, 2006 Event: Probability Seminar Speaker: Grégory Maillard, EURANDOM Subject:Parabolic Anderson Model on interacting particle systems'' Location: WMAX 216 Abstract: We study intermittency for the Parabolic Anderson Model when the diffusion is driven by a constant \kappa and the branching is induced by different choices of interacting particle systems. We consider the annealed Lyapunov exponents and we show that they display an interesting dependence on \kappa, with qualitatively different behaviors in different dimensions. Time and Date: 4:00-4:30 p.m., Wednesday, February 8, 2006 Event: IAM Student-Faculty Seminar Speaker: Michael Ward, UBC Subject:Eigenvalue Optimization for the Laplacian and the Neumann Green's Function'' Location: LSK 301 Abstract: An optimization problem for the fundamental eigenvalue »0 of the Laplacian in a planar simply-connected domain that contains N small identically-shaped holes, each of a small radius µ << 1, is considered. A Neumann boundary condition is imposed on the outer boundary of the domain and a Dirichlet condition is imposed on the boundary of each of the holes. For small hole radii µ, we derive an asymptotic expansion for »0 in terms of certain properties of the Neumann Green's function for the Laplacian. This expansion depends on the locations xi, for i = 1,...,N, of the small holes. For the unit disk, ring-type configurations of holes are constructed to optimize the eigenvalue with respect to the hole locations. This optimization problem gives the optimum places to insert localized traps inside a domain in order to minimize the lifetime of a Brownian particle. This eigenvalue optimization problem is also shown to be closely related to the problem of determining equilibrium vortex configurations in the Ginzburg-Landau theory of superconductivity. Finally we discuss a few interesting open problems related to eigenvalue optimization, including the problem of inserting small windows on the boundary of the domain to optimize heat loss and the problem in theoretical ecology of re-seeding a species that is on the verge of extinction. This is joint work with Theodore Kolokolnikov (Dalhousie University) and Michele Titcombe (University of Montreal). Time and Date: 12:30 p.m., Thursday, February 9, 2006 Event: Mathematics Colloquium Speaker: Andrew Rechnitzer, University of Melbourne Subject: The analytic structure of lattice models -- looking inside unsolved problems'' Location: MATH 104 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Abstract: What it means for a problem to be "solved" really depends on who you talk to; you can square the circle if you are happy to use more than a ruler and compass. In this talk, I will describe work that has lead to "unsolvability" results for a wide class of combinatorial problems that arise in statistical physics. The starting point for these results are techniques which allow us to peek inside the solutions of these problems without actually having to solve them. The structure of the solutions proves that they do not belong to the most pervasive class of functions in mathematical physics, so called differentiably-finite functions. This, in turn, shows that the models cannot be solved using many traditional combinatorial methods. Time and Date: 3:30--3:50 p.m., Thursday, February 9, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Matilde Lalin, Institute for Advanced Study Subject:Mahler measure as values of regulators'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: Regulators allows us, sometimes, to explain and compute examples of Mahler measure formulas for multivariate polynomials. I will sketch some ideas of how to use regulators for computations and show some old and new examples. Time and Date: 4:10--5:00 p.m., Thursday, February 9, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Nike Vatsal, UBC Subject:Special values of L-functions modulo p'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: It has been known since Euler that the values of the Riemann zeta function at negative integers are certain rational numbers, namely the Bernoulli numbers B_k. Similarly, the values of Dirichlet L-functions at s=0 are related to class numbers of certain number fields. These are simple instances of a common phenomenon, namely that the values of L-functions at critical points are algebraic, up to a simple factor, and that these algebraic numbers are related to algebraic quantities such as class numbers and Selmer groups. The present talk will be a survey talk on the algebraicity of special values of L-functions and their divisibility properties modulo primes. Time and Date: 4:00 p.m., Thursday, February 9, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Ulrich Haussmann, UBC Subject:Economic Equilibrium with Multivariable Utility'' Location: WMAX 216 Abstract: Consider a closed production-consumption economy with multiple agents and resources. It is shown that an Arrow-Debreu equilibrium exists. This paradigm is used to develop aggregation of utility functions of several variables without the Inada restriction. Time and Date: 4:00 p.m., Thursday, February 9, 2006 Event: Complex Fluids Seminar Speaker: Kerstin Wielage, Department of Mathematics, UBC Subject:Displacement of generalized Newtonian fluids along a plane channel'' Location: MATH 204 Abstract: In this talk results of a numerical study into the displacement of one generalized Newtonian fluid by another, along a plane channel are presented. Our motivation comes from the oil and gas industry, and specifically from the primary cementing of oil wells. In this process, drilling mud is displaced first by a spacer fluid and then by a cement slurry, along a narrow eccentric annulus. Here, the fully 2-dimensional displacements that occur along an azimuthal slice of the annulus are considered. These can either be interpreted as displacement of immiscible or miscible fluids. For immiscible fluids we use the diffuse-interface method [1,2] and for miscible fluids a reaction-diffusion formulation. In both cases the focus of our study is on the potentially beneficial effects of a non-monotone variation in fluid rheologies as might for example be caused by chemical reaction or fluid incompatibility. Results are shown especially for non-monotone viscosity variations. [1] D. Jacqmin, Calculation of two-phase Navier-Stokes flows using phase-field modeling, J. Comp. Phys. 155 (1999), pp. 96-127. [2] P. Yue, J.J. Feng, C. Liu, and J. Shen, A diffuse-interface method for simulating two-phase flows of complex fluids, J. Fluid Mech. 515 (2004), pp. 293-317. Time and Date: 3:00 p.m., Friday, February 10, 2006 Event: Discrete Mathematics Seminar Speaker: Andrew Rechnitzer, U. Melbourne Subject:Lattice paths, copolymers and the Morita approximation'' Location: MATX 1100 (note unusual room and day for this seminar) Abstract: Directed paths on regular lattices are idealised geometric models of polymers. Despite their apparent simplicity, they give rise to interesting combinatorial problems and display rich behaviour. These models can be further enriched by moving from homogeneous polymers, to heterogeneous copolymers constructed from two or more different types of building blocks with different properties. I will talk about some of these path models, the combinatorial challenges they present and the behaviour that they model. Time and Date: 3:30--4:20 p.m., Tuesday, February 14, 2006 Event: Joint SFU/UBC Discrete Math Seminar Speaker: Luis Goddyn, Simon Fraser University Subject:Silver Cubes'' Location: SFU Campus, ASB 10900 (IRMACS Lecture Theatre) Abstract: An n by n matrix is *silver* if, for i=1,...,n, every symbol in {1,2,...,2n-1} appears as an entry in either row i or column i. An IMO 1997 question introduced this definition, and asked whether a silver matrix of order 1997 exists. (In fact, one exists if and only if n=1 or n is even.) In this paper we investigate higher dimensional analogs, silver cubes. Finding the correct generalization is the first challenge. The cells on the main diagonal of a silver matrix are treated specially. What should serve as a "diagonal" in a d-dimensional n x n x ... x n silver cube? We propose that a "diagonal" should be a "maximum independent set in the d'th cartesian power of the complete graph of order n." This definition is motivated by "minimal defining sets" for colouring such graphs. The goal is to label the cells with symbols {1,2,...,d(n-1)+1} so that, for each cell c on the "diagonal", every symbol appears once in one of the d(n-1)+1 cells orthogonally translated from c. We present constructions, nonexistence proofs and connections with coding theory and projective geometry. This is joint work with M. Ghebleh, E. Mahmoodian and M. Verdian-Rizi. Time and Date: 3:00--4:00 p.m., Monday, February 20, 2006 Event: IAM Seminar Series Speaker: Ralf Wittenberg, Department of Mathematics, SFU Subject:One-Dimensional Spatiotemporal Chaos'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We discuss some aspects of spatiotemporal chaos in a family of one-dimensional PDEs including the Kuramoto-Sivashinsky (KS) equation, with particular attention to the importance of large spatial scales. We shall see that these long-wave modes act as a "heat bath" in the KS equation and maintain the spatiotemporal disorder. Addition of a destabilizing term at large scales induces a bifurcation sequence to an attracting shock-like solution; this observation has had interesting implications for the estimation of analytical bounds on the attractor. The main part of our story concerns relatively recent (ongoing) exciting developments on a sixth-order analogue of the KS equation, the Nikolaevskii equation. In this equation, which arises via the coupling of unstable short-wave modes with a neutrally stable long-wave mode, one observes a spatiotemporally chaotic state with strong scale separation. As such, a multiple-scale asymptotic description would seem to be in order, but as observed by Matthews and Cox, the asymptotically consistent scaling for the dynamics is different from the Ginzburg-Landau scaling one typically observes at onset. However, our computations indicate the need for corrections to the Matthews-Cox scaling hypothesis, and we infer the existence of a novel spatiotemporally complex attractor with different scaling regimes. Time and Date: 3:00 p.m., Monday, February 20, 2006 Event: Algebraic Geometry Seminar Speaker: Behrang Noohi Subject:Uniformization of analytic Deligne-Mumford curves'' Location: WMAX 110 (PIMS) Abstract:I will discuss the trichotomy hyperbolic/euclidean/spherical for (non-singular) Deligne-Mumford analytic curves. I will explain the classification of such curves by their uniformization types and use this to give an explicit presentation of a Deligne-Mumford curve as a quotients stack. This is joint work with Kai Behrend. Time and Date: 3:45 p.m., Monday, February 20, 2006 Event: Mathematics Departmental Tea Location: MATX 1115, (Math Lounge) Time and Date: 4:00--5:00 p.m., Monday, February 20, 2006 Event: Mathematics Colloquium Speaker: Adam D. Smith, Weizmann Institute Subject: Error-Correction and Randomness Extraction in Cryptographic Protocols'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30 p.m., Tuesday, February 21, 2006 Event: Discrete Mathematics Seminar Speaker: Adam D. Smith, Weizmann Institute Subject:Correcting Errors Without Leaking Partial Information'' Location: WMAX 216 Abstract: This work explores what kinds of information two parties must communicate in order to correct errors which occur in a shared secret string W. Any bits they communicate must leak a significant amount of information about W --- that is, from the adversary's point of view, the entropy of W will drop significantly. Nevertheless, we construct schemes with which Alice and Bob can prevent an adversary from learning any useful information about W. Specifically, if the entropy of W is sufficiently high, then there is no function f(W) which the adversary can learn from the error-correction information with significant probability. This leads to several new results: (a) the design of noise-tolerant "perfectly one-way" hash functions in the sense of Canetti, Micciancio and Reingold; (b) private "fuzzy extractors", useful for handling noisy secret keys without leaking sensitive information about the key; (c) noise tolerance and stateless key re-use in the "Bounded Storage Model" (resolving an open problem of Ding). The heart of our constructions is the design of randomness extractors with the property that the source W can be recovered from the extracted randomness and any string W' which is close to W. Joint work with Yevgeniy Dodis. Time and Date: 3:30 p.m., Tuesday, February 21, 2006 Event: DG-MP-PDE Seminar Speaker: Frederic Robert, Nice Subject:Quantization issues for fourth order elliptic equations in dimension four'' Location: WMAX 110 Abstract: In dimension four, the fourth order elliptic nonlinear equation \Delta^2 u=e^u (E) enjoys conformal invariance properties that allow blowing up of sequences of solutions to (E). This invariance corresponds to a similar one for second order equations in dimension two studied, among others by Brezis-Merle: they actually enlightened a quantization of the energy associated to the dimension two. Surprisingly, there is absolutely no such a quantization in dimension four, and the situation can become quite weird. In this talk, we will describe completely the blow-up in the general case and in interesting specific situations. Time and Date: 2:00 p.m., Wednesday, February 22, 2006 Event: Mathematical Biology Seminar Speaker: Leah Keshet, UBC Subject:Biopolymers: kinetics and behaviour'' Location: WMAX 216 Abstract: In this seminar, I will survey some of the dynamic behaviour of various biopolymers, and address the following question: what can we infer about the polymers based on their polymerization kinetics. Some of my remarks will be motivated by actin, the dominant component of the cytoskeleton. Other remarks will generalize to biological aggregates such as amyloid, a component of Alzheimer's disease senile plaques. Time and Date: 2:45-3:35 p.m., Wednesday, February 22, 2006 Event: PIMS Afternoon Tea Location: West Mall Annex, PIMS 1st Lounge Time and Date: 3:30 p.m., Wednesday, February 22, 2006 Event: Algebra Topology Seminar Speaker: Steve Mitchell, University of Washington Subject:K(1)-local homotopy theory and the Iwasawa algebra'' Location: WMAX 110 Abstract: The Iwasawa algebra is the power series ring in one variable over the p-adic integers (p a fixed prime). It has long been studied by number theorists in connection with Z_p-extensions of number fields. In particular, there is a beautiful classification theorem for finitely-generated modules over it that has been exploited to great advantage. It is exactly like the classical theorem for modules over a principal ideal domain, except that the classification only holds up to pseudo-isomorphism---the morphisms with finite kernel and cokernel. The Iwasawa algebra also arises in homotopy theory, as a ring of Adams operations on p-adic complex K-theory. Consequently the module theory alluded to above can be applied, not only to the K-groups themselves but to the entire K(1)-local'' stable homotopy category. This is the category obtained from the ordinary stable homotopy category by inverting the mod p K-equivalences. In this talk I will describe joint work with Rebekah Hahn, in which we explore the K(1)-local world from this Iwasawa-theoretic viewpoint. Time and Date: 3:30 p.m., Wednesday, February 22, 2006 Event: Probability Seminar Speaker: Michael Kozdron, University of Regina Subject:The configurational measure on mutually avoiding SLE paths'' Location: WMAX 216 Abstract: We discuss a new approach to the study of multiple chordals SLEs in a simply connected domain by considering configurational measures on paths instead of infinitesimal descriptions. We show how to construct these measures so that they are conformally covariant, and satisfy boundary perturbation and Markov properties, as well as a cascade relation. As an application of our construction, we derive the scaling limit of Fomin's identity in the case of two paths directly; that is, we prove that the probability that an SLE(2) and a Brownian excursion do not intersect can be given in terms of the determinant of the excursion hitting matrix. This talk is based on joint work with Greg Lawler of Cornell University. Time and Date: 4:00 p.m., Thursday, February 23, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Matthias Mueller, PIMS, UBC Subject:Robust utility maximization and BSDE'' Location: WMAX 216 Abstract: Robust utility means taking the expected utility with respect to a set of probability measures and taking the least favorable. We are able to solve the robust utility maximization problem in a Brownian framework for exponential, logarithmic and power utility functions. The utility, the optimal trading strategy as well as the density of the measure attaining the infimum in the robust utility are characterized by a Backward Stochastic Differential Equation. Time and Date: 4:00 p.m., Thursday, February 23, 2006 Event: Complex Fluids Seminar Speaker: Larry Li, Department of Mechanical Engineering, UBC Subject:An Experimental Study of Non-Newtonian Atomization'' Location: MATH 204 Abstract: An investigation into non-Newtonian atomization using pre-formulated substitute test liquids is presented. These liquids allowed for the decoupling of two common rheological phenomena: extension thickening and shear thinning. By maintaining similar values of surface tension, density, and steady shear viscosity in the test liquids, and independently varying the extensional viscosity, the effect of elasticity on the atomization process was studied. Flash photography was employed to elucidate details of the breakup process. Mean droplet velocities were quantified using Particle Image Velocimetry (PIV). Results showed that elasticity can significantly influence the breakup of a spray issuing from a co-axial air-blast atomizer operating at high aerodynamic Weber numbers (~1000). The development of filamentary structures and large scale ligaments hindered atomization by delaying droplet formation until farther downstream where relative air-to-liquid velocities were reduced. Consequently, larger droplets were predicted. This prediction was supported by PIV measurements indicating that the elastic liquids atomized into droplets which were better able to maintain their initial momentum. Time and Date: 3:00--4:00 p.m., Friday, February 24, 2006 Event: Mathematics Colloquium Speaker: Xiuxiong Chen, University of Wisconsin, Madison Subject: On the greatest lower bound of the Calabi energy'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, February 27, 2006 Event: IAM Seminar Series Speaker: W. Kendal Bushe, Department of Mechanical Engineering, UBC Subject:Fluctuations in the Autoignition Delay Time of Methane/Air Systems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We have recently been studying autoignition of natural gas mixtures in an internal combustion engine context. We are motivated by the possibility that natural gas could be used as an alternate fuel in heavy duty applications, with substantial benefits in terms of pollutant emissions. We are starting to understand that fluctuations in the autoignition delay time of even initially homogeneous mixtures are possible due to the random nature of inter-molecular collisions at the earliest stages of the ignition process. These fluctuations can have a severe impact on our ability to control engines, particularly as we try to push the engine to operate at more extreme conditions to minimize pollutants. The talk will start with an overview of the evidence we have that fluctuations in the ignition delay time are indeed significant. A relatively new method for predicting these fluctuations using a Monte Carlo method will then be presented and results from this method will be discussed. The talk will conclude with some prospects for future uses of this technique. Time and Date: 3:00 p.m., Monday, February 27, 2006 Event: Algebraic Geometry Seminar Speaker: Deepak Khosla, University of Texas, Austin Subject:Divisors on moduli spaces of curves: new techniques for calculation'' Location: WMAX 110 (PIMS) Abstract: The effective cone of \overline{\mathcal{M}}_g plays an important role in the study of the birational geometry of the moduli space \mathcal{M}_g of curves of genus g. In this talk we study the moduli space \mathcal{G}^r_d(\mathcal{M}_g) of curves with linear series and the forgetful map to \mathcal{M}_g to obtain potentially infinitely many counterexamples to a conjecture of Harris and Morrison concerning the shape of the effective cone of \overline{\mathcal{M}}_g. Time and Date: 3:45 p.m., Monday, February 27, 2006 Event: Mathematics Departmental Tea Location: MATX 1115, (Math Lounge) Time and Date: 4:00--5:00 p.m., Monday, February 27, 2006 Event: Mathematics Colloquium Speaker: Shakhar Smorodinsky, Courant Institute of Mathematical Sciences Subject: Coloring Geometric Hypergraphs'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30 p.m., Tuesday, February 28, 2006 Event: Discrete Maths Seminar Speaker: Shakhar Smorodinsky, Courant Institute of Mathematical Sciences Subject:On K-Sets in dimensions 2, 3 and 4'' Location: WMAX 216 Abstract: Let P be a set of n points in the Euclidean d dimensional space. A subset P' of P is called a k-set if its cardinality is k and there exists a half-space H such that P'= H\cap P (that is, P' can be separated from its complement by a hyperplane). The problem of determining the asymptotic of f_d(n,k), the maximum number of distinct k sets that an n element point set in R^d can have (for a fixed d) was posed more than 30 years ago by Lovasz and Erdos et al. Solution to this problem remains elusive even in the plane (i.e., d = 2). We survey the recent results that achieve the best known upper bounds in dimensions two 2, 3 and 4. This problem has many applications in computational geometry and some examples will be discussed. Time and Date: 3:30 p.m., Tuesday, February 28, 2006 Event: DG-MP-PDE Seminar Speaker: Rustum Choksi, SFU, PIMS Subject:A nonlocal isoperimetric problem'' Location: WMAX 110 Abstract: We will consider a nonlocal isoperimetric problem which is a paradigm for energy-driven pattern formation associated with long and short-range interactions. I will address several analytical issues associated with this problem, focusing on questions about periodicity of minimizers in n-space dimensions. Time and Date: 2:00 p.m., Wednesday, March 1, 2006 Event: Mathematical Biology Seminar Speaker: Jim Faeder, Los Alamos National Lab Subject:Rule-based modeling of biochemical networks'' Location: WMAX 216 Abstract: Biochemical networks, particularly those involved in eukaryotic signal transduction, often exhibit combinatorial complexity in the number of distinct chemical species, e.g. phosphorylation states and molecular complexes, that may arise dynamically. This complexity arises because the modular nature of the proteins involved permits each protein to have multiple binding partners and hence to form large, heterogeneous complexes. For networks marked by combinatorial complexity, the conventional approach of manually specifying each term of a mathematical model is untenable. To avoid this problem, modelers often make implicit assumptions to limit the number of species, but these are usually poorly justified and may adversely affect both the predictive and analytical utility of the model. As an alternative, we have developed software called BioNetGen that automatically generates the species and reactions implied by a set of modular proteins and their interactions. The basic approach is to represent biomolecular interactions and their effects as rules, which are evaluated automatically to generate a reaction network. The full network may be generated prior to a simulation or may be adaptively enlarged over the course of a simulation. In BioNetGen2, protein complexes are represented as graphs, with the nodes of the graph representing protein domains, node labels indicating the domain state, and edges representing binding interactions between domains. Time and Date: 3:00 p.m., Wednesday, March 1, 2006 Event: Seminar in Coding and Information Theory Speaker: Henry Pfister, EPFL Subject:Capacity-Achieving Codes for the BEC with Bounded Complexity'' Location: MATX 1102 Abstract: Error-correcting codes which employ iterative decoding algorithms are now considered state of the art in communications. In fact, there are a large number of code families which achieve a small gap to capacity with feasible decoding complexity. Examples are low-density parity-check (LDPC) codes, irregular repeat-accumulate (IRA) codes, and Raptor codes. For each of these code families, one can construct code sequences which provably achieve capacity on the binary erasure channel (BEC). In each case, however, the decoding complexity becomes unbounded as the gap to capacity vanishes. This talk will focus on recently constructed code families whose complexity remains bounded as the gap to capacity vanishes. Assuming only basic knowledge of LDPC codes, three closely related ensembles will be described: IRA codes, accumulate-repeat-accumulate (ARA) codes, and accumulate-LDPC (ALDPC) codes. Using the duality between these ensembles and simplified approach to density evolution, we will construct a variety of codes which achieve capacity with bounded complexity. Finally, the consequences for coding on general channels will be considered. Parts of this work are joint with Igal Sason and Ruediger Urbanke. Time and Date: 2:45-3:35 p.m., Wednesday, March 1, 2006 Event: PIMS Afternoon Tea Location: West Mall Annex, PIMS 1st Lounge Time and Date: 3:30 p.m., Wednesday, March 1, 2006 Event: Algebra Topology Seminar Speaker: Gabriel Indurskis, Department of Mathematics, UBC Subject:On the SL(2,C) character varieties of manifolds obtained from the Whitehead link exterior by Dehn filling - I'' Location: WMAX 110 Abstract: In the first part of this mini-series I will give an introduction to the Culler-Shalen theory of SL(2,C)-representations of the fundamental groups of 3-manifolds. I will in particular discuss the SL(2,C) representation and character varieties and their importance for 3-manifold topology. Furthermore, I will give an introduction to the Culler-Shalen seminorm, an important tool for the study of Dehn fillings of 3-manifolds. In the second part I will focus on an infinite family of 3-manifolds obtained by Dehn filling on one component of the Whitehead link exterior and will show how to compute their Culler-Shalen seminorms. To do this, I will use a "detour" through the so-called eigenvalue variety of the Whitehead link exterior (as introduced by S. Tillmann) to find a one-variable polynomial for each filled manifold whose non-trivial roots characterize so-called p-reps, i.e. representations which are parabolic on the peripheral subgroup. This can be seen as a generalization of a well-known method due to Riley. As an interesting side-effect, the connection to the Culler-Shalen seminorms gives a topological proof of the simplicity of the non-trivial roots of the infinite family of polynomials in question. Time and Date: 3:30 p.m., Wednesday, March 1, 2006 Event: Probability Seminar Speaker: Reda Messikh, Eurandom Subject:On the 2d Ising Wulff crystal near criticality'' Location: WMAX 216 Abstract: We study the behavior of the two-dimensional Ising model in a finite box at temperatures that are below, but very close to the critical temperature. In a regime where the temperature appoaches the critical point and, simultaneously, the size of the box grows fast enough, we establish a large deviation principle that proves the appearance of a round Wulff crystal in the vicinity of the critical point. Time and Date: 2:30 p.m., Thursday, March 2, 2006 **Please note this unusual time.** Event: PIMS-MITACS Math Finance Seminar Speaker: David Lando, Copenhagen and Princeton Subject:Decomposing Swap Spreads'' Location: WMAX 216 Abstract: We analyze a six-factor model for Treasury bonds, corporate bonds, and swap rates and decompose swap spreads into three components: A convenience yield from holding Treasuries, a credit risk element from the underlying LIBOR rate, and a factor specific to the swap market. In the later part of our sample, the swap-specific factor is strongly correlated with hedging activity in the MBS market. The model further sheds light on the relationship between AA hazard rates and the spread between LIBOR rates and GC repo rates and on the level of the riskless rate compared to swap and Treasury rates. (Joint work with Peter Feldhtter) Time and Date: 4:00 p.m., Thursday, March 2, 2006 Event: Complex Fluids Seminar Speaker: Shreyas Mandre, Department of Mathematics, UBC Subject:Roll waves and relatives'' Location: MATH 204 Abstract: Thin films flowing down inclines evolve into a series of propagating waves, as is commonly observed on rainy days. These waves, called roll waves, are a robust phenomena making their appearance on film thicknesses spanning orders of magnitude, from the sub-millimeter thin to several feet thick. This family of waves itself is a member of a more general class of flows of thin films with a dynamically evolving interface. I will present results from the treatment of two problems from this class. The first is that of the nonlinear evolution of turbulent roll waves. This problem was primarily motivated by hydraulic drainage systems, but analogies have sprung up in a variety of fields like granular flow, two-phase flows, ocean gravity currents, etc. My focus will be on the wavelength selection mechanism at work for these waves. The second problem I will present is the case when the interface evolves according to an elastic law, as in the general framework of flow-structure interaction. Instead of waves, I will address the possibility of elastic oscillations being induced by the flow. Motivation for studying these oscillations is derived from an assortment of fields, including biology, geology and music. I will also briefly discuss acoustic excitation in relation to elastic oscillations. Time and Date: 3:00--4:00 p.m., Friday, March 3, 2006 Event: Mathematics Colloquium Speaker: Martin Barlow, UBC Subject: Random walks, the heat equation, and percolation'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, March 6, 2006 Event: IAM Seminar Series Speaker: Steven Plotkin, Department of Physics and Astronomy, UBC Subject:How Does a Protein Fold? The Effects of Structure and Many-Body Interactions'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The theory for how a protein folds up to a biologically functional structure has occupied researchers for the last few decades. The difficulties stem from an incomplete knowledge of an accurate Hamiltonian, as well as non-trivial aspects of polymer physics that complicate the kinetics of folding. Here, I will give a fairly long introduction to some of the central issues in protein folding, and then go on to describe some recent results showing that relaxation rates increase significantly as the folding mechanism becomes increasingly heterogeneous. Time permitting, I will discuss the role of many-body interactions in the Hamiltonian, and show how accounting for them is essential for predicting how a protein folds up. Time and Date: 12:30 p.m., Tuesday, March 7, 2006 Event: UBC SCAIM Seminar Speaker: Maya Gupta, Department of Electrical Engineering, University of Washington Subject:Optimization problems in statistical learning'' Location: CS 238 (Note this alternate location, 2nd flr of the CS Bldg.) Abstract: Standard and new optimization problems in statistical learning are discussed. Statistical learning, sometimes called pattern recognition or machine learning, uses labeled samples to make inferences about new "test" samples. For example, given a number of emails labeled as "spam" or "not spam", one would like a program to learn how to classify new emails as "spam" or "not spam" automatically. A wide class of statistical learning techniques, including neural nets, linear regression, splines, and support vector machines, make such inferences based on different models that lead to different, but related, optimization problems. A different approach to statistical learning is nonparametric near-neighbor learning, in which a test sample is classified based on labeled samples that are most similar. We show that nonparametric near-neighbor learning is significantly improved by setting up an optimization problem that regularizes linear interpolation. The nonparametric near-neighbor optimization problem is qualitatively different than the optimization problems that occur in model-based learning (such as neural nets, linear regression, support vector machines, etc). We will discuss the open questions in this research and the optimization challenges. Example applications may include protein structure estimation, custom color enhancements, and pipeline integrity estimation. Time and Date: 3:30 p.m., Tuesday, March 7, 2006 Event: DG-MP-PDE Seminar Speaker: Takis Souganidis, U. Texas Subject:Recent advances to the theory of homogenization in random environments'' Location: WMAX 110 (PIMS Seminar Room) Abstract: In this talk I will describe recent advances to the theory of homogenization of nonlnear first- and second-order partial differential equations set in general stationary ergodic environments. I will also discuss some applications including moving interfaces and large deviations in random media. Time and Date: 4:00-5:00 p.m., Tuesday, March 7, 2006 Event: The Ivan and Betty Niven Distinguished Lectures Speaker: Ching-Li Chai, University of Pennsylvania Subject:Monodromy groups (Student Lecture)'' Location: MATH 105 Notes: (Refreshments will be served at 3:30 p.m., MATX 1115) Abstract: A monodromy group is the group of symmetries of a family of objects which are "locally isomorphic". These groups frequently occur in several areas of mathematics, including algebra, topology and number theory. In many situations one would like to show that the monodromy group is "as large as possible", subject to the obvious constraints. We will consider several examples of the monodromy problem in different flavors: local versus global, p-adic versus l-adic, etc. The first examples are from Galois theory with finite monodromy groups. In other examples from number theory the monodromy groups will be infinite. Time and Date: 2:00 p.m., Wednesday, March 8, 2006 Event: Mathematical Biology Seminar Speaker: Sam Isaacson, University of Utah Subject:Stochastic reaction-diffusion methods for modeling gene expression complex geometries'' Location: WMAX 216 Abstract: We will present several mathematical models for studying reaction-diffusion processes wherein both noise in the chemical reaction process and geometry may be important. In particular, we will examine the relation between the reaction-diffusion master equation model of spatially distributed stochastic chemical kinetics and models that track individual particles. Our analysis will demonstrate the importance of modeling point binding, equivalently binding to a small target, in understanding the reaction-diffusion master equation. Applications of the preceding models to studying the spatially and temporally distributed nature of eukaryotic gene expression and regulation will be discussed. Time and Date: 3:30 p.m., Wednesday, March 8, 2006 Event: Algebra Topology Seminar Speaker: Gabriel Indurskis, Department of Mathematics, UBC Subject:On the SL(2,C) character varieties of manifolds obtained from the Whitehead link exterior by Dehn filling - II'' Location: WMAX 110 Abstract: In the first part of this mini-series I will give an introduction to the Culler-Shalen theory of SL(2,C)-representations of the fundamental groups of 3-manifolds. I will in particular discuss the SL(2,C) representation and character varieties and their importance for 3-manifold topology. Furthermore, I will give an introduction to the Culler-Shalen seminorm, an important tool for the study of Dehn fillings of 3-manifolds. In the second part I will focus on an infinite family of 3-manifolds obtained by Dehn filling on one component of the Whitehead link exterior and will show how to compute their Culler-Shalen seminorms. To do this, I will use a "detour" through the so-called eigenvalue variety of the Whitehead link exterior (as introduced by S. Tillmann) to find a one-variable polynomial for each filled manifold whose non-trivial roots characterize so-called p-reps, i.e. representations which are parabolic on the peripheral subgroup. This can be seen as a generalization of a well-known method due to Riley. As an interesting side-effect, the connection to the Culler-Shalen seminorms gives a topological proof of the simplicity of the non-trivial roots of the infinite family of polynomials in question. Time and Date: 3:30 p.m., Wednesday, March 8, 2006 Event: Probability Seminar Speaker: Jean-Dominique Deuschel, Berlin Subject:Quenched invariance principle for random walks in random environment admitting a finite cycle representation'' Location: WMAX 216 Abstract: This is joint work with Holger Koesters. We consider a class of random walks in a random environment on Z^d admitting a finite cycle representation, that is the corresponding jump rates are labeled by finite oriented cycles with ergodic weights, eg. [K], [M]. The reversible random conductances model with trivial two points cycles is a particular case, see [S] thus our model extends to the non reversible situation. Assuming uniform irreducibility, we prove a quenched invariant principle for the rescaled process. The annealed CLT result has been proved recently in the special case of two-fold walks by Komorovski and Olla in [K]. We adapt the quenched proof of Sidoravicius and Sznitman, [S], to the non reversible case using corrector, the sector condition and the heat kernels upper bounds for centered random walks by Mathieu, [M]. [K] Komorowski, T; Olla, S. A note on the central limit theorem for two-fold stochastic random walks in a random environment. Preprint (2005). [M] Mathieu, P. Carne-Varopulos bounds for centered random walks. Ann of Prob (2006) [S] Sidoravicius, V ; Sznitman A Quenched invariance principles for walks on clusters of percolation or among random conductances. Probab. Theory Related Fields, 129, 219-244 Time and Date: 3:00--3:50 p.m., Thursday, March 9, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Kate Petersen, Queen's University Subject:Cusps and congruence subgroups of PSL(2,O_K)'' Location: UBC Campus, WMAX 110 Abstract: For a number field K, the groups PSL(2,O_K) have markedly different characteristics depending on whether the ring of integers O_K has infinitely many units or not. We'll discuss how this difference manifests itself in terms of the topology of certain quotients and connect it to a generalization of Artin's Primitive Root Conjecture. Time and Date: 4:00 p.m., Thursday, March 9, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Alexey Kuznetsov, McMaster University Subject:Explicit formulas for Laplace transforms of stochastic integrals'' Location: WMAX 216 Abstract: In this talk we present a general method to compute expected values of the form E[ e^{\int_0^t \phi(X_s) ds}g(X_t) ] for a general diffusion process X_t and certain functions \phi(x). Expectations of this form are the main building blocks in many areas of Mathematical Finance, and existence of explicit formulas is crucial for applications. We provide explicit formulas (given in terms of hypergeometric functions) in the case of CIR and Jacobi diffusions. We also discuss how these results fit in the general classification scheme of solvable diffusion models and how they can be applied to interest rate modelling, credit risk and utility based pricing. Time and Date: 4:00 p.m., Thursday, March 9, 2006 Event: Complex Fluids Seminar Speaker: Teodor Burghelea, Department of Mathematics, UBC Subject:Wave drag due to generation of capillary-gravity surface waves'' Location: MATH 204 Abstract: The onset of the wave resistance via the generation of capillary-gravity waves by a small object moving with a velocity V is investigated experimentally. Due to the existence of a minimum phase velocity V_c for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases, waves or rotons are produced at V>V_c due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to \sqrt{V-V_c} for various fluids. This observation contradicts the theory of Raphael and de Gennes. We also find that the reduced wave drag force for different fluids and different ball size may be scaled in such a way that all the data collapse on a single curve. The capillary-gravity wave pattern and the shape of the wave-generating region are investigated both experimentally and theoretically. Good agreement between the theory and the experimental data is found in this case. Time and Date: 4:10-5:00 p.m., Thursday, March 9, 2006 Event: Number Theory/Algebraic Geometry Seminar Speaker: Ching-Li Chai, University of Pennsylvania Subject:Canonical coordinates for leaves of p-divisible groups (2nd Niven Lecture)'' Location: UBC Campus, WMAX 110 Abstract: Let p be a prime number and g be a positive integer. Let M be the moduli space of abelian varieties of PEL type. A leaf in M is the locus corresponding to a fixed isomorphism class of polarized p-divisible group with prescribed endomorphisms. Although a leaf is defined by a "pointwise" condition, it turns out that the formal completion (or jet space) of a leaf at a point has a rigid structure: It is built up from a finite collection of p-divisible formal groups via a family of fibrations. This structural description can be regarded as a generalization of the Serre-Tate coordinates of the local deformation space of a ordinary abelian variety. We also explain a local rigidity result related to the action of the local stabilizer subgroup on the canonical coordinates. Time and Date: 3:00--4:00 p.m., Friday, March 10, 2006 Event: Mathematics Colloquium Speaker: Ching-Li Chai, University of Pennsylvania Subject: Hecke orbits (3rd Niven Lecture)'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, March 13, 2006 Event: IAM Seminar Series Speaker: Michael Novak, Faculty of Land and Food Systems, UBC Subject:Proper and Complete Surface Energy Balance of a Bare Drying Soil: Agassiz 1978 Revisited'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Despite its interest for researchers and various practitioners in the last thirty years or so, a complete theoretical description of a drying bare soil has not been presented. When a bare soil is wet enough, evaporation occurs at its surface. But as drying proceeds, the soil hydraulic conductivity for liquid water declines steeply and evaporation occurs in a zone just below the surface. Proper treatment of the diurnal dynamics of this zone requires a theory of coupled heat and mass transfer (of water in both liquid and vapour phases). The energy balance at the soil surface varies dramatically when evaporation shifts from the surface to below it, although fluxes of heat and water vapour from the soil vary less. In this talk I will describe the relevant physics, mathematics, and solution using a commercially available finite-element program (FEMLAB). Time and Date: 3:00 p.m., Monday, March 13, 2006 Event: Algebraic Geometry Seminar Speaker: Yunfeng Jiang, UBC Subject:The orbifold Chow ring of toric stack bundles'' Location: WMAX 110 (PIMS Seminar Room) Abstract: Generalizing the construction of toric Deligne-Mumford stacks by Borisov, Chen and Smith, we define extended toric Deligne-Mumford stacks so that we obtain some interesting stakcs when we twist them by principle torus bundles. We call them toric stack bundles. We compute the orbifold Chow ring of such toric stack bundles. As an application, we compute the orbifold cohomology ring of any µ-gerbe over a smooth variety B for a finite abelian group µ. Time and Date: 3:30--4:20 p.m., Tuesday, March 14, 2006 Event: Joint Discrete Mathematics - Computing Science SFU/UBC Seminar Speaker: Arie Bialostocki, University of Idaho Subject:Some Problems in view of recent developments of the Erdos Ginzburg Ziv Theorem'' Location: SFU Campus, ASB 10900, IRMACS Lecture Theatre Abstract: Two conjectures concerning the Erd¨os Ginzburg Ziv theorem were recently confirmed. Reiher and di Fiore proved independently the two dimension analogue of the EGZ theorem, as conjectured by Kemnitz, and Grynkiewicz proved the weighed generalization of the EGZ theorem as conjectured by Caro. These developments trigger some further problems. First, we will present computer experiments that at least for small numbers reveal very simple phenomena of zero sum theorems that seem to be difficult to prove. Next, we will examine the notion of generalization of Ramsey type theorems in the sense of a given zero sum theorem in view of the new developments. About the Speaker: Dr. Arie Bialastocki is a Professor of Mathematics at the University of Idaho - Moscow, Idaho. He attended Tel Aviv University and received from it a B.Sc., M.Sc., and Ph.D. in Mathematics. Dr. Bialostocki is the author and co-author of numerous papers with topics in combinatorics, graph theory, and group theory. For a few years he directed the Research Experience for Undergraduate (REU) Program in Discrete Mathematics. Time and Date: 2:00 p.m., Wednesday, March 15, 2006 Event: Mathematical Biology Seminar Speaker: Eirikur Palsson, SFU Subject:How do changes in the properties of the cAMP signaling system in Dictyostelium affect the patterns observed?'' Location: WMAX 216 (PIMS Seminar Room) Abstract: Here I will first introduce the model, a biologically realistic three dimensional mathematical model that facilitates the simulation and visualization of cell movement in multicellular systems. This model allows us to study how cell adhesion, stiffness, active force generation and chemotaxis affect the movement and signaling of cells in multicellular systems. I will show examples of its applications, compare the results with experimental data and present results that highlight the interplay of chemotaxis and adhesion in cell sorting and movements. I also point out other insights into the mechanism of cell movements that may be gained from the model. The building blocks of the model are individual deformable ellipsoidal cells; each cell having certain given properties, not necessarily the same for all cells. Since the model is based on known processes, the parameters can be estimated or measured experimentally. The cellular slime mold Dictyostelium discoideum is a widely used model system for studying a variety of basic processes in development, including cell-cell signaling, signal transduction, pattern formation and cell motility. I will show simulations of the chemotactic behavior of single cells, streaming during aggregation, and the collective motion of an aggregate of cells driven by a small group of pacemakers. The results are compared with experimental data and examples shown, that highlight the interplay of chemotaxis and adhesion on cell sorting and movements in Dictyostelium. The model predicts that the motion of two-dimensional slugs results from the same behavior that is exhibited by individual cells; it is not necessary to invoke different mechanisms or behaviors. Finally I will discuss how different models of the signaling system can influence the results. I show how changes in the activity of phosphodiesterase and whether it is secreted or membrane bound affect the aggregation and the resulting patterns observed. Such as how spirals may form. Time and Date: 3:30 p.m., Wednesday, March 15, 2006 Event: Algebra Topology Seminar Speaker: Behrang Noohi, Max Planck Institute, Bonn Subject:What is a topological stack?'' Location: WMAX 110 (PIMS Seminar Room) Time and Date: 3:30 p.m., Wednesday, March 15, 2006 Event: Probability Seminar Speaker: Kevin Buhr Subject:A Simple Construction of Arratia Flow'' Location: WMAX 216 Abstract: In his 1979 thesis and an uncompleted 1981 manuscript, Arratia described a coalescing Brownian flow that "lives" on the real line. Intuitively, Brownian motions start at every space-time point and evolve independently until they meet and coalesce. Arratia's unpublished results are often cited, and remarkably an entirely new construction recently appeared in Annals of Probability (Fontes et al., 2004). However, these existing constructions seem to be incomplete, indirect, or ugly, or some mixture thereof. In this talk, I'll give a simple, straightforward, and concrete construction using a particle lookdown system. This approach is in the spirit of Arratia's original direct but incomplete 1979 construction and is truer to the intuitive description of the flow. It also allows for nearly transparent proofs of certain flow properties and suggests some new connections between Arratia flow and genetic particle models. Time and Date: 4:00-4:30 p.m., Wednesday, March 15, 2006 Event: IAM Student-Faculty Seminar Speaker: Wan Chen, Department of Mathematics, UBC Subject:Residual velocities in steady free boundary problems of Vector Laplacian Type'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Free boundary problems (FBPs) are boundary value problems with a moving boundary. They have wide applications in fluid flow, phase change models and other fields. We provide a useful analytical technique of the well-posedness for steady state FBPs. Moreover, the analysis gives insight into choosing residual velocities with better numerical properties when we use a certain iterative tracking method to locate the steady interface. The advantages are demonstrated in a numerical example at the end. Time and Date: 4:00 p.m., Thursday, March 16, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Patrick Cheridito, Operations Research and Financial Engineering, Princeton University Subject:Time-consistency of indifference prices and monetary utility functions'' Location: WMAX 216 Abstract: We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that the agent's preferences are given by utility functions, which are updated in a time-consistent way as more information is becoming available. Our main result is that the agent's indifference prices are time-consistent if and only if his preferences can be represented with utility functions that are additive with respect to cash. We call such utility functions monetary. The proof is based on a characterization of time-consistency of dynamic utility functions in terms of indifference sets. As a special case, we obtain the result that expected utility leads to time-consistent indifference prices if and only if it is based on a linear exponential function. Time and Date: 3:00--4:00 p.m., Friday, March 17, 2006 Event: Mathematics Colloquium Speaker: Robert Moody, Mathematics and Statistics, University of Victoria Subject: Dynamics in the Theory of Diffraction in Systems with Long-range Aperiodic Order'' Location: MATX 1100 Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, March 20, 2006 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Philip Holmes, Department of Mechanical and Aerospace Engineering, NIMH Silvio O. Conte Center for Neuroscience Research, Princeton University Subject:Optimal Decisions in the Brain: From Neural Oscillators to Stochastic Differential Equations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The sequential probability ratio test (SPRT) is optimal in that it allows one to accept or reject hypotheses, based on noisy incoming evidence, with the minimum number of observations for a given level of accuracy. There is increasing neural and behavioral evidence that primate and human brains employ a continuum analogue of SPRT: the drift-diffusion (DD) process. I will review this and describe how a biophysical model of a pool of spiking neurons can be simplified to a phase oscillator and analysed to yield spike rates in response to stimuli. These spike rates tune DD parameters. This study is a small step toward the construction of a series of models, at different time and space scales, linking neural spikes to human decisions. This work is joint with Eric Brown, Jeff Moehlis, Rafal Bogacz and Jonathan Cohen at Princeton, and Garry Aston-Jones' group (Laboratory of Neuromodulation and Behavior, University of Pennsylvania). It provides a rich, if chaotic, example of applied mathematics in action, involving probability, stochastic differential equations, and nonlinear dynamical systems. Time and Date: 3:30-4:30 p.m., Tuesday, March 21, 2006 Event: Discrete Maths Seminar Speaker: Richard Ehrenborg, University of Kentucky Subject:The Mobius function of partitions with restricted block sizes'' Location: WMAX 216 (PIMS Seminar Room) Abstract: We compute the Mobius function of filters in the partition lattice formed by restricting to partitions by type. The Mobius function is determined in terms of the descent set statistics on permutations and the Mobius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Mobius function on integer compositions is determined by a topological argument. Here the permutahedron makes a cameo appearance. This is work in progress with Margaret Readdy. Time and Date: 3:30 p.m., Tuesday, March 21, 2006 Event: DG-MP-PDE Seminar Speaker: Weiyue Ding, Peking University and PIMS Distinguished Chair Subject:Recent progress in Schroedinger flow'' Location: WMAX 110 (PIMS Seminar Room) Abstract: Schroedinger flow is a Hamiltonian flow for mappings from a Riemannian manifold into a Kahler manifold with the energy E(u) as the Hamiltonian. It is also known as Schroedinger map'. In this talk I will survey on some results for the existence of solutions to the initial value problem of the flow, possible existence of finite-time blow-up of smooth solutions, and existence of special solutions of the flow. Time and Date: 2:00 p.m., Wednesday, March 22, 2006 Event: Mathematical Biology Seminar Speaker: Fiona Brinkman, SFU Subject:Trends in microbial protein networks and their evolution'' Location: WMAX 216 Abstract: I'll talk about how we've uncovered some relationships regarding how bacterial protein networks change as a function of bacterial genome size and time. This will include presenting relationships uncovered regarding different types of components of these networks, such as network regulators and proteins residing in particular 3D locations in the cell. I'll also go over a theory I am working on regarding how these networks change over time and are influenced by a possible large "gene pool" associated with viral organisms. The implications of all this on mathematically modeling microbial change over time will be discussed, including possible implications on predicting microbial disease outbreaks in populations. I'll also bring up some mathematical approaches we've developed to identify DNA sequence composition differences in microbes that may be related to the possible large gene pool that may be greatly influencing microbial evolution and influencing emergence of new microbial strains. Time and Date: 3:30-4:30 p.m., Wednesday, March 22, 2006 Event: Probability Seminar Speaker: Nicolas Petrelis, EURANDOM Subject:Polymer pinning at an interface'' Location: WMAX 216 Abstract: We will consider a model of heteropolymer in the neighborhood of an oil-water interface. The polymer will be also attracted by the interface itself (for instance because attractive droplets of a third solvent are spread close to the interface). This model gives rise to a localization-delocalization phase transition and a critical curve. We will consider new localization strategies to improve the existing lower bounds of the critical curve. Time and Date: 4:00-4:30 p.m., Wednesday, March 22, 2006 Event: IAM Student-Faculty Seminar Speaker: Hui Huang, Department of Mathematics, UBC Subject:Mesh Denoising with Intrinsic Texture'' Location: Room 301, LSK Bldg. Abstract: We describe an iterative refinement method that is designed to smooth, but not over-smooth, noisy triangle meshes. Our method not only preserves sharp features but also retains visually meaningful fine scale components or features, referred to as intrinsic texture''. An anisotropic diffusion method is first developed that is comparable in efficiency and performance to bilateral filtering. This then becomes the inner iteration in an iterative refinement process that gradually and adaptively increases the importance of data fidelity, yielding an efficient multiscale algorithm that is capable of handling irregular meshes and intrinsic texture. Time and Date: 3:00 p.m., Thursday, March 23, 2006 Event: DG-MP-PDE Seminar Speaker: Valery Serov, University of Washington Subject:Born approximation in the multidimensional inverse scattering problem with singular potentials'' Location: WMAX 110 Time and Date: 3:00--3:50 p.m., Thursday, March 23, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Renate Scheidler, Centre of Information Security and Cryptography, University of Calgary Subject:The real model of a hyperelliptic curve'' Location: SFU Campus, Room ASB 10900 Note there will be a tea break from 3:50 - 4:10 p.m. Abstract: Arithmetic geometers and cryptographers are familiar with what we call for our purposes the “imaginary model” of a hyperelliptic curve. Another less familiar description of such a curve is the so-called “real model”; the terminology stems from the analogy to real and imaginary quadratic number fields. Structurally and arithmetically, the real model behaves quite differently from its imaginary counterpart. While divisor addition with subsequent reduction (“giant steps”) is still essentially the same, the real representation no longer allows for unique representation of elements in the Jacobian by their reduced representatives. However, degree-zero divisors in the real model exhibit a so-called infrastructure, with an additional, much faster operation (“baby steps”). We present the real model of a hyperelliptic curve and its two-fold baby-step-giant-step divisor arithmetic. We go on to illustrate how to use these algorithms in the principal infrastructure for efficient cryptographic applications. Time and Date: 4:10--5:00 p.m., Thursday, March 23, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Peter Borwein, SFU Subject:Littlewood's 22nd problem'' Location: SFU Campus, Room ASB 10900 Abstract: Littlewood, in his 1968 monograph Some Problems in Real and Complex Analysis, poses the following research problem, which appears to still be open: "If the n_m are integral and all different, what is the lower bound on the number of real zeros of \Sigma_{1\leq m\leq n}\cos (n_m\theta )? Possibly N-1, or not much less." No progress appears to have been made on this in the last half century. Time and Date: 4:00 p.m., Thursday, March 23, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Ivar Ekeland, UBC Subject:Rational behavior with non-exponential discount, and what happens to Hamilton-Jacobi'' Location: WMAX 216 Time and Date: 4:00 p.m., Thursday, March 23, 2006 Event: Complex Fluids Seminar Speaker: Savvas G. Hatzikiriakos, Department of Chemical and Biological Engineering, UBC Subject:Wall Slip and Related Phenomena'' Location: MATH 204 Abstract: It is known that polymer melts slip when the wall shear stress exceeds a critical value. It is also well established in the literature that during the extrusion of polyolefins, when the wall shear stress exceeds the critical value for the onset of slip, small amplitude periodic distortions appear on the surface of polymer extrudates, which leads to commercially unacceptable products. Theses two phenomena are discussed in terms of their interrelationship, their implication in polymer rheology and processing by examining several critical factors i.e. interfacial tension and work of adhesion of the relevant interfaces. Use of certain processing additives to eliminate and control these phenomena will also briefly be discussed. These include fluoropolymers, boron nitride and nanoclays. The mechanisms by which these phenomena are controlled and eliminated will also be discussed. Time and Date: 3:00-4:00 p.m., Friday, March 24, 2006 Event: Mathematics Colloquium Speaker: Richard Ehrenborg, University of Kentucky Subject: Counting pattern avoiding permutations via integral operators'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, March 27, 2006 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: John Tyson, Department of Biology, Virginia Polytechnic Institute and State University Subject:Computational Cell Biology: From Molecular Networks to Cell Physiology'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The fundamental goal of molecular cell biology is to understand cell physiology in terms of the information encoded in the cell's genome. In principle, we know how this information is translated into functional proteins that carry out most of the interesting chores in a living cell. But to make a firm connection between molecular events and cell behavior involves many challenging computational problems at every step along the way. The early steps – sequence analysis, protein folding, molecular dynamics, metabolic control theory – are well established branches of biochemistry. But the 'last step', from networks of regulatory proteins to the physiological responses of a cell to its environment, is an especially challenging problem that has received little attention so far. Accurate and effective computational methods for deriving cell behavior from molecular wiring diagrams are crucial to future progress in understanding living cells and in modifying cell physiology for medical and technological purposes. A nice example of this challenge is the cell cycle: the sequence of events by which a growing cell duplicates all its components and partitions them more-or-less evenly between two daughter cells. The cell cycle is fundamental to all processes of biological growth, development and reproduction, and hence plays a central role in such important processes as carcinogenesis, wound healing, and tissue engineering. The molecular mechanism that controls DNA synthesis and nuclear division is so complex that its behavior cannot be understood by casual, hand waving arguments. By translating this mechanism into differential equations, we can analyze and simulate the behavior of the control system, comparing model predictions with the observed properties of cells. Theoretical models also provide new ways to look at the dynamics of cell cycle regulation. This approach is generally applicable to any complex gene-protein network that regulates some behavior of a living cell. Time and Date: 3:00 p.m., Monday, March 27, 2006 Event: Algebraic Geometry Seminar Speaker: Kevin Purbhoo, Department of Mathematics, UBC Subject:Geometry of the Horn Recursion'' Location: WMAX 110 (PIMS Seminar Room) Abstract: In 1962, A. Horn conjectured a recursive solution to the Hermitian sum problem, which asks: if we know the eigenvalues of two n x n Hermitian matrices, what can we say about the eigenvalues of their sum? The conjecture was initially quite mysterious, but over the last decade, it has been shown not only that Horn's conjecture is true, but that it has connections and implications in several different areas of mathematics. Among these implications is a strange recursive aspect to vanishing problems in the cohomology ring of Grassmannians. I will talk about some of the geometry behind this fact, and some of its generalisations. Time and Date: 3:30-4:20 p.m., Tuesday, March 28, 2006 Event: Joint SFU/UBC Discrete Math Seminar Speaker: Kee Y Lam, UBC Subject:The combinatorics of sums of squares as studied via topology'' Location: WMAX 216 (PIMS Seminar Room) Abstract: Historically, the well-known identity (x_1^2+x_2^2)(y_1^2+y_2^2 )=(x_1y_1-x_2 y_2)^2+(x_1y_2+x_2y_1)^2 had led to a sums of square problem, namely to determine all identities of the type (x_1^2 +..+ x_r^2 )(y_1^2 +..+ y_s^2 ) = f_1^2 +..+ f_n^2 where f1,.., fn belong to a polynomial ring Q[x1,.., xr ; y1,., ys]. In this generality the problem remains wide open. For the case when the commutative ring Q is Z, it reduces to a question of discrete mathematics, involving signed intercalate matrices. In this talk I shall explain what intercalate matrices are, and show how ideas from algebraic topology can be used in the study of the combinatorics of such matrices. Time and Date: 3:30 p.m., Tuesday, March 28, 2006 Event: DG-MP-PDE Seminar Speaker: Weiyue Ding, Peking University and PIMS Distinguished Chair Subject:Evolution of Minimal Tori in Riemannian Manifolds'' Location: WMAX 110 Abstract: We propose a new approach to obtain minimal surfaces of genus p\geq 1 in a closed Riemannian manifold by the L^2 negative gradient flow of the energy E(u, \sigma), where \sigma denotes the conformal structures on the genus p surface. In a recent work with Jiayu Li and Qinyue Liu, we concentrate in the case p=1, i.e. the surface being a 2-torus, and obtain results on the analysis of the flow including the existence of the initial value problem, blow-up of the map u(t) and degeneration of the conformal structure \sigma(t), energy identities when blow-up and degeneration occurs, and convergence at time infinity, etc. Time and Date: 2:00 p.m., Wednesday, March 29, 2006 Event: Mathematical Biology Seminar Speaker: Dmitry Kondrashov, University of Wisconsin-Madison Subject:Coarse-grained models of residue interactions within and between protein structures'' Location: WMAX 216 Abstract: Fluctuations of proteins near their native conformations play important roles in function. Simple coarse-grained models, such as the Gaussian Network Model, have been shown to capture some of the features of equilibrium protein dynamics. We extend this model to include more than one interaction parameter between residues, by using B-factors from 147 ultra-high resolution X-ray crystal structures to optimize the interaction parameters. By simply separating residue interactions into covalent and noncovalent we improve the average correlation between the model and the B-factors from 0.65 to 0.74. The high-resolution structures also provide data about the directionality of motion in the form of anisotropic B-factors. We perform a systematic comparison of a number of coarse-grained models of protein dynamics, and assess their fidelity to the data. We are also studying the evolution of interacting pairs of residues on the interfaces of protein complexes. We have found over 500 structures of mammalian protein dimers in the Protein Data Bank, and determined the contact matrices for the interfaces. We test the hypothesis of positive selection on the interacting residues by comparing orthologous sequences to an out-group to measure the frequency of cooperative changes in the interacting residue pairs. We then use the above coarse-grained models to identify residue pairs with the greatest involvement in low-frequency modes of motion, and compare their selection parameters to the rest of the protein interface residues. Time and Date: 3:30 p.m., Wednesday, March 29, 2006 Event: Algebra Topology Seminar Speaker: Alejandro Adem, UBC Subject:A Stringy Product for Twisted Orbifold K-theory'' Location: WMAX 110 Abstract: In this lecture I will outline the construction of a product for the twisted K-theory of the inertia orbifold, which extends the Pontryagin product in equivariant K-theory. The twisting is done using an element in the image of the inverse transgression. Examples from finite group cohomology will be given. Time and Date: 3:30-4:30 p.m., Wednesday, March 29, 2006 Event: Probability Seminar Speaker: James Martin, Oxford, UK Subject:Competition interfaces and interacting particles'' Location: WMAX 216 Abstract: The "corner growth model" is a simple model of random growth which is related to directed last-passage percolation and to the TASEP (totally asymmetric simple exclusion process). I'll discuss the "competition interface" formed between two clusters growing in the same space, and describe how this relates to the behaviour of a "second-class particle" in the TASEP. An almost sure limit theorem for the direction of the interface separating the two clusters corresponds to a strong law of large numbers for the path of the second-class particle. Depending on the initial conditions, the direction of the interface (and hence the speed of the particle) may be either deterministic or random. If time permits, I'll mention a few things about its fluctuations around the limiting direction. Joint work with Pablo Ferrari and Leandro Pimentel. Time and Date: 4:00-4:30 p.m., Wednesday, March 29, 2006 Event: IAM Student-Faculty Seminar Speaker: Lloyd Bridge, Department of Mathematics, UBC Subject:Numerical Methods for Capturing a Two-Phase/Vapour Interface in a Porous Medium'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We describe a model problem of water transport and phase change in a finite porous layer, which is of interest to our PEM fuel cell modelling group. The singular, degenerate nature of the mathematical model results in an indeterminate form for the interface velocity. In this talk, I will present a front capturing method which avoids the need for explicit implementation of this velocity. The method is shown to accurately capture the interface location, by way of an exact similarity solution and numerical convergence study for a model problem. I will present some computational results and discuss further direction for this work. Time and Date: 12:30 p.m., Thursday, March 30, 2006 Event: UBC SCAIM Seminar Note this is on Thursday instead of usual Tuesday. Speaker: Gene Golub, Department of Computer Science, Stanford University Subject:A History of Numerical Linear Algebra'' Location: ICICS/CS 238, 2nd floor of Computer Science Bldg., 2366 Main Mall Abstract: From the days of the first ballistic computations on digital computers, the vast majority of computer time used for scientific computation is spent on linear algebra problems. Pioneers like Lanczos, von Neumann, and Wilkinson led a revolution in advanced computing using machines like the ENIAC and ACE in the early and middle years of this century. We shall describe some pioneers in numerical linear algebra and their influence. Over the years, many effective techniques have been developed for solving scientific and engineering computing problems from ballistics to quantum mechanics. We shall discuss several of these problems in linear algebra and describe, in outline, their solution. Within the last decade, parallel and vector computers have sparked a new revolution with profound affects on numerical analysis. Some techniques banished as inferior for conventional computers have proved to be attractive alternatives for machines with advanced architectures. Supercomputer research has also led to improved algorithms for conventional serial computers as well. Finally, we shall discuss some of the latest advances, results, and current directions in scientific computation and numerical linear algebra. Time and Date: 4:00 p.m., Thursday, March 30, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Ivar Ekeland, UBC Subject:Rational behavior with non-exponential discount, and what happens to Hamilton-Jacobi, II'' Location: WMAX 216 Time and Date: 4:00--4:50 p.m., Thursday, March 30, 2006 Event: Graduate Student Seminar Speaker: Erick Wong, Department of Mathematics, UBC Subject:Numbers of the form x^2+ky^2'' Location: MATX 1102 Abstract: Consider the sequence of numbers representable as the sum of two squares (i.e. {0,1,2,4,5,8,9,10,...}). It's easy to see by looking modulo 4 that this sequence never contains 4 consecutive integers, and it's a nice puzzle to prove that this maximum run of 3 occurs infinitely often. Answering a question of M. Rosenfeld, the talk will focus on these sorts of combinatorial properties for the more interesting, or at least more general class of quadratic forms x^2 + ky^2 (where k>0 is fixed). The majority of exposition will not require much more than foggy memories of undergraduate number theory. Time and Date: 4:00 p.m., Thursday, March 30, 2006 Event: Complex Fluids Seminar Speaker: Tom Peacock, MIT Subject:Bumps, Knives & Bouncing Beams: Lab Investigations of Internal Waves'' Location: MATH 204 Abstract: There is great interest in developing a more complete understanding of the generation, propagation and dissipation of internal waves. We thus present detailed experimental results concerning recent lab investigations on: (i) the effects of rotation on internal wave propagation; (ii) the nonlinear reflection of internal waves from an inclined boundary; and (iii) internal wave generation by topographic features. The results have been obtained using the digital schlieren method - a non-intrusive optical approach that provides detailed quantitative information about a time-varying experimental density stratification. Time and Date: 3:00-4:00 p.m., Friday, March 31, 2006 Event: Mathematics Colloquium Speaker: Anette Hosoi, Department of Mechanical Engineering, MIT Subject: Building a better snail: lubrication, optimization and adhesive locomotion'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00 p.m., Monday, April 3, 2006 Event: Algebraic Geometry Seminar Speaker: Uzi Vishne, IAS and Bar Ilan University Subject:TBA'' Location: WMAX 110 (PIMS Seminar Room) Abstract: Given an algebraic surface embedded in a projective space, one may study the fundamental group of its Galois cover with respect to a generic projection to CP2. A presentation of such a group can be obtained (in principal) by the van Kampen theorem, and (in practice) by an algorithm developed by Moishezon-Teicher. However, a presentation is known to be one of the worst possible descriptions of a group. Various surfaces were studied by Teicher and others over the last 20 years, and their respective groups were identified. I will sketch the main techniques involved in this process. Lately, a general perspective emerged which relates these groups to presentations of the symmetric groups, and to certain large Coxeter groups. I will describe the main ideas, and discuss the most difficult case dealt with so far -- a group with 54 generators and almost 2000 relations, which turns out to be virtually nilpotent. Based on joint works with M. Amram, R. Lawrence, L.H. Rowen and M. Teicher. Time and Date: 3:45 p.m., Monday, April 3, 2006 Event: Mathematics Departmental Tea Location: MATX 1115, (Math Lounge) Time and Date: 4:00-5:00 p.m., Monday, April 3, 2006 Event: Mathematics Colloquium Speaker: Gang Tian, Princeton University Subject: Geometry of low dimensional manifolds'' Location: MATH 105 Notes: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00 p.m., Wednesday, April 5, 2006 Event: Mathematical Biology Seminar Speaker: Codina Cotar, Department of Mathematics, UBC Subject:A Reward Model for Mate Choice and Sexual Selection'' Location: WMAX 216 Abstract: Females are the choosy sex, their choice being made on the basis of the quality of the males. The benefits they receive from the males for the offspring are either indirect, for example good genes, or direct, such as territories, male parental care and absence of contagious parasites. The presence or absence of attributes as good genes or absence of contagious parasites in a male will determine if he is a high-quality male or a low-quality male. This interaction between female and male decision rules raises two important questions: Do we expect high-quality males to give less care to the young than low-quality ones? Do we expect females to prefer high-quality males? The problem of how much time to spend with females, for the males, and what males to choose, for the females, is game theoretical. The existence of an optimal Nash strategy for males and females is proven under a general female choice rule. The optimal strategy is then analyzed. Time and Date: 3:30 p.m., Wednesday, April 5, 2006 Event: Algebra Topology Seminar Speaker: Enrique Torres-Giese, Department of Mathematics, UBC Subject:Commuting Elements in Lie Groups'' Location: WMAX 110 Abstract: In this talk we discuss the topology and geometry of the space of pairs of commuting elements in a Lie group. We will see part of the work of Adem and Cohen on SU(2) as well as some recent advances in the case of U(2). Time and Date: 3:30-4:30 p.m., Wednesday, April 5, 2006 Event: Probability Seminar Speaker: Ed Perkins, UBC Subject:Pathwise uniqueness for parabolic stochastic pde's'' Location: WMAX 216 Abstract: Consider the SPDE: du/dt=u"+g(u)dW/dtdx where dW/dtdx is space-time white noise and g is Holder continuous of index h. It is shown that if 2h^3-h>3/4 then pathwise uniqueness holds. The proof is an infinite dimensional extension of the Yamada-Watanabe Theorem. This work is joint with Leonid Mytnik. Time and Date: 3:00--3:50 p.m., Thursday, April 6, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Denis Charles, Microsoft Subject:Some applications of the graph of supersingular elliptic curves over a finite field'' Location: SFU Campus. Correct room number is K9509 (not ASB 10900). Note there will be a tea break from 3:50 - 4:10 p.m. Abstract: The graph of supersingular elliptic curves over a finite field connected by isogenies has many applications in computational number theory. In this talk we look at some old (in number theory) and new (in cryptography) applications of these graphs. In particular, we discuss new constructions of secure hash functions and pseudorandom number generators from these graphs. We will also study the interesting graph-theoretic properties of this graph. If time permits, I will sketch a generalization of these graphs to graphs of superspecial abelian varieties. The new results in this talk are from joint work with Eyal Goren and Kristin Lauter. Time and Date: 4:10--5:00 p.m., Thursday, April 6, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Patrick Ingram, Department of Mathematics, UBC Subject:In my defense: Integral points on elliptic curves'' Location: SFU Campus. Correct room number is K9509 (not ASB 10900). Abstract: In a talk not completely unrelated to my thesis defense, I will examine the question “For which elliptic curves E, which integral points P on E, and which integers n is nP also an integral point?” Most (if not all) of the attention will be devoted to congruent number curves. Time and Date: 4:00 p.m., Thursday, April 6, 2006 Event: PIMS-MITACS Math Finance Seminar Speaker: Ulrich Horst, UBC Subject:Climate Risk, Securitization, and Equilibrium Bond Pricing'' Location: WMAX 216 Abstract: We propose a method of pricing financial securities written on non-tradable underlyings such as temperature or precipitation levels. To this end, we analyze a financial market where agents are exposed to financial and non-financial risk factors. The agents hedge their financial risk in the stock market and trade a risk bond issued by an insurance company. From the issuer's point of view the bond's primary purpose is to shift insurance risks related to non-catastrophic weather events to financial markets. As such its terminal payoff and yield curve depend on an underlying climate or temperature process whose dynamics is independent of the randomness driving stock prices. We prove that if the bond's payoff function is monotone in the external risk process, it can be priced by an equilibrium approach. The equilibrium market price of climate risk and the equilibrium price process are characterized as solution of non-linear backward stochastic differential equations. Transferring the BSDEs into PDEs, we represent the bond prices as smooth functions of the underlying risk factors. The talk is based on joint work with M. Muller. Time and Date: 4:00 p.m., Thursday, April 6, 2006 Event: Complex Fluids Seminar Speaker: Chun Y. Seow, Department of Pathology and Laboratory Medicine, James Hogg iCAPTURE Centre for Cardiovascular and Pulmonary Research, St. Paul's Hospital, UBC Subject:Plasticity in cell structure'' Location: MATH 204 Abstract: Mechanical properties of biological materials are often characterized in terms of their elasticity or viscoelasticity, despite the fact that, in situ, these materials behave "plastically" and often exhibit an amazing ability to adapt to their physical environment. The fact that these materials are "alive" sometime is lost in mathematical modeling and engineering analysis. Adaptation of smooth muscle cell to length change is used as an example in this seminar to illustrate how plastic restructuring of intracellular cytoskeleton and contractile apparatus facilitates cell function. Time and Date: 3:00-4:00 p.m., Friday, April 7, 2006 Event: Mathematics Colloquium Speaker: Uzi Vishne, IAS and Bar Ilan University Subject: Isospectral manifolds and Cayley graphs'' Location: MATX 1100 Notes: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date:10:00 a.m., Monday, April 10, 2006 Event: Algebraic Geometry Seminar Speaker: Andrew Dancer, Oxford Subject:Adding branes to hyperkahler manifolds'' Location: WMAX 110 (PIMS Seminar Room) Notes: Please note time change for the seminar. There will be an algebraic geometry hike afterwards. Abstract: We study quaternionic (especially hyperkahler) analogues of Lerman's symplectic cut construction. In low dimensions this can be physically interpreted as adding a brane to a hyperkahler manifold. Time and Date:3:30--4:30 p.m., Tuesday, April 11, 2006 Event: Discrete Mathematics Seminar Speaker: Jerry Griggs, Mathematics, U of South Carolina Subject:Channel Assignments in Infinite Graphs'' Location: WMAX 216 Time and Date:2:00 p.m., Wednesday, April 12, 2006 Event: Mathematical Biology Seminar Speaker: Stan Maree, University of Utrecht Subject:Polarisation and cell movement: a multiscale modelling approach'' Location: WMAX 216 Abstract: Cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. To understand the intricated interplay which brings about cell motility, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarise, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. This is joint work with Alexandra Jilkine, Adriana Dawes, and Leah Keshet and was funded by NSERC, MITACS, NWO and NSF. Time and Date:3:30 p.m., Wednesday, April 12, 2006 Event: Algebra Topology Seminar Speaker: Michael Thaddeus, Columbia University Subject:Gerbes in orbifold cohomology and mirror symmetry'' Location: WMAX 110 Abstract: I will explain why twisting by a gerbe is a natural operation in both orbifold cohomology and mirror symmetry, and show how many examples of Calabi-Yau orbifolds whose twisted orbifold Hodge numbers are mirror to each other may be easily constructed. They are quotients of tori by a finite group action. Time and Date:3:30-4:30 p.m., Wednesday, April 12, 2006 Event: Probability Seminar Speaker: Codina Cotar, Department of Mathematics, UBC Subject:Edge Reinforced Random Walk: How long till attracting edge?'' Location: WMAX 216 Abstract: Edge reinforced random walk is a process where the probability to move along an edge is proportional to a function, called the weight function, of the number of visits to that edge. It was recently established (by V. Limic and P. Tarres) that the walk is attracted to an edge with probability 1, under fairly general assumptions on the weight function. We obtain further information on the time of appearance of the attracting edge. This is work in progress, jointly with Vlada Limic. Time and Date: 1:30 -- 2:30 p.m., Monday, April 24, 2006 Event: UBC Mini Motives Conference, Algebraic Geometry Seminar Speaker: Arvind Nair, Tata Institute for Fundamental Research, Mumbai, Maharashtra, India Subject:On the motive of a Shimura variety'' Location: WMAX 110 (PIMS) Abstract: Shimura varieties are of interest as a source of motives/Galois representations about which much can be said using the methods of representation theory. For various reasons one would like to have a Grothendieck motive for such a variety. If the Shimura variety is projective this is immediate. If it is not projective (as in most classical examples, e.g. the moduli space of principally polarized abelian varieties), the desired Grothendieck motive should realize to the intersection cohomology of the minimal compactification of Baily and Borel. I'll show that if the Shimura variety is related to abelian varieties, then a motive can be constructed which realizes to the subspace of intersection cohomology satisfying the generalized Ramanujan conjecture at (any) one finite prime. (This is the "essential" part according to standard conjectures in representation theory.) In the case when the Shimura variety is a modular curve this specializes to the Eichler-Shimura-Deligne-Scholl motive for classical modular forms. Time and Date: 3:00 -- 4:00 p.m., Monday, April 24, 2006 Event: Algebraic Geometry Seminar Speaker: Elham Izadi, University of Georgia in Athens, Georgia, USA Subject:The Hodge conjecture for the primitive cohomology of theta divisors'' Location: WMAX 110 (PIMS) Abstract: I will first discuss the meaning of the Hodge conjecture in general and then specialize to abelian varieties. The primitive cohomology of the theta divisor of an abelian variety gives a special Hodge structure for which one can ask whether the Hodge conjecture is true. Using Prym-embedded curves, this question was answered in the affirmative by myself and van Straten for abelian fourfolds. In this talk which is about joint work with Csilla Tamas, I will discuss the case of abelian fivefolds and show in particular that Prym-embedded curves do NOT solve the Hodge conjecture. I will, however, introduce a different family of curves which is very likely to give an answer to the Hodge conjecture. Time and Date: 4:30 -- 5:30 p.m., Monday, April 24, 2006 Event: Algebraic Geometry Seminar Speaker: Kai Behrend, UBC, Vancouver, BC Subject:On the motive of the stack of bundles'' Location: WMAX 110 (PIMS) Abstract: Let G be a split connected semisimple group over a field K. We give a conjectural formula for the motive of the stack of G-bundles over a curve C, in terms of special values of the motivic zeta function of C. The formula is true if C=P1 or G=SLn. If K=C, upon applying the PoincarŽ or Serre characteristic, the formula reduces to results of Teleman and Atiyah-Bott on the gauge group. If K=Fq, upon applying the counting measure, it reduces to the fact that the Tamagawa number of G over the function field of C is |¹1(G)|. This is joint work with Ajneet Dhillon. Time and Date: 2:00 p.m., Wednesday, April 26, 2006 Event: PIMS Collaborative Research Group in Mathematical Modelling and Computation in Biology, Invited Speaker Speaker: Arpita Upadhyaya, University of Maryland Subject:Actin' pushy and pulling springs: Two forms of biological motion'' Location: WMAX 216 (PIMS) Abstract: A fundamental attribute of living cells is their ability to move. I will talk about two forms of biological motion driven by different physical mechanisms. The polymerization of the protein, actin, appears to be the source of the propulsive force for eukaryotic cell motion. While the alphabet soup of proteins that initiate and control actin polymerization is being scrupulously characterized, it is not clear how this generates a force to push. I will describe experiments in which we have reconstructed motility using phospholipid vesicles as model cell membranes in order to probe the polymerization forces. Vorticella, one of the most powerful cellular machines, is a single celled organism with a cell body attached to a substrate by a slender stalk which contains a rod-like polymeric structure - the spasmoneme. Vorticella motility is characterized by an extremely rapid contraction which is powered by the collapse of the spasmoneme. We have conducted high-speed imaging experiments to study the dynamics of contraction. Time and Date: 3:30-4:30 p.m., Wednesday, April 26, 2006 Event: Probability Seminar Speaker: Rongfeng Sun, EURANDOM Subject:Renormalization analysis of hierarchically interacting two-type branching models'' Location: WMAX 216 (PIMS) Abstract: Linearly interacting diffusions model the evolution of colonies of populations. When the interaction kernel is of an appropriate form and the diffusions are indexed by the hierarchical group, the large scale space-time behavior of the system exhibits universality which can be fully characterized using a renormalization analysis first developed by Dawson and Greven. Such renormalization analysis has previously been successfully carried out for interacting diffusions which are either one-dimensional or live on a compact state space. In most of these cases, there is a single type of large scale space-time behavior and the system exhibits so-called full universality. In this talk, we give an overview of the renormalization program and then discuss recent progress in the analysis of hierarchically interacting two-type branching diffusions, where each diffusion lives on [0,\infty)^2 and the structure of the system's large scale space-time behavior is much richer. This is work in progress joint with D. Dawon, A. Greven, F. den Hollander and J. M. Swart. Time and Date: 3:00--4:00 p.m., Monday, May 1, 2006 Event: Algebraic Geometry Seminar Speaker: Elham Izadi, University of Georgia in Athens, Georgia, USA Subject:Mixed Hodge structures on the cohomology of theta divisors'' Location: WMAX 110 (PIMS) Abstract: I will show two mixed Hodge structures on the cohomology of the theta divisor of a general abelian variety: One obtained from a degeneration to a general jacobian, the other from a degeneration to a general product. Time and Date: 3:30--4:30 p.m., Wednesday, May 3, 2006 Event: Probability Seminar Speaker: Matthias Mueller, PIMS Subject:Backward SDE and equilibrium prices'' Location: WMAX 216 Abstract: The first part of the talk gives a survey about BSDE. Linear BSDE have been introduced by Bismuth (1973) in Control Theory. The existence of solutions for Lipschitz BSDE was proven by Peng, and for quadratic BSDE by Lepeltier/San Martin and by Kobylanski. A nonlinear Feynman-Kac formula allows the representation of semilinear PDE by BSDE and vise versa. Furthermore, the Malliavin derivatives of BSDE can be represented as the solution of a linear BSDE. We apply BSDE to an economical problem. The goal is the pricing of a bond that depends on a non-financial risk factor, e.g. weather. An equilibrium price can be calculated using a quadratic BSDE. Price means here a probability measure Q equivalent to the "real world" measure P. Random payouts are then priced by the expectation under Q. Prices at intermediate times are taken as conditional expectations under Q. We show that or bond completes the market. In mathematical terms: the process gained by the successive conditioned Q-expectations of the random variable modelling the payout of the bond have the representation property: every random variable in L1(Q) can be written as stochastic integral with respect to the price process. Time and Date: 10:00--11:00 a.m., Friday, May 5, 2006 Event: Algebra Topology Seminar Speaker: Duane Randall, Loyola University Subject:Coincidences and the Kervaire Invariant'' Location: WMAX 110 Abstract: We study the concepts of homotopy disjointness and homotopy disjointness by small deformation for mappings between spheres. Joint work with Daciberg Goncalves produced the following result. The existence of a mapping f: S^(4n-2) -> S^(2n) with n>4 which is homotopy disjoint from itself, but not by small deformation, produces a solution to the Strong Kervaire Invariant One Problem. The converse is also true. Recent related work of Ulrich Koschorke is also discussed. Time and Date: 2:00--3:00 p.m., Wednesday, May 10, 2006 Event: PIMS Probability Afternoon Speaker: Rami Atar, Technion (visiting UW) Subject:On simplicity of the second Neumann eigenvalue'' Location: West Mall Annex, Room 110 Note: from 1:40--2:00 and 3:00--3:30 p.m. coffee will be served in the 1st floor PIMS Lounge. Abstract: I will review results and open problems regarding simplicity of the second Neumann Laplacian eigenvalue on domains, and properties of the corresponding eigenfunctions, and present a new simplicity result for a family of smooth planar domains, that is based on analysis of mirror Couplings. Joint work with K. Burdzy. Time and Date: 3:30--4:30 p.m., Wednesday, May 10, 2006 Event: Probability Seminar Speaker: Gady Kozma, IAS Subject:What every mathematician should know about analysis on graphs, and a counterexample to Davies' conjecture'' Location: West Mall Annex, Room 110 Abstract: We construct a graph G with two vertices x,y such that the ratio of the heat kernels p(x,x;t)/p(y,y;t) does not converge. Note: Dinner: 6:30 p.m. Contact Ed Perkins if you are interested in attending the dinner. Time and Date: 1:30 p.m., Friday, May 19, 2006 Event: Joint Computer Science/Electrical and Computer Engineering/Mathematics Seminar Speaker: Ian F. Blake, University of Toronto Subject:The discrete logarithm problem in cryptography'' Location: Kaiser Bldg. Room 2020 Abstract: The discrete logarithm problem in the field of integers modulo a prime, was first proposed in 1976 as a one-way function for application to the key exchange problem in cryptography. Since then the problem has been intensively investigated in a variety of algebraic settings and for a variety of cryptographic primitives and protocols. Many of the questions that have arisen in these settings remain unanswered. This talk, intended for a general audience, looks at some of these interesting applications and questions. Biography:Ian F. Blake received his undergraduate education at Queen's University in Kingston, Ontario and his Ph.D. at Princeton University in New Jersey. From 1967 to 1969 he was a Research Associate with the Jet Propulsion Laboratories in Pasadena, California. From 1969 to 1996 he was with the Department of Electrical and Computer Engineering at the University of Waterloo where he was Chairman from 1978 to 1984. He has spent sabbatical leaves with the IBM Thomas J. Watson Research Center, the IBM Research Laboratories in Switzerland and M/A-Com Linkabit in San Diego, California. From 1996-1999 he was with the Hewlett-Packard Labs in Palo Alto, California. He is a Fellow of the IEEE, a Fellow of the Institute for Combinatorics and its Applications and a member of the Association of Professional Engineers of Ontario, and a Fellow of the Royal Society of Canada. His research interests are algebraic coding theory, digital communication theory, and cryptography. Time and Date: 3:00 p.m., Wednesday, May 24, 2006 Event: Mathematical Biology Seminar Speaker: Jean Francois Ganghoffer, LEMTA-ENSEM, Nancy, France Subject:Modelling of cell adhesion -- a probabilistic approach'' Location: Math Annex 1102 (note unusual time and place) Abstract: Rolling is an important manifestation of biological cell adhesion, especially for the leukocyte cell in the immune process. It combines several phenomena such as the affinity, the junction and failure between specific adhesion molecules, and an active deformation of the cell during the motility. Several models were developed in a probabilistic or a deterministic context. The focus is here on the local mechanical description (2D) of the kinetics of adhesion of the contact interface of a single cell with a wall (e.g., the blood vein), in terms of the failure and creation of connections during the rolling. The failure and adhesion are considered as being modeled by stochastic fields. The local model focuses on the interfacial zone, as a preliminary step towards an integrated model including the cell membrane behavior. Hence, the net effect of the fluid flow is represented by a punctual force, coupled to the Van der Waals, electrostatic forces and the viscoelastic behavior of the interfacail bonds. Numerical simulations emphasize the rolling phenomenon and the kinetics of creation and rupture of the ligands-receptors connections. Perspectives in terms of the coupling of the interface behavior with a stochastic finite element description of the cell membrane in a 3D context are mentioned. Time and Date: 3:30 p.m., Wednesday, May 24, 2006 Event: Probability Seminar Speaker: Peter Love, D-Wave Systems Inc. Subject:Quantum Information Theory for Mathematicians'' Location: WMAX 216 (PIMS Facility) Abstract: In this talk I will give an overview of quantum information theory, with an emphasis on some of the underlying mathematics. In particular, quantum algorithms depend on a physical property of quantum systems,entanglement, which may be characterized in terms of invariants of unitary groups. I will discuss this in the context of Grovers search algorithm. Time and Date: 3:30 p.m., Wednesday, May 31, 2006 Event: Probability Seminar Speaker: T. Kumagai, RIMS Kyoto Subject:On the existence of cut points for Brownian motion on fractals'' Location: WMAX 216 (PIMS Facility) Time and Date: 11:00 a.m., Tuesday, June 6, 2006 Event: PIMS Distinguished Lecture Speaker: Olivier Druet, Ecole Normale Supérieure de Lyon Subject:Quantification of Blow-up Levels for a 2-D Elliptic Equation with Critical Exponential Nonlinearity'' Location: WMAX 216 (PIMS Facility) Notes: Talk preceded by coffee and cookies Abstract: We study sequences of solutions of some elliptic PDE’s, on 2-dimensional bounded domain, with critical Moser-Trudinger exponential nonlinearity. We prove that lack of compactness occur only when standard bubbles appear and thus we can quantify the levels of blow-up of the underlying functional. The main difficulties, compared to the higher-dimensional situation (Yamabe-type equations), are that subtracting a bubble to a solution changes the nature of the equation satisfied by it and that one has to avoid degenerate bubbles, which could a priori appear as in the study of Chern-Simon vortices. Time and Date: 3:30 -- 4:30 p.m., Wednesday, June 21, 2006 Event: Probability Seminar Speaker: Janko Gravner, UC Davis Subject:Digital Snowflakes'' Location: WMAX 216 (PIMS Facility) Abstract:Several mathematical models of snow crystal growth will be discussed. For a popular class of cellular automata known as Packard's Snowflakes, one can develop a fairly complete rigorous theory, addressing limiting density, fractal shapes and exact solvability. The bulk of this theory is limited to the deterministic cases, although something can be said about random perturbations. The talk will also address a more realistic mesoscopic snowflake model, which offers some hope of at least empirical analysis. This talk will be accessible to most undergraduates and is on joint work with David Griffeath (Univ. of Wisconsin). Time and Date: 2:00 p.m., Thursday, June 22, 2006 Event: Algebra/Topology Seminar Speaker: Simona Paoli, Macqarie University Subject:Modelling homotopy n-types in algebraic topology and category theory'' Location: WMAX 110 (PIMS Facility) Abstract: Homotopy n-types are topological spaces with trivial homotopy groups in dimension greater than n. They arise naturally in algebraic topology and category theory. Both these areas of mathematics have seen the development of models of n-types. In this talk I will describe some of these models and I will address the question on how to compare some of them. I will also talk about some recent results I have obtained about this comparison problem. Time and Date: 2:00 p.m., Friday, June 23, 2006 Event: Complex Fluid Seminar Speaker: Philippe Coussot, Institut Navier, Paris and the University of Western Ontario, Department of Physics and Astronomy Subject:Solid-liquid transition, flow and aging of pasty materials'' Location: MATH 204 Abstract:Pasty materials such as concentrated suspensions, emulsions, foams and gels are unable to flow unless a stress larger than a critical value is applied to them. Thus they can be basically considered as simple yield stress fluids. We first show how such a model can describe the flow around a bead moving through a paste at rest, by comparing the theoretical prediction for the drag force with results of tests with various bead sizes and densities in a Carbopol gel. Then we study the formation of paste droplets under gravity after the exit from a duct and show again how the simple yield stress model is able to predict data for a negligibly thixotropic gel. Discrepancies between theory and experiments are nevertheless observed for pasty materials exhibiting significant thixotropy effects, such as ketchup, muds, mayonnaise, etc. In order to clarify the behavior of these fluids we carried out systematic creep tests for different stress levels and different times of rest, along with Magnetic Resonance Imaging Velocimetry tests in a Couette geometry. We show that: (i) for a stress below the yield stress these materials remain solid but undergo residual, irreversible deformations over long time which exhibit some trends typical of aging in glassy systems; (ii) as a result of thixotropy (or aging) in the solid regime the elastic modulus increases logarithmically with the time of rest; (iii) in the liquid regime the effective behavior of the material can be well represented by a truncated power-law model, (iv) a fundamental parameter of the solid-liquid transition is a critical shear rate (associated with the yield stress) below which the material cannot flow steadily. Time and Date: 2:00 p.m., Monday, July 31, 2006 Event: Dynamical Systems Seminar Speaker: Ulrich Speidel, Department of Computer Science, University of Auckland Subject:Applications of T-code based information measures'' Location: MATX 1118 Abstract: T-codes are a family of variable-length codes invented in the 1980's by Mark Titchener. Originally considered as an alternative for Huffman codes and noted for their excellent self-synchronisation properties, the difficulty of finding a suitable code for a given source prevented more widespread use. In the 1990's, however, Titchener and Nicolescu discovered that each T-code could be derived from the knowledge of any one of its longest code words, which differ only by their last symbol. Moreover, for each finite string, there exists exactly one T-code whose longest code words have this string as their common prefix. This lets us analyze strings with tools hitherto used only on code sets. In particular, the recursive construction of T-codes gives rise to a complexity measure for strings, the T-complexity. This can alternatively be interpreted as the weighted number of steps required in the recursive construction of the string (a concept similar to Lempel and Ziv's 1976 production complexity), or as the number of bits required to address each internal node in the decoding tree of the corresponding T-code set, giving a physical "meaning" to T-complexity. "Linearization" of T-complexity yields an information and an entropy measure, which has been shown experimentally to be a good approximation to the Kolmogorov-Sinai entropy of the logistic map, establishing a link to Shannon entropy and symbolic dynamics. The talk presents an introduction to these measures and points out a number of possible applications. In particular, I will comment on the use of the measures in network event monitoring. Time and Date: 2:00 p.m., Tuesday, August 1, 2006 Event: Complex Fluid Seminar Speaker: Robert Owens, Departement de mathematiques et de statistique, Universite de Montreal Subject:On the rheology and constitutive modelling of human blood'' Location: MATH 204 Abstract: Human blood is a complex fluid consisting of a suspension in plasma of formed elements such as platelets, white blood cells and red blood cells. Of these cells, by far the greatest proportion (some 98%) consists of red blood cells. The rheology of blood is therefore primarily determined by the behaviour of the red blood cells at different shear rates. At low shear rates the red blood cells may agglomerate into long column-like structures called rouleaux, which are easily broken up as the shear rate increases. In the first part of the talk we will give a brief presentation of results from modelling blood as a suspension of "sticky" dumbbells. We outline the derivation of a structure-dependent Maxwell-type equation for the elastic stress and demonstrate that our model predicts shear-thinning, viscoelasticity and thixotropy. Agreement with the experimental data of Bureau et al. [Biorheology 17 (1980) 191-203] in the case of a simple triangular step shear rate flow is shown to be convincing. In the second part of the talk we use the new constitutive model to investigate the steady, oscillatory and pulsatile flow of blood in a straight, rigid walled tube at modest Womersley numbers. Comparisons are made with the experimental results of Thurston [Microvascular Research 9 (1975) 145-157] for the pressure drop per unit length against volume flow rate and oscillatory flow rate amplitude. Agreement in all cases is good. In the presentation of the numerical and experimental results in both parts of the talk we discuss the microstructural properties of human blood that account for its fascinating rheological behaviour in the simple classes of flows considered. Time and Date: 12:30--1:30 p.m., Tuesday, August 22, 2006 Event: UBC SCAIM Pizza Seminar Speaker: Michael Overton, New York University Subject:The Search for the Nearest Defective Matrix'' Location: ICICS/CS 238 Time and Date: 2:00--3:00 p.m., Tuesday, August 22, 2006 Event: Special Algebraic Geometry Seminar Speaker: Jiun-Cheng Chen, National Center of Theoretical Sciences, Taiwan Subject:Characterizing projective spaces'' Location: WMAX 216 (PIMS) Time and Date: 1:30 p.m., Wednesday, August 30, 2006 ***Please note time has been changed to the afternoon so there is no conflict with the 10:00 a.m. Math grad orientation.*** Event: Differential Geometry Seminar Speaker: Xiuxiong Chen, University of Wisconsin-Madison Subject:Geometric flow in Kahler manifold'' Location: WMAX 216 (PIMS) Abstract: We will discuss some recent results on the Calabi flow, short time existence, stability and extension theorem. The Calabi flow is a 4th order parabolic flow which is gradient flow of certain convex functional in infinite dimensional space. If we have time, we will also discuss a small energy theorem on Kahler Ricci flow. Time and Date: 3:00 p.m., Tuesday, September 5, 2006 Event: Mathematics Colloquium Speaker: Stephen Gelbart, Weizmann Institute of Science Subject: Prime numbers, Riemann, and Langlands'' Location: WMAX 110 (PIMS) Note: Refreshments will be served at 2:45 p.m. in the 1st floor PIMS Lounge. Time and Date: 4:00 -- 5:00 p.m., Wednesday, September 6, 2006 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Alex Mogilner, Department of Mathematics and Center for Genetics and Development, University of California at Davis Subject:System Level Mathematical Analysis of Mitosis'' Location: Room 301, LSK Bldg., UBC Note: Refreshments will be served before the seminar in the IAM Lounge, Room 306. Abstract: Mitotic spindle goes through distinct morphological states characterized by increasing spindle length and distances between chromosomes. A complete picture of how the spindle assembles is still lacking. We performed an In Silico model screen to identify all potential mechanisms of spindle self-organization. We trained' the computer to assemble a set of models and screened the models in a multi-dimensional parameter space. To identify models that fit experimental data we used stochastic optimization and genetic algorithms. We found multiple models quantitatively describing the spindle in which the timing of force activity must be fine tuned, in contrast to the kinetic and mechanical parameters that show robustness to change. Time and Date: 3:00--4:00 p.m., Friday, September 8, 2006 Event: Mathematics Colloquium Speaker: Dominik Schoetzau, UBC Subject: Discontinuous Galerkin methods for incompressible fluid flow'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (Lounge, MATX 1115). Time and Date: 3:00--4:30 p.m., Monday, September 11, 2006 Event: Algebraic Geometry Seminar Speaker: Angelo Vistoli, University of Bologna Subject:Linearly reductive finite group schemes'' Location: WMAX 110 (PIMS) Note: Talk will be preceded by coffee, and followed by an organizational meeting. Abstract: I will report on joint work with Dan Abramovich and Martin Olsson. We classify linearly reductive finite group schemes in positive or mixed characteristic, and use this to define a good replacement for the notion of orbifold in positive or mixed characteristic. Time and Date: 3:30 p.m., Tuesday, September 12, 2006 Event: Algebra/Topology Seminar Speaker: V.S. Sunder, Institute of Mathematical Sciences, Chennai Subject:Planar algebras and (1+1)-dimensional TQFTs (Part 1)'' Location: WMAX 110 Abstract: In this joint work with Vijay Kodiyalam (IMSc, Chennai) and Vishwambhar Pati (ISI, Bangalore), we construct a certain 'cobordism category' D whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between (1+1-dimensional) unitary topological quantum field theories (TQFTs) defined on D, on the one hand, and Jones' subfactor planar algebras, on the other. Time permitting, we shall show how this leads to an alternate description of Kuperberg's 'quantum invariant' of 3-manifolds associated to Hopf algebras. Time and Date: 12:00 p.m., Wednesday, September 13, 2006 Event: Mathematical Biology Seminar Speaker: Arthur Sherman, Laboratory of Biological Modeling, NIDDK/NIH Subject:Ionic and Metabolic Mechanisms in Pulsatile Insulin Secretion'' Location: WMAX 216 Abstract: Insulin is secreted in pulses with a period of about 5 minutes from the beta-cells of the pancreas. These pulses are in turn driven by oscillations of cytosolic calcium. Two parallel streams of investigation over more than two decades have studied metabolic oscillations and ionic mechanisms as possible sources of the calcium oscillations. We propose that the two are linked by a potassium channel, K(ATP), that senses the ATP and ADP levels in the cell. This directly transduces metabolic oscillations into oscillations of membrane potential and calcium. However, calcium can also affect metabolism by stimulating ATP-consuming pumps, by depolarizing the mitochondria, and by directly activating Krebs cycle enzymes. A unified model that combines the above elements and can thereby explain a diverse set of experimental observations using only a few simple assumptions will be presented. Time and Date: 3:30 p.m., Wednesday, September 13, 2006 Event: Probability Seminar Speaker: Jason Schweinsberg, UCSD Subject:The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus'' Location: WMAX 216 Abstract: Let x and y be points chosen uniformly at random from the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order n^2 (log n)^{1/6}, resolving a conjecture of Benjamini and Kozma. We also show that the scaling limit of the uniform spanning tree on the four-dimensional discrete torus is the Brownian continuum random tree of Aldous. Our proofs use the techniques developed by Peres and Revelle, who studied the scaling limits of the uniform spanning tree on a large class of finite graphs that includes the d-dimensional discrete torus for d >= 5, in combination with results of Lawler concerning intersections of four-dimensional random walks. Time and Date: 3:30 p.m., Wednesday, September 13, 2006 Event: Algebra/Topology Seminar Speaker: V.S. Sunder, Institute of Mathematical Sciences, Chennai Subject:Planar algebras and (1+1)-dimensional TQFTs (Part 2)'' Location: WMAX 110 Time and Date: 3:15--4:15 p.m., Wednesday, September 13, 2006 Event: IAM-PIMS-MITACS 2006 Distinguished Colloquium Series Speaker: William L. Kath, Engineering Sciences and Applied Mathematics, Department of Neurobiology and Physiology, Northwestern University Subject:Models of Initiation and Propagation of Dendritic Spikes in Hippocampal CA1 Pyramidal Neurons'' Location: Room 301, Leonard S. Klinck Bldg. Note: The 3:15 p.m. colloquium will be followed by IAM Potluck/BBQ at Spanish Banks. Abstract: In computational models of hippocampal CA1 pyramidal neurons with active dendrites, distal synaptic inputs trigger dendritic spikes, but in many cases these spikes do not propagate reliably to the soma to produce output action potentials in the axon. The computational models show, moreover, that the probability of axonal action potential initiation increases dramatically if the distal dendritic inputs are accompanied by small amounts of more proximal synaptic input. In this case, the propagation of the dendritic spikes appears to be gated by the more proximal inputs. The mechanisms for this phenomenon, as well as experimental results designed to test the predictions of the computational models, will be discussed. Time and Date: 2:00 p.m., Thursday, September 14, 2006 Event: Joint UBC SCAIM Seminar/Math Biology Seminar Speaker: David Lloyd, Department of Mathematics, University of Surrey, UK Subject:Nucleation of localised pattern in continuous media'' Location: WMAX 216 Abstract: The formation of patterns from quiescence under the continuous variation of a parameter has long been of interest across the physical and life sciences since the pioneering work of Alan Turing. We describe how spatially localised patches of pattern arise spontaneously in experiments in a wide variety of nonlinear media including liquid crystals, autocatalytic chemical reactions, gas discharge systems, optical crystals and in solidification. Perhaps the most intriguing examples of such patterns are small circularly symmetric spatially localised subharmonic excitations (dubbed \emph{oscillons}) that occur in vertically vibrated granular materials, viscous fluids and plasmas. Oscillons tend to form tightly packed strongly interacting clusters which coexist with an undeformed background and cannot be captured by theories of weakly interacting localised atoms. Here we present a predictive theory for the nucleation and pattern selection of \emph{multi-dimensional} localised structures in quite general continuous media, via the interplay between linear instability and nonlinear bistability. We show how specific kinds of localised patterns (spots, targets, hexagonal arrays etc.) are selected and emerge subcriticality depending on the amount of bistability between the background and finite-amplitude cellular patterns. These parameter regions of localised pattern overlap as the amount of hysteresis in the system is increased, explaining experimental results showing competition between different localised patterns. Furthermore, using a Maxwell point argument that goes well beyond one-dimensional theory, we reveal a complex {\em snaking} transition diagram that provides the mechanism by which larger localised clusters form and self completion occurs. Time and Date: 3:00 p.m., Thursday, September 14, 2006 Event: DG-MP-PDE Seminar Speaker: Walter Strauss, Brown University Subject:Steady water waves with vorticity: theory and computation'' Location: WMAX 216 Time and Date: 3:30 p.m., Thursday, September 14, 2006 Event: Algebra/Topology Seminar Speaker: Akira Yasuhara, Tokyo Gakugei University Subject:On classifications of links up to C_n-moves'' Location: WMAX 110 Abstract: A C_n-move (n\in{\Bbb N}) is a local move on links defined by Habiro, which can be regarded as a 'higher order crossing change'. The C_n-equivalence is an equivalence relation on links generated by C_n-move. The C_m-equivalence implies the C_n-equivalence for m>n. So the C_n-classification, which is the classification up to C_n-equivalence, of links becomes finer as n increases. The C_2-classification of links and the C_3-classification of links with 2 or 3 components, or of algebraically split links are known. Here we give several classifications of certain sets of links by using Milnor invariants. More precisely, we give the following classification: (1) C_n-classification of n-component Brunnian links. (2) C_{n+1}-classification of n-component Brunnian links which are C_n-equivalent to trivial. (3) C_4-classification of 2-component links, 3-component Brunnian links or n-component Brunnian links which are C_3-equivalent to trivial. Time and Date: 4:00 p.m., Thursday, September 14, 2006 Event: Math Finance Seminar Speaker: Trian Pirvu, Department of Mathematics, UBC Subject:Closed form solution for maximizing CRRA type utility'' Location: WMAX 216 Abstract: This paper studies the problem of optimal investment in incomplete markets when the agents have CRRA type utility. Closed form solutions are obtained up to some unhedgeble risk represented by a process orthogonal on the stock price. The myopic component of the optimal portfolio is obtained by means of minimal Hellinger martingale measure, which in our setup coincides with the minimal martingale measure. We employ Haussmann's formula to derive the hedging component and the unhedgeble risk. We show that the optimal portfolio is robust with respect to stopping. The talk is based on joint work with Ulrich G. Haussmann. Time and Date: 3:00 p.m., Friday, September 15, 2006 Event: Mathematics Colloquium Speaker: Steph van Willigenburg, UBC Subject: A combinatorial classification of skew Schur functions'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:45 p.m., Friday, September 15, 2006 Event: UBC-SFU Joint SCAIM/CSC Seminar Speaker: William L. Kath, Engineering Sciences and Applied Mathematics, Northwestern University Subject:Methods for simulating the effects of noise in soliton-based lightwave systems'' Location: UBC Robson Square, C225 Abstract: Lightwave communication systems are used to transmit information at extremely high data rates. In the process, however, various physical impairments deform the propagating signal and can lead to errors. Error probabilities are designed to be small, and thus overall system performance is determined by extremely rare events. The application of importance sampling (one member of a general family of variance reduction techniques) to the numerical simulation of transmission impairments induced by amplified spontaneous emission noise in soliton-based optical transmission systems will be discussed. The method, which is based upon the soliton structure of the equations, allows numerical simulations to be concentrated on the noise realizations that are most likely to result in transmission errors, leading to speedups of several orders of magnitude over standard Monte Carlo methods. In addition, connections between this method and classical exit time problems of stochastic differential equations will be demonstrated. Time and Date: 3:00--4:00 p.m., Monday, September 18, 2006 Event: IAM Seminar Series Speaker: Frederic Yui-Ming Wan, Department of Mathematics, University of California at Irvine Subject:Morphogen Gradients in Biological Systems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Receptor-mediated Decapentaplegic (Dpp) degradation is seen by biologists to play an important role in allowing for the formation of relatively stable PMad patterns of signaling Dpp gradient in (and thereby the development of) the wing imaginal disc of a Drosophila fruit fly. To the extent that receptors act as a "sink" for BMP proteins such as Dpp, localized expression of ectopic (or an abnormal amount of) the Dpp receptor Thickvein (tkv) would cause a net flux of free Dpp morphogens toward the site of receptor over-expression. One possible consequence would be a depression of Dpp signaling in adjacent areas, since less Dpp morphogens are now available for binding with the same concentration of receptors at the adjacent areas. However, recent experiments on Dpp-Sog interaction designed to examine this possible effect were inconclusive. The principal goal of the present talk will be to address this problem. The talk will consist of three parts: 1) a brief introduction to the tissue-patterning phase of biological development of an organism; 2) a description of the controversy at the turn of this century that attracted the speaker to work in this field, and the possible resolution he and his two collaborators provided by modeling, analysis and computation; and 3) formulation of a mathematical model that accounts for the essential biological processes responsible for a possible depression of Dpp signaling outside the area of elevated tkv in a Drosophila embryo and the information extracted from this model by the method of matched asymptotic expansions about the question of reduced signaling. Time and Date: 3:00 p.m., Monday, September 18, 2006 Event: Algebraic Geometry Seminar Speaker: Hsian-Hua Tseng, Department of Mathematics, UBC Subject:A Mirror Theorem for Complete Intersection Orbifolds in Weighted Projective Spaces'' Location: WMAX 110 (PIMS) Abstract: The famous mirror formula for quintic threefolds, conjectured to Candelas, de la Ossa, Green, and Parkes, provides detail information on genus zero Gromov-Witten invariants of the quintic threefold. Mirror formula has been extended to larger classes of manifolds, e.g. nef complete intersections in toric manifolds (by the works of Givental, Lian-Liu-Yau, and others). Recent advance in orbifold theory has motivated a search for a mirror theorem for orbifolds. Such a generalization will be improtant for mirror symmetry in higher dimension, as one cannot insist on working with mainfolds by passing to crepant resoultions. In this talk we will discuss an approach to establish a mirror theorem for orbifolds, and explain such a mirror theorem for complete intersection orbifolds in weighted projective spaces. Time and Date: 3:30 p.m., Tuesday, September 19, 2006 Event: DG-MP-PDE Seminar Speaker: Antoine Mellet, Department of Mathematics, UBC Subject:L^p estimates for compressible Navier-Stokes equations'' Location: WMAX 110 Abstract: I will show how some techniques, that were originally developed in the framework of elliptic and parabolic equations by E. De Giorgi in the 60's, can be used to derive new bounds for the velocity field in compressible Navier-Stokes equations. Time and Date: 3:30--4:30 p.m., Tuesday, September 19, 2006 Event: Discrete Mathematics Seminar Speaker: Greg Martin, UBC Subject:Comparing sumsets and difference sets'' Location: WMAX 216 Abstract: Since addition is commutative but subtraction is not, the subset S+S of a finite set S is predisposed to be smaller than the difference set S-S. As Mel Nathanson wrote: "Even though there exist sets S that have more sums than differences, such sets should be rare, and it must be true with the right way of counting that the vast majority of sets satisfy |S-S| > |S+S|.'' We talk about joint work with Kevin O'Bryant in which we probe this statement from various angles, indicating what's right and what's wrong with Nathanson's belief. Time and Date: 3:30 p.m., Tuesday, September 19, 2006 Event: Algebra/Topology Seminar Speaker: Dusan Repovs, Institute for Mathematics, Physics and Mechanics, University of Ljubljana Subject:Embeddings of Cantor sets in R^3'' Location: MATH ANNEX 1118 Abstract: The first part of the talk will be a historical survey on wild Cantor sets in R^3, the first such set being constructed by Louis Antoine already in the 1920's in his dissertation, after he was blinded while serving in the French army during WWI. In the main part of the talk we shall present a new general technique for constructing wild Cantor sets in R^3 which are nevertheless Lipschitz homogeneously embedded into R^3. Applying the well-known Kauffman version of the Jones polynomial we shall show that our construction produces even uncountably many topologically inequivalent wild Cantor sets in R^3. These Cantor sets have the same number of components in the interior of each stage of the defining sequence and are Lipschitz homogeneous. We shall also present construction of rigid wild Cantor sets in R^3 with simply connected complement. In conclusion, we plan to state some open problems and conjectures. Time and Date: 2:00 p.m., Thursday, September 21, 2006 Event: Mathematical Biology Seminar Speaker: Richard Bertram, Department of Mathematics, Florida State University Subject:Mathematical Analysis of the Neural Control of Hormone Secretion'' Location: WMAX 216 Abstract: The pituitary is one of the primary glands of the body. Many hormones are released from a variety of cells within the pituitary, and these hormones regulate the release of hormones from other glands and have direct actions on the brain, muscles, and organs. The timing of hormone release from the pituitary is important, and is determined largely through interactions with a region of the brain called the hypothalamus. These interactions are quite complex, and serve as a good application area for mathematical modeling and computer simulations. The focus of this seminar is recent mathematical modeling and analysis of interactions between the hypothalamus and pituitary lactotrophs, pituitary cells that secrete the hormone prolactin. We discuss possible mechanisms for circadian oscillations in prolactin secretion in pregnant rats, and the much faster oscillations (period of several seconds) in electrical activity of the lactotrophs, using models of cellular dynamics at very different temporal and spatial scales. Time and Date: 3:00 p.m., Friday, September 22, 2006 Event: Mathematics Colloquium Speaker: Michael Doebeli, UBC Subject: Evolution of diversity: Pattern formation in phenotype space'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, September 25, 2006 Event: IAM Seminar Series Speaker: Traian Pirvu, Department of Mathematics, UBC Subject:Pricing in Complete and Incomplete Markets'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We begin by reviewing the binomial asset pricing model, which is a complete market model. In the limit, the binomial model converges to an exponential Brownian motion model, a setup where Black-Scholes-Merton equation was derived. In reality, markets are incomplete for many reasons (e.g. jumps, market closures, illiquidity), and perfect risk transfer is not possible. We introduce a novel approach of pricing in incomplete markets "via" risk measures. Time and Date: 3:00--4:30 p.m., Monday, September 25, 2006 Event: Algebraic Geometry Seminar Speaker: Jason Bell, SFU Subject:Primitivity in twisted homogeneous coordinate rings'' Location: WMAX 110 (PIMS) Abstract: Given a projective k-scheme X, an automorphism \sigma of X and an invertible sheaf L on X, one can form the twisted homogeneous coordinate ring \bigoplus_{n\ge 0} H^0(X,L_n), where L_n=L\otimes L^{\sigma}\otimes \cdots\otimes L^{\sigma^{n-1}}. We study the question of primitivity of such rings. A ring R is primitive if it has a maximal left ideal which does not contain a nonzero two sided ideal. We show in many cases that primitivity of twisted homogeneous coordinate rings is equivalent to the quotient division ring having trivial centre and to the ring having finitely many height one primes. This gives a Dixmier-Moeglin correspondence for many classes of twisted homogeneous coordinate rings. Time and Date: 3:30--4:30 p.m., Tuesday, September 26, 2006 Event: Discrete Mathematics Seminar Speaker: Kalle Karu, UBC Subject:Kalai's conjecture and its cd-index analogue'' Location: WMAX 216 Abstract: In 1997 Braden and MacPherson proved a conjecture of Kalai, stating that the g-polynomial of a polytope is bounded by the product of two g-polynomials -- of a face F and the dual face F*. Billera and Ehrenborg in 2000 proved a similar theorem, but with g-polynomial replaced by the cd-index. In this talk I will explain how the theorem applies more generally to certain fans, CW-complexes and Eulerian posets. This is a joint work with Richard Ehrenborg. Time and Date: day events, Wednesday--Friday, September 27--29, 2006 Event: PIMS CRG on Mathematical Modelling and Computation in Biology Workshop Speaker: All speakers and seminars are listed at http://www.pims.math.ca/science/2006/06disdyn/schedule.html (PIMS). Subject:Bridging the scales of disease dynamics 2006'' Location: WMAX 110 and 216 (PIMS) Time and Date: 3:30 p.m., Wednesday, September 27, 2006 Event: Probability Seminar Speaker: Matthieu Merle, Department of Mathematics, UBC Subject:Probability of hitting a far point for the voter model'' Location: MATH 202 Abstract: We consider a voter model on the integer lattice started with a single one at the origin. In dimensions 2 and 3, we establish the precise asymptotic behaviour of the probability for the voter model to hit a distant point. We use the scaling limit of the voter model started from a single one in terms of super-Brownian motion under its excursion measure. This invariant principle was proved by Bramson Cox and Le Gall, as a consequence of a theorem of Cox, Durrett and Perkins. We also derive less precise estimates in dimension less than 4. Time and Date: 4:00 p.m., Thursday, September 28, 2006 Event: Math Finance Seminar Speaker: Jean-Pierre Fouque, UCSB Subject:Perturbations Methods in Default Modeling'' Location: MATH 202 Abstract: Stochastic volatility has played a central role in modeling equity derivative markets. In the recent years the market in credit-linked derivative products has grown tremendously and had generated a need for more sophisticated models of default. We show that stochastic volatility incorporated in first passage models can create reasonable default probabilities over a wide range of maturities. To achieve that, one has to carefully calibrate the time scales of volatility. Regular and singular perturbation techniques associated to slow and fast time scales can be used to make this approach tractable. We then address the multi-name case and we show that default correlations created by stochastic volatility give interesting loss distributions. Perturbation techniques are again used to compute these distributions and the related CDO tranche prices. Time and Date: 4:00 p.m., Thursday, September 28, 2006 Event: Complex Fluids Seminar Speaker: Pengtao Yue, Department of Mathematics and Department of Chemical and Biological Engineering, UBC Subject:Simulation of bubble growth in polymer foaming'' Location: MATH 203 Abstract: Bubble growth plays an important role in determining the cell size distribution in thermoplastic foams. In this work, the diffusion-driven bubble growth in a polymer melt is computed by direct numerical simulation. The pressure and mass inside each bubble follow the equation of state for an ideal gas. A finite element method is used to calculate the gas concentration and flow variables in the polymer melt. Henry's law is employed to relate the bubble pressure and the gas concentration at the bubble surface. An Arbitrary Lagrangian-Eulerian (ALE) technique is used to handle the moving boundary. Within each time step, the whole system is solved iteratively. By modeling the polymer melts as Oldroyd-B fluids, we will study the influence of rheology on single bubble growth and interactions between multiple bubbles. Time and Date:3:00--4:00 p.m., Monday, October 2, 2006 Event: IAM Seminar Series Speaker:Razvan Fetecau, Department of Mathematics, SFU Subject:Leray-Type Regularizations of the Burgers and the Isentropic Euler Equations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We consider the following scalar equation: u_t + uu_x – \alpha^2 u_{txx} – \alpha^2 u_{xxx} = 0, (1) with \alpha > 0. We may rewrite (1) as v_t + uv_x = 0, (2) where v = u – \alpha^2 u_{xx}. (3) One can think of (2) as the inviscid Burgers equation, v_t + vv_x = 0, where the convective velocity in the nonlinear term is replaced by a smoother velocity field u. This idea goes back to Leray (1934), who employed it in the context of the incompressible Navier-Stokes equation. Leray's program consisted in proving existence of the solutions for his modified equations and then showing that these solutions converge, as \alpha\rightarrow 0, to solutions of Navier-Stokes. We apply Leray's ideas in the context of Burgers equation. We show strong analytical and numerical indication that (2)-(3) (or equivalently (1)) represent a valid regularization of the Burgers equation. That is, we claim that solutions u^\alpha (x,t) of (1) converge strongly, as \alpha\rightarrow 0, to unique entropy solutions of the inviscid Burgers equation. Interestingly, for all \alpha > 0, the regularized equation possesses a Hamiltonian structure. We also study the stability of the traveling waves for equation (1). These traveling waves consist of "fronts", which are monotonic profiles that connect a left state to a right state. The front stability results show that the regularized equations (1) mirrors the physics of rarefaction and shock waves in the Burgers equation. Finally, we apply the Leray regularization to the isentropic Euler equations and use the weakly nonlinear geometrical optics (WNGO) asymptotic theory to analyze the resulting system. Time and Date:3:00--4:30 p.m., Monday, October 2, 2006 Event: Algebraic Geometry Seminar Speaker:Kalle Karu, UBC Subject:Ehrhart analogue of the h-polynomial'' Location: WMAX 110 (PIMS) Abstract: In this talk I will explain how the Ehrhart problem of counting lattice points in a polyhedron is equivalent to a problem in orbifold cohomology. This equivalence can be used to prove a conjecture of Stanley that relates the Ehrhart generating polynomial to toric h-polynomials. Time and Date:12:30--1:30 p.m., Tuesday, October 3, 2006 Event: UBC SCAIM Seminar Speaker: Anne Kvaernoe, Norwegian University of Science and Technology, Trondheim, Norway and SFU Subject:Exponential integrators'' Location: WMAX 216 Abstract: Numerical schemes for ordinary differential equations, using matrix exponentials, were introduced in the 1960's as a way to overcome the stability restrictions of explicit methods. However, such methods were not considered as a practical mean of solving stiff ODEs until quite recently. Due to improvements in the efficient computation of the exponential function, exponential integrators have emerged as a viable alternative for the integration of spatially discretized nonlinear parabolic and hyperbolic differential equations. In this talk an overview on the construction of exponential integrators will be given, implementation issues will be discussed, and examples of the methods applied to some well known problems like the nonlinear Schroedinger, the Kuramoto-Shivashinski and the Gray-Scott equations will be presented. Time and Date:3:30 p.m., Tuesday, October 3, 2006 Event: DG-MP-PDE Seminar Speaker:Joao Marcus do O, Universidade Federal da Paraiba (Brazil) and UBC Subject:Semilinear elliptic systems with exponential nonlinearities in two dimensions'' Location: WMAX 110 Abstract: We study the existence of nontrivial solutions for the following system of two coupled semilinear Poisson equations: \left\{ \begin{array}{rlllllll} -\Delta u &=& g(v), & v & > & 0 & \textrm{in} &\Omega, \\ -\Delta v &=& f(u), & u & > & 0 & \textrm{in} & \Omega, \\ u &=& 0, & v & = & 0 & \textrm{on} &\partial \Omega ,\end{array}\right. where \Omega is a bounded domain in \Re^2 with smooth boundary \partial\Omega , and the functions f and g depend exponentially with respect to u and v. Time and Date:3:30 p.m., Oct. 4th Event: Algebra/Topology Seminar Speaker:Jeff Smith, UBC Subject:The moduli space of homotopy G-spheres" Location: WMAX 110 Abstract: I will discuss joint work with Jesper Grodal. A homotopy G sphere is a space that is homotopy equivalent to a sphere and has an action of the group G. Two homotopy G spheres are equivalent if there is a zigzag of equivariant weak equivalences that connects them. We classify homotopy G spheres for all finite groups. We compute the monoid of homotopy classes of self maps of each homotopy G sphere and we show that most of the higher homotopy groups of the space of self maps finite. Time and Date:3:30 p.m., Wednesday, October 4, 2006 Event: Probability Seminar Speaker:Adam Timar, Department of Mathematics, UBC Subject:Neighboring clusters at Bernoulli percolation'' Location:WMAX 216 Abstract:The study of Bernoulli percolation on general infinite transitive graphs was initiated by a paper of Benjamini and Schramm in 1996, and has been intensive since then. One of the interesting phenomena is that for certain graphs there is a value of p when there are infinitely many infinite components. This is conjectured to be a characterizing property of nonamenable graphs. Haggstrom, Peres and Schonmann asked whether it can happen that two infinite components of such a percolation come at distance 1 from each other at infinitely many places. We give a negative answer to this question. Time and Date:3:00--3:50 p.m., Thursday, October 5, 2006 Event: SFU/UBC Number Theory Seminar Speaker:Igor Pritsker, Oklahoma State University Subject:Polynomial inequalities, Mahler's measure, and multipliers'' Location:UBC Campus, WMAX 110 Abstract:We shall discuss polynomial inequalities for integral norms defined by the contour and the area integral over the unit circle. The common feature of these inequalities is that they are obtained by using coefficient multipliers. Special attention will be devoted to Mahler's measure. Time and Date:4:10--5:00 p.m., Thursday, October 5, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Matilde Lalin, PIMS, SFU, UBC Subject:Functional equations for Mahler measures of genus-one curves'' Location:UBC Campus, WMAX 110 Abstract:The Mahler measure of an n-variable polynomial P is the integral of log |P| over the n-dimensional unit torus T^n with the Haar measure. Consider a family of two-variable polynomials whose coefficients depend on one parameter. Then the Mahler measure is a function of that parameter. Mat Rogers has discovered several examples for which this function satisfies functional equations. They all correspond to families of elliptic curves. We may deduce these functional equations from modularity properties or evaluations of elliptic regulators following works by Rodriguez-Villegas, Zagier, Deninger, etc. Time and Date:4:00 p.m., Thursday, October 5, 2006 Event: Complex Fluids Seminar Speaker:Chunfeng Zhou, Department of Chemical and Biological Engineering Subject:The Shape of Bubbles and Drops Rising in a Nematic Liquid Crystal'' Location:MATH 203 Abstract:This work is motivated by recent experimental observation of unusual "inverted-heart" shapes that a bubble assumes when rising in an anisotropic fluid. A possible explanation is in terms of the molecular orientation of the matrix fluid with respect to the bubble surface. In this work, we use numerical simulations to test such a hypothesis. The moving interface problem is formulated in a diffuse-interface framework. The anisotropic fluid is represented by a simplified Leslie-Ericksen theory for nematic liquid crystals, with director anchoring on the surface of an isotropic drop. The simulations are carried out using axisymmetric finite elements. Results show an array of drop shapes, depending on the interplay among inertial, capillary, anchoring and elastic effects. Drops with sufficiently strong planar anchoring and moderate elasticity rising in a medium with vertical far-field orientation assume the inverted-heart observed in experiments. This is shown to be mainly due to the competition between interfacial tension, anchoring energy and bulk elastic energy. Furthermore, two boojum defects appear on the upper and lower poles. The size of the defects plays an significant role in shaping the rising bubble. Time and Date:3:00 p.m., Friday, October 6, 2006 Event: Mathematics Colloquium Speaker:Dan Coombs, UBC Subject: Virus Competition at Multiple Scales" Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--1:30 p.m., Tuesday, October 10, 2006 Event: UBC SCAIM Seminar Speaker: Ray Spiteri, U. Saskatchewan Subject:Do we know WENO?'' Location: WMAX 216 (PIMS) Abstract: The weighted essentially non-oscillatory (WENO) methods are popular spatial discretization methods for hyperbolic partial differential equations. In this talk I show that the combination of the widely used fifth-order WENO spatial discretization (WENO5) and several of the most popular time integration methods are in fact linearly unstable (and hence not convergent) when numerically integrating hyperbolic conservation laws. We find that a sufficient condition for the combination of an explicit Runge-Kutta (ERK) method and WENO5 to be linearly stable is that the linear stability region of the ERK method should include the part of the imaginary axis of the form [-\mu,\mu], for some \mu>0. The linear stability analysis also provides insight (and busts some myths) about the behaviour of ERK methods applied to nonlinear problems and problems with discontinuous solutions. We confirm the predictions of our analysis by means of numerical tests. Time and Date: 3:30--5:00 p.m., Tuesday, October 10, 2006 Event: Joint Mathematics Colloquium/Discrete Math Seminar Speaker: Joachim Rosenthal, Mathematics Institute, University of Zurich Subject: Three challenges of Claude Shannon'' Location: WMAX 110 (PIMS Facility) Note: Refreshments will be served at 3:15 p.m. in the 1st floor PIMS Lounge. Time and Date: 3:30 p.m., Tuesday, October 10, 2006 Event: DG-MP-PDE Seminar Speaker: Tai-Peng Tsai, UBC Subject:Regularity criteria for Navier-Stokes equations'' Location: WMAX 216 (Note special location.) Abstract: In the talk I will first review various known regularity criteria and partial regularity theory for 3D incompressible Navier-Stokes equations. I will then talk about a joint work with Gustafson and Kang on regularity criteria based on scaled space-time norms of the velocity, the vorticity, or their gradients. Time and Date: 2:30 p.m., Wednesday, October 11, 2006 Event: Algebraic Geometry Seminar Speaker: Jonathan Hanke, Duke University Subject:TBA'' Location: WMAX 110 Time and Date: 3:30 p.m., Wednesday, October 11, 2006 Event: Algebra/Topology Seminar Speaker: Liam Watson, U. Quebec at Montreal Subject:Aspects of Khovanov homology'' Location: WMAX 110 Abstract: Khovanov's construction of a homology theory for knots allows us to view the Jones polynomial as an Euler characteristic, provides a stronger knot invariant, and is the main tool for Rasmussen's combinatorial proof of the Milnor conjecture. In this talk I introduce Khovanov's construction, as well as Bar-Natan's "local" theory which allows for very fast computation of this invariant, among other things. Time and Date: 3:30 p.m., Wednesday, October 11, 2006 Event: Probability Seminar Speaker: Jeremy Quastel, U. Toronto Subject:Effect of noise on front propagation in KPP equations'' Location: WMAX 216 Abstract: We study random traveling waves in KPP equations with appropriate additive noise. We prove a very explicit conjecture of Brunet and Derrida concerning the dramatic slowdown of these fronts by the noise. This is joint work with Carl Mueller and Leonid Mytnik. Time and Date: 2:00 p.m., Thursday, October 12, 2006 Event: Mathematical Biology Seminar Speaker: Yoichiro Mori, Department of Mathematics, UBC Subject:Implicit Immersed Boundary Methods with Boundary Mass'' Location: WMAX 216 Abstract: The immersed boundary method is a general framework used to handle fluid-structure interactions. One computational bottleneck of the immersed boundary methods is that the elastic structures are often very stiff, necessitating the use of a very fine time step. In this talk, we will present an immersed boundary scheme in which the position of the immersed elastic structure is treated implicitly. We show that the resulting implicit method allows much greater time steps to be used compared with an explicit method, and that the computational cost is greatly reduced in certain test situations. We shall also show that the implicit method provides a natural way in which to add addtional mass to the immersed elastic structure. Time and Date: 3:00 p.m., Friday, October 13, 2006 Event: Mathematics Colloquium Speaker: Jozsef Solymosi, UBC Subject: On the Sum-Product Conjecture'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00--3:00 p.m., Monday, October 16, 2006 Event: Learning Seminar in Topology Speaker: Enrique Torres-Giese, Graduate Student, Mathematics, UBC Subject:TBA" Location: WMAX 110 (PIMS) Time and Date: 3:00--4:00 p.m., Monday, October 16, 2006 Event: IAM Seminar Series Speaker: Adam Oberman, Department of Mathematics, SFU Subject:Fully Nonlinear Elliptic PDEs: Applications and Solution Methods" Location: Room 301, Leonard S. Klinck Bldg. Abstract: This will be an accessible talk about modeling using fully nonlinear elliptic PDEs. Modern applications of these PDEs are to Image Processing and Math Finance. Also the Level Set Method for curve evolution, optimal control, and the visibility problem. I'll discuss some interesting models, overview the relevant theory, and then show how to build solutions. Examples will include: level set motion by mean curvature, the convex hull, the infinity Laplacian, as well as examples from math finance and control theory. We will present results which allow schemes to be built for a wide class of equations. Time and Date: 3:00 p.m., Monday, October 16, 2006 Event: Algebraic Geometry Seminar Speaker: Sam Payne, Clay Institute and Stanford U. Subject:Integral cohomology of singular toric varieties" Location: WMAX 110 Abstract: The singular cohomology and Chow cohomology, with Q-coefficients, of projective toric varieties with at worst orbifold singularities are well-understood, but interesting problems remain for toric varieties with more serious singularities and for cohomology with Z-coefficients. I will present a computation of the equivariant Chow cohomology of singular toric varieties with Z-coefficients in terms of piecewise-polynomial functions on fans, using Kimura's inductive methods with envelopes and resolutions of singularities. As time permits, I will also discuss some open questions and conjectures about the singular cohomology of toric varieties and its relation to Chow cohomology, and about the cohomology of real toric varieties. Time and Date: 3:30 p.m., Tuesday, October 17, 2006 Event: PDE/Geometry/Math Physics Student Seminar Speaker: Nassif Ghoussoub, UBC Subject:Open problems related to certain mathematical models for MEMS devices'' Location: WMAX 216 Time and Date: 3:30 p.m., Wednesday, October 18, 2006 Event: Algebra/Topology Seminar Speaker: Melissa Macasieb, Department of Mathematics, UBC Subject:Arithmetic Fuchsian groups of genus two'' Location: WMAX 110 Abstract: A hyperbolic 2- or 3-orbifold M is called arithmetic if M = H^2/G or H^3/G where G is an arithmetic Fuchsian or Kleinian group, respectively. Considerable work has been done in the last two decades classifying these groups. I will explain how arithmetic Fuchsian and Kleinian groups can be described in terms of quaternion algebras over number fields and discuss some results and open questions regarding these groups. Time permitting, I will outline the classification of derived arithmetic Fuchsian groups of genus 2. Time and Date: 2:00 p.m., Thursday, October 19, 2006 Event: Mathematical Biology Seminar Speaker: Lin Wang, Department of Mathematics, UBC Subject:Impact of Travel between Patches for Spatial Spread of Disease'' Location: WMAX 216 Abstract: A patch model is proposed to study the impact of travel on the spatial spread of disease between patches. The basic reproduction number for the i-th patch in isolation, is obtained along with the basic reproduction number of the system, \mathcal{R}_0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of \mathcal{R}_0 on the travel rates between the two patches are obtained. For parameters relevant for influenza, the effects of travel restrictions are also discussed. Results show that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease. Time and Date: 3:00--3:50 p.m., Thursday, October 19, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Jason Bell, SFU Subject:Christol's theorem and quasi-automatic functions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Note: 3:50-4:10 tea break Abstract: A theorem of Christol states that a power series expansion f(t)\in F_q[[t]], with q a power of a prime p, is algebraic over F_q[t] if and only if the sequence of coefficients of f(x) is “p-automatic”, that is, there is a finite state machine which inputs the base p-expansion of a number n and outputs the coefficient of t^n in f(t). Kedlaya pointed out that it is more natural to work in the ring of Hahn power series F_q((t^Q)), since F_q[[t]] is not algebraically closed. We will discuss his analogue of Christol's theorem for Hahn power series in terms of quasi-automatic functions. Furthermore, we give a quasi-automatic analogue of a theorem of Cobham which states that if a sequence is k- and l-automatic and k and l are multiplicatively independent then the sequence is eventually periodic. We show that if f is k-quasi-automatic and l-quasi-automatic and k and l are multiplicatively independent, then f is “quasi-periodic”, a property which is very similar to being periodic. This is joint work with Boris Adamczewski. Time and Date: 3:00 p.m., Thursday, October 19, 2006 Event: DG-MP-PDE Seminar Speaker: Michel Rascle, Nice Subject:Fluid Mathematical Models of Traffic Flow'' Location: WMAX 110 Abstract: I will start with a few basic facts on other types of description (microscopic, kinetic ...). Then I will talk about fluid models, of "first order" : Lighthill-Whitham-Richards (LWR) , i.e. a scalar conservation law, robust and (too ?) simple. The first type of "second order models" (Payne-Whitham) was based on the gas dynamics system and had severe drawbacks, like predicting sometimes cars moving backwards (!). After the classical paper of Daganzo ("Requiem ...", 95), we introduced with Aw (Resurrection ...", 2000) a very simple fixing of this PW model, which definitely cures these inconsistencies. I will show the (rigorous) relations between this class of models and the microscopic "Follow the Leader" models. Finally, if time allows, I will describe some applications to flows on a network, and related issues, like homogenization problems, or hybrid schemes. Time and Date: 4:00 p.m., Thursday, October 19, 2006 Event: Math Finance Seminar Speaker: Santiago Moreno, Department of Mathematics, UBC Subject:Minimizing Risk in a Principal-Agent Model'' Location: WMAX 110 Abstract: We will be working with a principal-agent model under adverse selection. We will assume the Principal is endowed with some initial risk W_T, which she wishes to hedge (for the moment our model is time-stationary). The Principal faces a set \Theta of agents whose individual types (\theta\in\Theta ) are private information; however, the distribution of those types (given by d\mu (\theta )) is information known a priori. The Principal's aim is to design a set of contracts (X(\theta ), \pi(X(\theta )) in order to minimize \rho\left(W_T+\int_{\Theta}(\pi(X(\theta))-X(\theta))d\mu (\theta)\right) where \rho(\cdot) is a convex, law-invariant risk measure. The agents evaluate these contracts via U(X,\theta)=E[X]-\theta Var[X]-\pi(X) The Mean-Variance preferences of the agents, together with the Individual Rationality and the Incentive Compatibility constraints which must be satisfied by (X(\theta). \pi(X(\theta )), allow us to write the Principal's problem as an optimal control problem where the control variable v(\theta ) is a convex, non-increasing and positive function which satisfies -v'(\theta )=Var[X(\theta )]. We explore the existence of solutions to this problem and give some examples of closed-form solutions in a finite-state probability space for \rho(X) = AV@R_{\lambda} (X). Time and Date: 4:00 p.m., Thursday, October 19, 2006 Event: Complex Fluids Seminar Speaker: Andreas Putz, Department of Mathematics, UBC Subject:Sedimentation Problems in Viscoplastic Fluids - An Experimental Study'' Location: MATH 203 Abstract: We have studied the flow around a sedimenting spherical particle in a Carbopol solution which displays viscoplastic behaviour. The two dimensional flow fields around these particles are obtained using laser illumination techniques combined with Particle Image Velocimetry. We will discuss the topological properties of these flow fields and attempt to classify these properties with respect to the relevant physical quantities. We will also discuss the differences between the experimentally obtained flow field and numerical calculations based on Bingham or Herschley-Bulkley models. Time and Date: 4:10--5:00 p.m., Thursday, October 19, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Michael Coons, SFU Subject:General moment theorems for non-distinct unrestricted partitions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: (joint work with Klaus Kirsten, Baylor University) A well-known result from Hardy and Ramanujan gives an asymptotic expression for the number of possible ways to write an integer as the sum of smaller integers. In this vein, we consider the general partitioning problem of writing an integer n as a sum of summands from a given sequence L of non-decreasing integers. Under suitable assumptions on the sequence L, we obtain results using the associated zeta-function and saddle-point techniques. We also calculate higher moments of the sequence L as well as the expected number of summands and the variance. Then applications are made to various sequences, including those of Barnes and Epstein types. Time and Date: 3:00 p.m., Friday, October 20, 2006 Event: Mathematics Colloquium Speaker: Stephen Gustafson, UBC Subject: Schroedinger maps'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, October 23, 2006 Event: IAM Seminar Series Speaker: Alex Vladimirsky, Department of Mathematics, Cornell University Subject:Going with the (Information) Flow: On Efficient Computations and Boundary Value Problems'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The direction of information propagation can be used to de-couple certain systems of nonlinear equations. This fundamental principle is the basis of Dijkstra's classical method for finding shortest paths on graphs. We will use the continuous analogue of this principle to build efficient (non-iterative) numerical methods for a wide class of static first-order partial differential equations. We will treat a number of problems in continuous and hybrid optimal control (e.g., optimal traveling on foot and using the buses), in anisotropic front propagation (e.g., first-time arrivals in seismic imaging), in optimal control under uncertainty (e.g., optimal traveling when the map is not quite known), and in dynamical systems (e.g., approximation of "geometrically stiff" invariant manifolds). Time and Date: 3:00 p.m., Monday, October 23, 2006 Event: Algebraic Geometry Seminar Speaker: Jim Bryan, UBC Subject:The quantum McKay correspondence in dimension two'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Abstract: Let G be a finite subgroup of SU(2). The classical McKay correspondence describes the cohomology ring of Y the minimal resolution of C^2/G in terms of the representation theory of G. We give a description of the quantum cohomology of Y in terms of a root system canonically associated to G. Implications for the Crepant Resolution Conjecture may be discussed. Time and Date: 11:00 a.m. -- 12:00 p.m., Tuesday, October 24, 2006 Event: Probability Seminar Speaker: Robert J. Adler, Technion, Haifa, Israel Subject:Gaussian processes, kinematic formulae and Poincare's limit'' Location: WMAX 110 Abstract: The main aim of this talk will be to prove the specific result that the mean invariant measures of the excursion sets f^{-1}(D) of the vector-valued isotropic Gaussian process f on the n-sphere have a specific form, highly reminiscent of the Kinematic Fundamental Formula of classical Euclidean Integral Geometry. I will also explain why this very special result has broad implications for other smooth Gaussian and related processes on far more general parameter spaces, and what some of their applications are. This is joint work with Jonathan Taylor. Time and Date: 12:30--1:30 p.m., Tuesday, October 24, 2006 Event: UBC SCAIM Seminar Speaker: Manfred Trummer, SFU Subject:Some mathematical challenges in nuclear medical imaging problems'' Location: WMAX 216 Abstract: We give a brief description of some of the challenging problems in medical imaging, particularly those related to nuclear medicine. We will describe some recent progress made in dual-isotope SPECT image reconstruction - obtaining two images from a simultaneous scan with two isotopes, as well as our work on dynamic SPECT, the reconstruction of time varying images. Time and Date: 3:30 p.m., Tuesday, October 24, 2006 Event: PDE/Geometry/Math Physics Student Seminar Speaker: Nassif Ghoussoub, UBC Subject:Open problems related to certain mathematical models for MEMS devices, (Part II)'' Location: WMAX 110 Time and Date: 3:00 -- 4:00 p.m., Wednesday, October 25, 2006 Event: Algebra/Topology Seminar (Pls note new time of seminar.) Speaker: Dale Rolfsen, UBC Subject:A knot theoretic equivalent to Kervaire's conjecture for groups'' Location: WMAX 110 Abstract:In 1965, Michel Kervaire conjectured that if G is a nontrivial group, then the free product G*Z cannot be normally generated by a single element. In other words, a group cannot be killed by adding a new generator and a single relation. Although settled in many cases (G finite, G torsion-free), the problem remains open. Recently, Francisco Gonzalez-Acuna and Arturo Ramirez proposed a knot-theoretic conjecture which is equivalent to Kervaire's conjecture: if E is the exterior of a knot in the 3-sphere and F is a nonseparating surface properly embedded in E, then the fundamental group of E/F is infinite cyclic. There is some hope that advances in knot theory may settle this conjecture, and hence Kervaire's conjecture for groups. I will discuss these conjectures and outline a proof of their equivalence. Time and Date: 2:00 p.m., Thursday, October 26, 2006 Event: Mathematical Biology Seminar Speaker: Kevin Painter, Mathematics, Heriot Watt University, U.K. Subject:Modelling cell migration in the ECM and its role in tumour invasion'' Location: WMAX 216 Abstract: Cell migration plays an essential role during both embryonic development (e.g. gastrulation, neural crest migration) and in the normal physiological responses of the adult (e.g. immune response, wound healing). The extracellular matrix (ECM) plays a vital role in regulating movement by both providing a scaffold through which cells can generate traction and imparting specific migratory cues through ECM-bound proteins. The ECM also provides specific guidance to cells through preferential movement by the cells along the matrix fibres, a process known as contact guidance. The acquired ability of tumour cells to break free from the main mass and migrate into the surrounding ECM is a key stage in increased tumour malignancy. Individual cell migration in the ECM can be classified into two main groups: amoeboid and mesenchymal. In the former, cells move quickly and have negligible effect on the structure of the surrounding ECM. Mesenchymal migration, however, is much slower and extensive matrix degradation takes place through the focussed expression of specific matrix degrading proteins by the cells (pericellular proteolysis). In this talk, I will describe both discrete and continuous models for amoeboid and mesenchymal cell migration. Numerical investigations will be used to demonstrate a potential role of contact guidance and matrix degradation in directing the macroscopic organisation of cells and the matrix. I will consider applications in the context of models for tumour invasion. Time and Date: 3:00 -- 4:30 p.m., Thursday, October 26, 2006 Event: Working Seminar on SL(2,C) Character Varieties of 3-Manifold Groups Speaker: Gabriel Indurskis, Department of Mathematics, UBC Subject:Introduction to SL(2,C) Representation and Character Varieties'' Location: Ponderosa Annex E, Room 117 Abstract: To start off our working seminar, I will give a quick introduction of SL(2,C) representation and character varieties of finitely presented groups, only later specializing to fundamental groups of 3-manifolds. I will try to give some overview of the kind of results linking the algebraic geometry with the topology, and will discuss some possible topics for future talks. Recommended reference: Peter Shalen's notes on "Representations of 3-manifold groups", available online at http://www.math.uic.edu/~shalen/handbook.ps Note: Please note that we will meet Thursdays 3-4:30pm every two weeks, alternating with the Number Theory seminar. Time and Date: 3:00 p.m., Thursday, October 26, 2006 Event: DG-MP-PDE Seminar Speaker: John Toth, McGill University Subject:Complex zeros of Laplace eigenfunctions'' Location: WMAX 216 Abstract: As is well-known, it is difficult to determine the zeros of a real polynomial, whereas it is much simpler to determine the complex zeros of its holomorphic continuation. Since eigenfunctions \phi_{\lambda}(x) of the Laplacian with eigenvalue \lambda^{2} on a real analytic Riemannian manifold are analogous to real polynomials of degree \sim \lambda , it is reasonable to expect that the complex zeros of the analytic continuation \phi_{\lambda}^{C} of \phi_{\lambda} to the complexification M_{C} of M will also be simpler to determine than the real zeros (ie. the nodal hypersurface). This expectation is indeed correct when (M,g) has ergodic geodesic flow and I will discuss some recent results on the asymptotic distribution of the complex zeros \{ \phi_{\lambda}^{C}(z) = 0 \} in this case. Time and Date: 4:30 p.m., Thursday, October 26, 2006 Event: Math Finance Seminar Speaker: Stathis Tompaidis, University of Texas at Austin Subject:Asset Selection and Under-Diversification with Financial Constraints and Income: Implications for Household Portfolio Studies'' Location: WMAX 216 Abstract: We offer a rational explanation for the observed under-diversification of household portfolios in a complete market, partial equilibrium setting with an investor with CRRA preferences, whose investment opportunity set includes both a riskless asset and multiple risky assets, and who receives an income stream. We show that when the investor faces a margin requirement based on his current wealth, he shifts his portfolio towards undiversified portfolios with fewer assets that offer higher expected returns. We identify the ratio of financial wealth to financial wealth augmented by discounted lifetime labor income as the variable that governs the investor's behavior. We also consider the general equilibrium cross-sectional implications of margin requirements in an overlapping-generations model. Time and Date: 4:00--5:00 p.m., Thursday, October 26, 2006 Event: Fluid Mechanics Seminar Speaker: G.M. Homsy, University of California, Santa Barbara Subject:The Effects of Gravity Modulation on Fluid Mixing'' Location: WMAX 110, coffee at 3:45 in 1st flr PIMS lounge. Abstract: We study the mixing characteristics of two miscible fluids under the action of a harmonically varying vertical gravity force. The two fluids initially meet at a sharp but continuous vertical interface, and the time-dependent Boussinesq equations are solved numerically and the evolution of the interface is observed and characterized. The three important are the Grashof number, Gr based on the frequency; the Schmidt number, Sc; and the aspect ratio of the domain, A. For small values of Gr, the interface oscillates about the vertical centerline without any deformation. For intermediate Gr, the interface folds onto itself, and the propagation of these folds in time and space is observed to be self-similar for small times. For higher values of Gr, instabilities develop which lead to enhanced mixing and which are explained on the basis of combined Kelvin-Hemhotz and Rayleigh-Taylor instabilities. For still higher values of Gr, the flow becomes disordered and transiently turbulent. The study is extended to include both correlated and uncorrelated stochastic gravity modulation. Ensemble averages of realizations exhibit dispersive spreading of the interface at a rate which is amplified by Gr, and which is larger for correlated jitter. Many of the phenomena occurring for deterministic jitter also occur in the stochastic case, but at a lower equivalent Gr. Accordingly, the rate of mixing for stochastic jitter is higher than that for deterministic harmonic jitter. Note: Please note this will be the first of a mthly seminar offered through the IAM on fluid mechanics. Time and Date: 4:00--5:00 p.m., Thursday, October 26, 2006 Event: Graduate Student Seminar Speaker: Mclean Edwards, Department of Mathematics, UBC Subject:Sum-preserving rearrangements of series'' Location: MATH 102 Abstract: To take a rearrangement of a series is to sum the terms in that series with a permutation in the ordering of the natural numbers. When dealing with series, it would be useful to know which rearrangements are sum preserving. For more than a quarter of a century we have known the necessary and sufficient conditions for permutations to be sum preserving, and I will present various characterizations of these results. I will also demonstrate the result that the class of sum-preserving permutations contain a subclass of rearrangements that, while ensuring all convergent series remain convergent, allow some divergent series to converge under the new ordering. This talk will be accesible to everyone and has the potential to benefit many areas of research. I will be providing a small handout summerizing the results of the first part of the talk, and will be recruiting research collaborators to help answer questions raised by the second part of this seminar. Time and Date: 3:00 p.m., Friday, October 27, 2006 Event: Mathematics Colloquium Speaker: Patrick Brosnan, UBC Subject: Motives and Feynman diagrams'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, October 30, 2006 Event: IAM Seminar Series Speaker: Anmar Khadra, Department of Mathematics, UBC Subject:Analyzing the robustness of synchrony in GnRH neurons when a common pool of GnRH hormone is considered'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Gonadotropin Releasing Hormone (GnRH) secreted by GnRH neurons plays key roles in the onset of puberty and the regulation of hormone secretion in the pituitary. GnRH neurons are intrinsically capable of generating pulsatile and episodic neurosecretion of this hormone, but the underlying mechanism for GnRH-pulse generator still remains obscure. The discovery of GnRH receptors allowing GnRH to exert autocrine regulation on its own release, led Krsmanovic et al. (2003) to propose a mechanism underlying this effect. A mathematical model describing the proposed mechanism has been developed by Khadra et. al. (2006). The model was further extended to study synchrony in GnRH neurons by incorporating the idea of a common pool of GnRH hormone. In this talk, we shall analyze several aspects of this mathematical model, particularly robustness. We shall show that coupling of a heterogeneous family of GnRH neurons will not significantly alter the general behaviour of the pulse generator. Indeed, we shall show that no more than 50% of these coupled neurons must be active participants in the process to generate pulsatility. The effects of averaging in the parameter-values, as well as the volume of the extracellular medium will be also discussed. In addition, several model predictions explaining the type of behaviour observed experimentally upon the injection of GnRH-agonist will be stated. These results will further demonstrate the properties of synchrony observed and the reliability of the model proposed. Time and Date: 3:00 -- 4:30 p.m., Monday, October 30, 2006 Event: Algebraic Geometry Seminar Speaker: Amin Gholampour, Department of Mathematics, UBC Subject:The quantum McKay correspondence in dimension three'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Abstract: Let G be a finite subgroup of SO(3). There is a canonical crepant resolution of C^3/G given by the G-Hilb, the Hilbert scheme of G clusters in C^3. The generalized McKay correspondence of Bridgeland, King and Reid, describes the classical geometry of G-Hilb in terms of representation theory of G. More precisely, they give an equivalence between the derived categories of G-Hilb and [C^3/G]. We describe the quantum cohomology of G-Hilb in terms of a root system canonically associated to G. Implication for the Crepant Resolution Conjecture may be discussed. Time and Date: 3:30--4:30 p.m., Tuesday, October 31, 2006 Event: Discrete Mathematics Seminar Speaker: Josephine Yu, UC Berkeley Subject:The Newton Polytope of the Implicit Equation'' Location: WMAX 216 Abstract: We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. The tropicalization of an algebraic variety is a polyhedral fan, and we give a combinatorial description of this fan for a parametrized variety without computing the defining ideal. If this image is a hypersurface then our approach gives a construction of the Newton polytope of the defining polynomial. Time and Date: 3:00--4:00 p.m., Wednesday, November 1, 2006 Event: Probability Day at UBC Speaker: Mark Holmes, Eurandom Subject:Some self-interacting random walks'' Location: WMAX 216 Abstract: We will discuss two different classes of self-interacting random walks. Firstly, in joint work with Akira Sakai, we consider a simple model of a random walk with reinforcement but with very short term spatial memory. The simplicity of these "Senile random walks" enables us to prove many things such as recurrence/transience and an exact expression for the diffusion constant. Secondly, in joint work with Remco van der Hofstad, we derive an expansion for general self-interacting random walks. We use the expansion to prove a central limit theorem for a class of once reinforced random walks with non-zero drift (all dimensions) and for excited random walk (high dimensions), when the reinforcement and excitement parameters are sufficiently small. Time and Date: 4:00--5:00 p.m., Wednesday, November 1, 2006 Event: 2nd Probability Seminar Speaker: Gord Slade, UBC Subject:Invasion percolation on regular trees'' Location: WMAX 216 Abstract: We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behaviour of its connectivity functions, and of its volume both at a given height and below a given height. We find that the power laws of the scaling are the same as for the incipient infinite cluster for ordinary percolation, but the scaling functions differ. Thus, somewhat surprisingly, the invasion percolation cluster and the incipient infinite cluster are globally different. However, far above the root, the two clusters do have the same law locally. In addition, we use recent work of Barlow, Jarai, Kumagai and Slade to analyse simple random walk on the invasion percolation cluster, and show that the spectral dimension is 4/3, as it is on the incipient infinite cluster. This is joint work with Omer Angel, Jesse Goodman and Frank den Hollander. Time and Date: 5:00 p.m., Wednesday, November 1, 2006 Event: Contemporary Immunology: How the Physical Sciences and Mathematics are Shaping Immunology: Speaker Series Speaker: Michael Gold, Professor of Microbiology and Immunology, UBC Subject:Immunology, math, and physics: What's the problem?'' Location: Coach House, Green College. Notes: All attendees are welcome to stay for dinner after the talk. Reservations + ticket purchase must be made in advance. Pls visit http://www.iam.ubc.ca/~omer/spkr_series/ for more information. Time and Date: 3:00 -- 4:00 p.m., Thursday, November 2, 2006 Event: Algebra/Topology Seminar (Pls note unusual day and location of this week's seminar.) Speaker: Hendryk Pfeiffer, Max Planck Institute for Gravitational Physics Subject:Two-dimensional extended TQFTs and Khovanov homology'' Location: MATX 1118 Abstract: An n-dimensional Topological Quantum Field Theory (TQFT) associates vector spaces with (n-1)-manifolds and linear maps with n-dimensional cobordisms. For closed n-manifolds, the TQFT yields a topological invariant. I extend the notion of a 2-dimensional TQFT from cobordisms to manifolds with corners ('open-closed cobordisms') and show how to classify such extended TQFTs. As an application, I sketch how these extended TQFTs can be used in order to extend the construction of Khovanov homology from links to tangles. Time and Date: 3:00--3:50 p.m., Thursday, November 2, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Chris Sinclair, PIMS, SFU, UBC Subject:Heights of polynomials and random matrix theory'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: We will discuss a method for producing asymptotic estimates for the number of integer polynomials of degree N with bounded (but large) Mahler's measure. This method also produces a closed form for averages of class functions over ensembles of asymmetric random matrices. In this talk I will explain why this is important, and its potential for resolving some open problems surrounding certain ensembles of random matrices. Time and Date: 3:30--4:30 p.m., Thursday, November 2, 2006 Event: PDE/Geometry/Math Physics Student Seminar Speaker: Gustavo de Oliveira, UBC Subject:Brenier's L^2 theory for scalar conservation laws'' Location: MATH 104 Abstract: We will start with a brief introduction to conservations laws, and then discuss the L^2 theory of multidimensional scalar conservations laws, following the paper of Yann Brenier (http://arxiv.org/pdf/math.AP/0609761) . Time and Date: 4:00 -- 5:00 p.m., Thursday, November 2, 2006 Event: Complex Fluids Seminar Speaker: Dajun Wang, Department of Mechanics and Engineering Science, Peking University, Beijing Subject:Bell-Chime, Dragon Washbasin, ... Modern Scientific Information Hidden in Ancient Chinese Science and Technology'' Location: MATH 203 Abstract: In China, many of ancient cultural relics are indeed treasures that combine arts with engineering technology and science. As the carriers of ancient science and technology, they are rich in sophisticated scientific information. Modern science is needed to reveal it. Furthermore, new scientific phenomena, methods and results may be discovered, which is helpful to the development of modern sciences. In this lecture, the properties of mechanics discovered by investigating the two pieces of Chinese antiquity are represented. Some interesting modern research topics motivated from this study are described. 1. Culture and science of ancient Chinese music bells (about 500 B.C.) Classification of ancient Chinese bells; Historical significance of ancient music bells; Outstanding music performance: dual tones and short duration; Scientific principles: qualitative and experimental mode analysis; Vibration decay caused by material damping and air radiation. 2. Scientific mystery of Dragon Washbasin (about 1000 A.D.) Beautiful and complicated motion of water inside the basin; Measurement of motion of basin and water; The mechanism of shell vibrating and water spurting: self-excited vibration of two systems caused by dry friction between them; Generation of gravity water waves with low frequencies in an elastic vessel subjected to lateral excitation with high frequency. Time and Date: 4:10--5:00 p.m., Thursday, November 2, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Shabnam Akhtari, Department of Mathematics, UBC Subject:The Diophantine equation aX^4-bY^2=1'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: In a series of papers over nearly forty years, Ljunggren derived remarkably sharp bounds for the number of solutions to various quartic Diophantine equations, particularly those of the shape aX^4-bY^2=±1, typically via a sophisticated application of Skolem's p-adic method. More recent results along these lines are well surveyed in a paper of Walsh. For general a and b, however, there is no absolute upper bound for the number of integral solutions to aX^4-bY^2=1 available in the literature. Computations and assorted heuristics suggest the following conjecture of Walsh: For any positive integers a and b, the equation aX^4-bY^2=1 has at most two solutions in positive integers X and Y. In this talk, we will appeal to a classical result of Thue from the theory of Diophantine approximation to deduce the following result: For any positive integers a and b, the equation aX^4-bY^2=1 has at most three solutions in positive integers X and Y. Time and Date: 1:30 -- 2:30 p.m., Friday, November 3, 2006 Event: Special PIMS Geometry Seminar Speaker: Gang Tian, Princeton University Subject:Canonical metrics and collapsing manifolds'' Location: WMAX 110 Time and Date: 3:00 p.m., Friday, November 3, 2006 Event: Mathematics Colloquium Speaker: Kalle Karu, UBC Subject: Combinatorics of the blowup-blowdown conjecture'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, November 6, 2006 Event: 2006-07 IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Peter A. Forsyth, David R. Cheriton School of Computer Science, University of Waterloo Subject:Hedging under Jump Diffusion with Transaction Costs'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: In this talk, we consider the problem of hedging a contingent claim, where the underlying asset follows a jump diffusion process. The no-arbitrage value of the claim is given by the solution of a Partial Integro-Differential Equation (PIDE), which in general must be solved numerically. By constructing a portfolio consisting of the underlying asset and a number of liquidly traded options, we devise a dynamic hedging strategy. At each hedge rebalance time, we minimize both the jump risk and the cost of buying/selling due to bid-ask spreads. Simulations of this strategy show that the standard deviation of the profit and loss of the hedging portfolio is greatly reduced compared with the standard hedging strategy. Time and Date: 4:30--5:30 p.m., Monday, November 6, 2006 Event: PIMS 10th Anniversary Speaker Series Speaker: James Arthur, University of Toronto Subject:A History of the Trace Formula'' Location: WMAX 110 (West Mall Annex, PIMS-UBC Facility) Note: Coffee and refreshments will be served half an hour before the talk. Abstract: The trace formula is a far reaching generalization of the Poisson summation formula. It relates spectral data of deep arithmetic significance to explicit but complicated geometric data. With its applications to the Langlands programme, some already realized and others still far away, the trace formula represents a mathematical equation of great power. In trying to give some sense of its history, we will begin with Selberg's original discovery of a formula that gave remarkable relations between the spectral and geometric properties of Riemann surfaces. We shall then describe Langlands' ideas for using this formula to establish reciprocity laws between different kinds of arithmetic quantities. Finally, we will say something about the present state trace formula, as it applies to spaces and groups of arbitrary dimension. Time and Date: 3:30--4:30 p.m., Tuesday, November 7, 2006 Event: DG-MP-PDE Seminar Speaker: Adam Oberman, SFU Subject:TBA'' Location: WMAX 110 Time and Date: 3:30--4:30 p.m., Tuesday, November 7, 2006 Event: Discrete Mathematics Seminar Speaker: Robert Tseng, UBC Subject:Perfect Matchings under Vertex Deletion'' Location: WMAX 216 Time and Date: 2:00 p.m., Thursday, November 9, 2006 Event: Mathematical Biology Seminar Speaker: Peter Borowski, recently of Max-Planck-Institute, currently UBC Subject:A stochastic two-state signalling module with negative feedback'' Location: WMAX 216 Abstract: Motivated by the negative feedback calcium exerts on the gating dynamics of a calcium-conducting ion channel in olfactory receptor neurons, we develop an abstract two-state (open/closed) signalling module with negative feedback. The coupling between the gating dynamics of the channel and the conducted ion makes the effective dynamics of the channel non-Markovian and difficult to treat in a Langevin-approach. We make use of two different techniques to describe the stochastic dynamics of the module. First, we calculate the steady state probability distribution using a Master/Fokker-Planck-type equation. Second, a path-integral formulation based on the temporal statistics of the channel state-flips is developed to calculate dynamical properties of the module. The feedback effect is built into the model in a systematic way in the form of a weak perturbation. Analytic results are obtained for the open probability of the channel as well as the auto-correlation and response functions (both for the discrete channel variable and the continuous calcium concentration). Monte Carlo simulations are performed which support the analytical predictions in the weak feedback limit and provide results beyond linear perturbation theory. Time and Date: 3:00 p.m., Thursday, November 9, 2006 This seminar has been postponed one week til November 16th, same time, same place. Event: Working Seminar on SL(2,C) Character Varieties of 3-Manifold Groups Speaker: Gabriel Indurskis, Department of Mathematics, UBC Subject:Applications of SL(2,C) character varieties to 3-manifold topology'' Location: WMAX 110 Abstract: In continuation of the intro from last time, I will give an overview of some applications of SL(2,C) character varieties to 3-manifold topology. We will then discuss possible topics for the following seminars and will assign speakers. Please contact me if you already have a good topic to talk about, and otherwise have a look at the references before next week. Time and Date: 3:00--3:50 p.m., Thursday, November 9, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Yoonjin Lee, SFU Subject:Construction of cubic function fields from quadratic infrastructure'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: We present an efficient method for generating non-conjugate cubic function fields of a given squarefree discriminant, using the infrastructure of the dual real function field assisociated with the hyperelliptic field of the same discriminant. This method was first proposed by Shanks for number fields in an unpublished manuscript from the 1970s. Time and Date: 3:30--4:30 p.m., Thursday, November 9, 2006 Event: PDE/Geometry/Math Physics Student Seminar Speaker: Gustavo de Oliveira, UBC Subject:Brenier's L^2 theory for scalar conservation laws, Part II'' Location: Math 104 Time and Date: 4:00 p.m., Thursday, November 9, 2006 Event: Math Finance Seminar Speaker: Marcel Rindisbacher, University of Toronto Subject:Dynamic Asset Allocation: a Portfolio Decomposition Formula and Applications'' Location: WMAX 216 Abstract: This paper establishes a new decomposition of the optimal portfolio policy in dynamic asset allocation models with arbitrary vNM preferences and Ito prices. The formula rests on a change of numeraire which consists in taking pure discount bonds as units of account. When expressed in this new numeraire the dynamic hedging demand is shown to have two components. If the individual cares solely about terminal wealth, the first hedge insures against fluctuations in a long term bond with maturity date matching the investor's horizon and face value determined by bequest preferences. The second hedge immunizes against fluctuations in future bond return volatilities and market prices of risk. When the individual also cares about intermediate consumption the first hedging component becomes a coupon-paying bond with coupon payments tailored to the consumption needs. The decomposition formula is used to examine the existence of preferred habitats, the investment behavior of extremely risk averse individuals, the demand for long term bonds, the optimal international asset allocation rule, the preference for I-bonds in inflationary environments and the integration of fixed income management and asset allocation. Time and Date: 4:00--5:00 p.m., Thursday, November 9, 2006 Event: Complex Fluids Seminar Speaker: Diwen Zhou, Department of Chemical and Biological Engineering, UBC Subject:The influence of polymer on drop deformation in confined flow'' Location: MATH 203 Abstract: The diffuse-interface model and AMPHI (Adaptive Meshing for Phase Field (\phi )) method are applied to simulate the drop deformation in confined flow. One of the component could be viscoelastic, which is specified by Oldroyd-B (Giesekus) model. We have explored the drop deformation in Newtonian system and compared our results with the previous theory. Meanwhile, the effects of polymer in different parameters for the drop deformation are investigated. Generally, the existence of polymer will change the effective viscosity of the component that contains the polymer. By this way, the effective Capillary number and effective viscosity ratio would be changed and drop would deform larger or smaller than Newtonian system. Time and Date: 4:10--5:00 p.m., Thursday, November 9, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Karl Dilcher, Dalhousie Subject:A Pascal-type triangle characterizing twin primes'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: It is a well-known property of Pascal's triangle that the entries of the kth row, without the initial and final entries 1, are all divisible by k if and only if k is prime. In this talk I will present a triangular array similar to Pascal's that characterizes twin prime pairs in a similar fashion. The proof involves generating function techniques. Connections with orthogonal polynomials, in particular Chebyshev polynomials, will also be discussed. If time allows, I will talk about another triangle, the so-called Stern-Brocot tree, and about some recent work on related number and polynomial sequences. Time and Date: 4:00--5:00 p.m., Thursday, November 9, 2006 Event: Graduate Student Seminar Speaker: Ignacio Rozada, Department of Mathematics, UBC Subject:Networks in large-scale epidemic simulations'' Location: MATH 102 Abstract: Network theory has recently become a very important tool in large-scale epidemic simulations. It is now possible to do simulations in the individual level for large cities and even whole countries. The problem of efficiently partitioning a large network is important when performing simulations on very large networks in computer clusters. We present a fast multiscale algorithm based on an application of spectral theory to find the minimum cut of the network. We use a coarsening method specifically designed for networks with irregular degree distributions. The coarsening method preserves the degree distribution, and simple dynamical processes behave very similarly in both the coarse and the original networks. Time and Date: 3:00 p.m., Friday, November 10, 2006 Event: Mathematics Colloquium Speaker: Ailana Fraser, UBC Subject: Variational Methods in Riemannian Geometry'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Tuesday, November 14, 2006 Event: DG-MP-PDE Seminar Speaker: Benjamin Texier, Universite Paris 7 Subject:Galloping instability of viscous shock waves'' Location: WMAX 110 (PIMS Facility) Abstract: This is joint work with Kevin Zumbrun (Indiana University). Motivated by physical and numerical observations of time oscillatory galloping'', spinning'', and cellular'' instabilities of detonation waves, we study Poincare--Hopf bifurcation of traveling-wave solutions of viscous conservation laws. The main difficulty is the absence of a spectral gap between oscillatory modes and essential spectrum, preventing standard reduction to a finite-dimensional center manifold. We overcome this by direct Lyapunov--Schmidt reduction, using detailed pointwise bounds on the linearized solution operator. Time and Date: 1:00 p.m., Wednesday, November 15, 2006 Event: Mathematical Biology Seminar (unusual time and location) Speaker: Jason Haugh, Chemical and Biomolecular Engineering, NCSU Subject:Analysis of intracellular signal transduction at various scales of biological abstraction'' Location: MATH 102 Time and Date: 3:00--4:00 p.m., Wednesday, November 15, 2006 Event: Algebra/Topology Seminar Speaker: Simon Rose, Department of Mathematics, UBC Subject:Finite subset spaces of the circle and a theorem of Bott'' Location: WMAX 110 Abstract: By considering the circle as the boundary of the hyperbolic plane we are able to describe the first three unordered configuration spaces of the circle by considering them as particular quotients of the group of isometries of the hyperbolic plane. After determining how these join together and calculating their fundamental group, we describe their union exp_3(S^1) as a simply connected Seifert-Fibred space, hence S^3. Moreover, a slight variation of this method reveals that the inclusion of S^1 into this space is in fact the trefoil knot. Time and Date: 5:00 p.m., Wednesday, November 15, 2006 Event: Contemporay Immunology: How the Physical Sciences and Mathematics are shaping Immunology: Speaker Series Speaker: Jason Haugh, Chemical and Biomolecular Engineering, NCSU Subject:Cytokine receptor signaling in immune cells: a case study in complexity'' Location: Coach House, Green College. Notes: All attendees are welcome to stay for dinner after the talk. Reservations + ticket purchase must be made in advance. Please visit www.iam.ubc.ca/~omer/spkr_series/ for more information. Time and Date: 2:00 p.m., Thursday, November 16, 2006 Event: Algebraic Geometry Seminar Speaker: Hanspeter Kraft, University of Basel Subject:A Galois correspondence for reductive groups and applications to the First Fundamental Theorems'' Location: WMAX 110 Abstract: Following some unpublished ideas of Lex Schrijver we will explain a new approach to the First Fundamental Theorems (FFTs) from classical invariant theory. It uses the tensor product of the two tensor algebras T(V) and T(V^*) with the aim to set up a Galois correspondence between reductive subgroups of GL(V) and certain subalgebras. As a consequence, one gets -- in a unified way -- the well-known FFTs for the classical groups and -- in addition -- also new FFTs for other groups. Time and Date: 3:00 p.m., Thursday, November 16, 2006 Event: Working Seminar on SL(2,C) Character Varieties of 3-Manifold Groups (Postponed from Nov. 9.) Speaker: Gabriel Indurskis, UBC Subject:Applications of SL(2,C) character varieties to 3-manifold topology'' Location: WMAX 110 Abstract: In continuation of the intro from last time, I will give an overview of some applications of SL(2,C) character varieties to 3-manifold topology. We will then discuss possible topics for the following seminars and will assign speakers. Please contact me if you already have a good topic to talk about, and otherwise have a look at the references before next week. Time and Date: 3:00--4:00 p.m., Thursday, November 16, 2006 Event: DG-MP-PDE Student Seminar Speaker: Nassif Ghoussoub, UBC Subject:Open problems related to certain mathematical models for MEMS: The dynamical case'' Location: WMAX 216 Time and Date: 4:00--5:00 p.m., Thursday, November 16, 2006 Event: Complex Fluids Seminar Speaker: Bulent Guzel, Department of Mechanical Engineering, UBC Subject:Laminar-Turbulent Transition in Non-Newtonin Pipe Flows'' Location: MATH 203 Abstract: Non-Newtonian fluids are transported in pipelines in different type of industries, such as petroleum, mining and pulp & paper processing industries. Simple visco-plastic models mostly describe these fluids. Turbulent flow is a desirable flow regime for solid transportation (keeping the particles in suspension) and for efficient mud removal, in the cementing of oil wells. However, the difficulties of having a non-Newtonian rheology in the design of pipeline systems have not been solved yet. One problem is in finding a suitable rheological description for some transported slurries. Another problem is in predicting the transition from laminar to turbulent flow, for a given rheological model. A reliable criterion for the transition point is of great importance to properly design a hydraulic system because the basic parameters, such as head loss (drag), wear rates, cuttings transport, mixing, heat transfer and coarse material deposition, are all affected significantly in transition from laminar to turbulent flow. Although there have been many experimental studies conducted and phenomenological theories advanced to predict these hydraulic parameters, (particularly for frictional losses), their results are lacking in general applicability to a wide range of non-Newtonian fluids. Underlying this failure are two factors. First, there is considerable complexity in the rheology of non-Newtonian fluids that are transported in pipelines, i.e. a visco-plastic model is nearly always a necessary simplification of even more complex behaviour. Second, there is very little study of the fundamental mechanisms leading to transition in the non-Newtonian fluids literature, from either experimental, computational or theoretical standpoints. Here, we show a range of experimental results for Xanthan and Carbopol pipe flows. Our objective is to get validation of the theoretical and phenomenological criteria for transition from laminar to turbulent flow in pipe with visco-plastic fluids and to investigate the effect of the unyielded plug region on transition and elucidate the mechanism of transition for viscoplastic fluids. Time and Date: 3:00 p.m., Friday, November 17, 2006 Event: Mathematics Colloquium Speaker: Hanspeter Kraft, University of Basel Subject: On Hilbert's 13th Problem'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, November 20, 2006 Event: IAM Seminar Series Speaker: Uri Ascher, Department of Computer Science, UBC Subject:Artifical Time Integration'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then discrete, and it is expected to be "close enough" to the dynamics of the continuous system (which is typically easier to analyze), provided that small time steps -- hence many iterations -- are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this talk we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. Time and Date: 3:00 -- 4:30 p.m., Monday, November 20, 2006 Event: Algebraic Geometry Seminar Speaker: Kai Behrend, UBC Subject:On the categorification of Donaldson-Thomas invariants'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Abstract: Donaldson-Thomas invariants are weighted Euler characteristics. My goal is the construction of a cohomology theory which underlies these weighted Euler characteristics. A 'toy model' for Donaldson-Thomas type moduli spaces is the intersection of two Lagrangian submanifolds inside a (complex) symplectic manifold. Thus a natural starting point for this program is to construct the required cohomology theory for such Lagrangian intersections. If the symplectic manifold is a cotangent bundle, the required cohomology theory is not difficult to write down. In recent research, I was able to show that this construction globalizes. There is thus a deRham type cohomology theory for Lagrangian intersections. We will try to explain how this works. Time and Date: 12:30--1:30 p.m., Tuesday, November 21, 2006 Event: UBC SCAIM Seminar Speaker: Peter Arbenz, ETH Zurich, Switzerland Subject:Multi-level Micro-Finite Element Analysis for Human Bone Structures'' Location: WMAX 216 Abstract: Using microarchitectural bone imaging, it is possible to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. In combination with microstructural finite element (microFE) analysis this could provide a powerful tool to improve strength assessment and individual fracture risk prediction. However, the resulting microFE models are very large and require dedicated solution techniques. So, in this paper we investigate the efficient solution of the resulting large systems of linear equations by the conjugate gradient algorithm with smoothed aggregation multilevel preconditioning. We introduce a variant of smoothed aggregation preconditioning in which the matrix of the finest level is stored in an element-by-element fashion. In this way, a large fraction of the overall storage requirement is saved. The implementation is based on the Trilinos framework and, in particular, on the multilevel solver package ML. We report on numerical results showing that our approach leads to a fully parallel finite element solver. Our numerical results show that a human bone model of about 5 million elements can be solved in about a minute. These short solution times will allow to assess the mechanical quality of bone in vivo on a routine basis. Furthermore, our highly scalable solution methods make it possible to analyze the very large models of whole bones measured in vitro, which can have up to 1 billion degrees of freedom. Time and Date: 3:30--4:30 p.m., Tuesday, November 21, 2006 Event: Discrete Mathematics Seminar Speaker: Murray Elder, Stevens Institute of Technology Subject:Generic subsets of Thompson's group'' Location: WMAX 216 Abstract: Richard Thompson constructed an example of a group which is called "F" that has many unusual properties. One way to consider its elements is in terms of pairs of rooted binary trees. This viewpoint lends itself nicely to counting subsets of elements with particular properties. Meanwhile in cryptography, interest turned to finding algebraic structures (like groups) on which to base cryptosystems. These groups should have problems or properties that are hard to decide (in some sense). A property of a group or set is "generic" if one can place a probabilistic measure on elements so that the subset of elements enjoying the property has measure 1. So in an effort to make sense of this we try it out on Thompson's group F - we define a measure and look for properties of the group, or subgroups of the group, that are in this sense "generic". This is joint work with Jennifer Taback, Bowdoin, Maine, and should be accessible to all. Time and Date: 3:00--4:00 p.m., Wednesday, November 22, 2006 Event: Algebra/Topology Seminar Speaker: James Clarkson, Department of Mathematics, UBC Subject:A Geometric Proof of the Blakers-Massey Theorem'' Location: WMAX 110 Abstract: In this talk we give a geometric proof of the Blakers-Massey Theorem using Mather's Cube Theorems. As an application, we use this result to compute the James Splitting of \Omega S^n. Time and Date: 4:00--5:00 p.m., Wednesday, November 22, 2006 Event: Probability Seminar Speaker: Nathanael Berestycki, UBC Subject:Hydrodynamic limits of spatially structured coalescents'' Location: WMAX 216 Abstract: We are motivated by a question arising in population genetics, and try to describe the effect of migratory fluxes and spatial structure on the genealogy of a population. This leads to the study of systems particles performing simple random walk on a given graph, and where particles coalescence according to a certain mechanism (typically, Kingman's coalescent) when they are on the same site. We obtain various asymptotic results for this process, at both small and large time scales, which are of intrerest to population genetics. We will also discuss some related conjectures. Joint work with Omer Angel, Alan Hammond and Vlada Limic. Time and Date: 3:00--3:50 p.m., Thursday, November 23, 2006 Event: SFU/UBC Number Theory Seminar (note unusual location) Speaker: Luis Goddyn, SFU Subject:Two lower bounds for subset sums'' Location: UBC Campus, MATH 100 Abstract: I present two new results in additive number theory. First, let A be a finite subset of an abelian group G, and let S(A) denote the set of all group elements representable as a sum of a subset of A. We derive the following quadratic lower bound on the size of S(A): |S(A)| = |H| + |A-H|2/64. Here H = {g a^^^ G : S(A)+g = S(A)} is the stabilizer of S(A). It may be possible to improve our constant 1/64, but not beyond 1/4. This implies a result of Erdös/Heilbronn, and improves a difficult theorem of Van Vu regarding the integers modulo n. Second, let A = (A1, A2, ..., An) be a sequence of subsets of an abelian group, and let Sk(A) denote the set of group elements representable as a sum of k elements taken from distinct sets in A. Let H be the stabilizer of Sk(A). We prove the following generalization of Kneser's theorem: |Sk(A)| = |H| (1 - k + SQ min{k, r(A,Q)}). Here the sum runs over all H-cosets Q, and r(A,Q) is the number of indices i for which Ai contains an element of Q. This result is a very special case of a little-known conjecture of Schrijver and Seymour regarding group-weighted matroids. However it is already strong enough to imply a large number of results and conjectures by Cao, Gao, Grynkiewicz, Hamidoune, Bollobás, and Leader, mostly in the spirit of the following classic result of Erdös, Ginsberg, and Ziv: Every set of 2n-1 integers contains an n-subset which sums to 0 modulo n. This is joint work with Matt DeVos, Bojan Mohar, and Robert Samal. Time and Date: 3:30--4:30 p.m., Thursday, November 23, 2006 Event: DG-MP-PDE Student Seminar Speaker: Jingyi Chen, UBC Subject:Some PDEs arising from geometry'' Location: WMAX 216 Time and Date: 4:00--5:00 p.m., Thursday, November 23, 2006 Event: Fluid Mechanics Seminar Speaker: G.M. Homsy, University of California, Santa Barbara Subject:Micro Fluid Mechanics: Some Interface Dynamics Problems'' Location: WMAX 110 Abstract: Interface dynamics is of considerable importance in multiphase microfluidic devices such as microheat pipes, and in dewetting dynamics. We consider a liquid meniscus inside a wedge of included angle [pic] that wets the solid walls with a contact angle [pic]. Under an imposed axial temperature gradient, the Marangoni stress moves fluid toward colder regions while the capillary pressure gradient drives a reverse flow, leading to a steady state. The fluxes driven by these two mechanisms are found by numerical integration of the parallel flow equations. Perturbation theory is applied to derive an expression for the capillary pressure, which is typically dominated by the transverse curvature of the circular arc inside the cross section, and corrected by a higher order axial curvature resulting from the axial variation of the interface. Lubrication theory is then used to derive a thin film equation for the shape of the interface. Numerical solutions indicate that for sufficiently large Marangoni numbers, M, the Marangoni stress creates a virtual dry region. It is found that dryout occurs more easily for larger wedge and/or contact angles. When the meniscus has a convex interface, it is susceptible to Rayleigh capillary instabilities. A dynamic contact-line condition is considered in which the contact angle varies linearly with the slipping speed of the contact line with a slope of G, with G=0 representing perfect slip and fixed contact angle. A nonlinear thin film equation is derived and numerically solved for the shape of the contact line as a function of parameters. The results show that the evolution process consists of a successive formation of bulges and necks in decreasing length and time scales, eventually resulting a cascade structure of primary, secondary and tertiary droplets. The numerical results agree qualitatively with very recent experimental results. Time and Date: 4:10--5:00 p.m., Thursday, November 23, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Lior Silberman, Harvard Subject:Arithmetic quantum chaos in the higher-rank case'' Location: UBC Campus, MATH 100 Abstract: I shall discuss joint work with Akshay Venkatesh on the quantum unique ergodicity conjecture for locally symmetric spaces. In the case of a (co-compact) lattice in PGL3(R) associated to an order in a division algebra of degree 3 over Q, we show that any non-degenerate sequence of Hecke-Maass eigenforms becomes equidistributed in the measure-theoretic sense. We first reduce the problem to showing the equidistribution of a limit measure on the homogeous space of the lattice which is invariant under the action of a Cartan subgroup. By recent measure rigidity results it then suffices to show that elements of the Cartan subgroup act with "positive entropy". I will describe this property and how we establish it using harmonic analysis on the building and a (global) diophantine argument on the group. Time and Date: 3:00 p.m., Friday, November 24, 2006 Event: Mathematics Colloquium Speaker: Frank Ruskey, Dept. of Computer Science, University of Victoria, BC Subject: Venn and Euler Diagrams: Recent Results and Open Problems'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Monday, November 27, 2006 Rescheduled for Wed. Nov. 29th, 3:30-4:30 p.m., same location. Event: IAM Seminar Series Speaker: Karlheinz Grochenig, Department of Mathematics, University of Vienna Subject:Time-Frequency Analysis: From Wireless Communications to Abstract Harmonic Analysis'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: In the talk I will discuss the relation between problems in wireless communications and time-frequency analysis. I will explain the basic principle of OFDM (orthogonal frequency division multiplexing) and its formulation in time-frequency analysis. Surprisingly, the so-called pulse-shaping problem is equivalent to a problem on twisted convolution, and its general solution requires experience in and tools from abstract harmonic analysis. Similarly, the modeling of the transmission channel leads to new and interesting problems on pseudodifferential operators. Their treatment is outside the standard theory of PDEs and requires a genuine time-frequency approach. The talk is intended for a general audience and does not require any prerequisites. Time and Date: 3:00--4:30 p.m., Monday, November 27, 2006 Event: Algebraic Geometry Seminar Speaker: Dong-Kwan Shin, Konkuk University (visiting UBC) Subject:Computation of plurigenera of a canonical threefold'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Abstract: For a canonical threefold, there are few known results about plurigenera. We know that a sufficient multiple of canonical divisor generates a nontrivial linear system and that there is a universal multiple. In this talk, we are going to introduce an algorithm for computing plurigenera. Furthermore, when the algebraic euler characteristic is small, especially 1 or 2, we are going to compute plurigenera. Time and Date: 4:00--5:00 p.m., Monday, November 27, 2006 Event: PIMS 10th Anniversary Activities Lecture Speaker: Garrett Odell, Director, Center for Cell Dynamics, Friday Harbor Laboratory, University of Washington Subject:For making genetic networks operate robustly, unintelligent non-design suffices'' Location: WMAX 110 Abstract: Five years ago we (George von Dassow, Ed Munro, Eli Meir, and I) made mathematical/computer models of two ancient and famous genetic networks that act early in diverse embryos to establish spatial gene expression patterns prefiguring the body plan. Our models revealed these networks to be astonishingly robust. That is, they continue to make the correct spatial pattern in the face of thousand-fold variations in the strengths of most functional forms of interactions among participating genes. After getting over my surprise that it was even possible to design networks with such properties, I now believe only networks having this kind of robustness can be functionally heritable in polymorphic populations. What general design features might endow genetic networks with the kind of extreme robustness we found in two real networks? To probe for answers, I wrote a computer program that haphazardly generates randomly connected networks made from about the same number of biochemically sensible parts that constitute the segment polarity and neurogenic networks. We (Bjorn Millard, Ed Munro, and I) devised computer algorithms that discover and catalog the stable expression patterns any network can make, and, from all these, distills those patterns the network can make robustly with respect to variations of its parameters. The bottom line is that 19 out of 20 random networks that our program created (i.e. networks devoid of any purposeful design whatever) could make at least one, and usually many, complex stable spatial expression patterns with the same high robustness that the real, evolved, segment-polarity and neurogenic networks exhibit. Several of the random, non-designed networks turn out to be much more robust than either real network. Only 1 out of 20 random networks is a complete loser; it did not make any interesting pattern at all. Our algorithms for finding patterns any network can stabilize show that it's possible to replace the network's differential equation model, which keeps track of continuous concentrations of gene products changing continously through time, by discrete logic models with quantized far-apart concentrations. Unfortunately, there are many different ways to do this -- different ways for different parameter values -- no way appropriate for all parameter values. The in silico result that thoughtless, haphazard, non-design produces networks whose robustness seems inspired begs questioning what else unintelligent non-design might be capable of. Time and Date: 3:30--4:30 p.m., Tuesday, November 28, 2006 Event: DG-MP-PDE Seminar Speaker: Malabika Pramanik, UBC Subject:L^2 decay estimates for oscillatory integral operators in several variables with homogeneous polynomial phases'' Location: WMAX 110 Abstract: Oscillatory integral operators mapping L^2(\mathbb R^{n_1}) to L^2(\mathbb R^{n_2}) play an important role in many problems in harmonic analysis and partial differential equations. We will briefly discuss the applicability of these operators in various contexts and give an overview of the current literature. We also mention recent results (joint with Allan Greenleaf and Wan Tang) where, extending earlier work of Phong and Stein in the case n_1 = n_2 = 1, we obtain optimal decay rates for the L^2 operator norm of oscillatory integral operators in 2+2 variables with generic phases. Some other higher dimensional situations are also addressed. Time and Date: 3:30--4:30 p.m., Tuesday, November 28, 2006 Event: Discrete Mathematics Seminar Speaker: Kevin Purbhoo, UBC Subject:Puzzles, Tableaux, and Mosaics'' Location: WMAX 216 Abstract: The Littlewood-Richardson numbers show up in a number of different areas of mathematics. They are structure constants of the ring of symmetric functions, which connects them to representation theory and cohomology of Grassmannians. There are now several well known combinatorial rules for computing Littlewood-Richardson numbers. I will talk about two of the main ones: the original rule of Littlewood and Richardson, which is phrased in terms of tableaux, and the Knutson-Tao puzzle rule'', which looks very different. Most every other known rule is just a variant on one or the other. Yet it is not immediately obvious why these two are rules are the same, or why they are correct. I will give a new construction---mosaics---which interpolates between puzzles and tableaux. Then a miracle will occur: just using the fact that one can interpolate between them, a new and pleasant proof of correctness (for both rules) will appear out of thin air. Time and Date: 3:00--4:00 p.m., Wednesday, November 29, 2006 Event: Algebra/Topology Seminar Speaker: Jesper Grodal, Department of Mathematics, University of Chicago and University of Copenhagen Subject:Homotopical group theory I: p-compact groups'' Location: WMAX 110 Time and Date: 4:00--5:00 p.m., Wednesday, November 29, 2006 Event: Probability Seminar Speaker: Yuval Peres, UC Berkeley and Microsoft Research Subject:The Rotor-router model and Diaconis-Fulton Addition'' Location: WMAX 216 Abstract: Given two sets A and B in the lattice, the Diaconis-Fulton sum is a random set obtained by putting one particle in every point of the symmetric difference, and two particles in every point of the intersection, of A and B. Each "extra" particle performs random walk until it reach an unoccupied site, where it settles. The law of the resulting random occupied set A+B does not depend on the order of the walks. We find the (deterministic) scaling limit of the sums A+B when A and B consist of the lattice points in some overlapping planar domains. The limit is described by focusing on the "odometer" of the process, which solves a free boundary obstacle problem for the Laplacian. The same scaling limit is obtained when the random walks are replaced by deterministic rotor walks, as proposed by Jim Propp. In particular, when a singleton at the origin is added to itself n times Internal Diffusion-limited aggregation (IDLA) arises; Lawler, Bramson and Griffeath (1992) proved the limit shape for IDLA is a disk and we prove the analogous result for rotor-router aggregation. (Joint work with Lionel Levine.) Time and Date: 2:00 p.m., Thursday, November 30, 2006 Event: Mathematical Biology Seminar Speaker: Gerda de Vries, Department of Mathematical and Statistical Sciences, University of Alberta Subject:Mathematical models in radiation biology'' Location: WMAX 216 Abstract: In this talk, I will review concepts in radiation biology that allow us to model the effectiveness of radiation therapy in the treatment of cancer. In particular, I will focus on the Tumour Control Probability (TCP), which is the probability that no cancerous cells survive the treatment. Early TCP formulae are based on simple binomial and Poissonian statistics. They are of limited value, since they do not take cell proliferation during the treatment period into account. Recent TCP formulae are based on dynamic models of a cell population, taking cell proliferation into account. I will conclude with a discussion of how and when the TCP formulae are related to each other, and how they can be used to compare the efficacy of different treatment schedules. Time and Date: 3:00--4:30 p.m., Thursday, November 30, 2006 Event: Working Seminar on SL(2,C) Character Varieties of 3-Manifold Groups Speaker: Melissa Macasieb, Department of Mathematics, UBC Subject:The action on a tree associated to an ideal point of the character variety'' Location: WMAX 110 Abstract: Let G be the fundamental group of a compact, orientable, irreducible 3-manifold M. I will discuss the correspondence between ideal points of a curve in the character variety X(G) and actions of G on a tree (following Culler-Shalen). This is a particular case of Bass-Serre theory concerning subgroups of SL_2(K), where K is a local field. I will spend some time discussing the tree for SL_2(K) and its relation to graphs of groups, and time permitting, how this relates to the existence of incompressible surfaces in M. Time and Date: 4:00--5:00 p.m., Thursday, November 30, 2006 Event: UBC SCAIM Seminar/Computer Science Distinguished Lecture Series Speaker: Philip Gill, UC San Diego Subject:New Challenges for Large Scale Constrained Optimization'' Location: Hugh Dempster Pavilion (DMP) Room 310, 6245 Agronomy Road Abstract: Numerical optimization involves the minimization or maximization of an objective function'' subject to functional constraints on the variables. Practical optimization problems may involve very general functions and millions of variables and constraints. The need to solve such enormous problems has motivated a radical shift away from the type of algorithm developed in the 1990's. At that time, research focused on methods that make progress along a sequence of directions formed from the solutions of two subproblems: one formulated to give a direction satisfying the constraints, and the other designed to reach optimality. These directions are obtained by solving two systems of linear equations formed by oblique or orthogonal projection. This paradigm works well for problems with up to several thousand variables. However, projection is inherently unsuitable for handling very large problems, or problems with special structure in the derivatives. Recent research has focused on replacing the constrained problem by a sequence of unconstrained subproblems parameterized by a scalar parameter. The idea of replacing a constrained optimization problem by a sequence of unconstrained problems has been around for many years. The crucial property of this new approach is that the unconstrained problem is formulated in terms of both the primal and dual optimization variables. This property allows the formulation of algorithms that are not only rapidly convergent, but also require the solution of just one (unprojected) system of linear equations at each step. Time and Date: 4:00--5:00 p.m., Thursday, November 30, 2006 Event: Complex Fluids Seminar Speaker: Joerg Rottler, Department of Physics and Astronomy, UBC Subject:Yield and flow of glassy materials'' Location: MATH 203 Abstract: Noncrystalline (glassy) solids are part of a fascinating class of disordered systems that generally exhibit slow dynamics. Much of the "sluggish" behavior of glassy materials is due to the many constraints that the molecules experience in dense, "jammed" configurations. Of much current interest is how these materials yield and flow under the application of an external drive such as stress or strain. Defects such as dislocations, the carriers of plasticity in crystals, are not present in an amorphous material with no long range order. In addition, the mechanical response of glasses often exhibits complex history dependence due to its intrinsic out-of-equilibrium dynamics (aging). In this talk, we show how molecular simulations can be used to gain insight into the deformation and flow mechanisms that operate in amorphous solids. We first illustrate how generic glassy behavior can be obtained from relatively simple molecular models for polymer and metallic glasses, and then study some aspects of their mechanical response, for instance the parameters that control the flow of material at finite stress (creep) as well as the shear yield stress. Based on the numerical "experiments", we develop a phenomenological model that universally describes aging effects in a wide range of data. Time permitting, we conclude by describing the fracture phenomenon of crazing, a large strain deformation in which a dense polymer glass is transformed into a network of fibrils and voids. The simulations show how this process is controlled by the molecular level properties of the polymer glass, in particular the topological constraints called chain entanglements that also determine the rubbery response of polymer melts. Time and Date: 4:00--5:00 p.m., Thursday, November 30, 2006 Event: Graduate Student Seminar Speaker: Alex Duncan, Department of Mathematics, UBC Subject:The Surreal Numbers'' Location: MATH 102 Time and Date: 3:00 p.m., Friday, December 1, 2006 Event: Mathematics Colloquium Speaker: George Homsy, UC Santa Barbara Subject: Multimedia Fluid Mechanics'' Location: MATX 1100 Note: Tea and coffee will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 4:00--5:00 p.m., Friday, December 1, 2006 Event: CRM/Fields/PIMS Prize Distinguished 2006 Lecture Speaker: Nicole Tomczak-Jaegermann, University of Alberta Subject:High dimensional convex bodies: phenomena, intuitions and results'' Location: WMAX 110 Abstract: Phenomena in large dimensions appear in a number of fields of mathematics and related fields of science, dealing with functions of infinitely growing number of variables and with objects that are determined by infinitely growing number of parameters. In this talk we trace these phenomena in linear-metric, geometric and some combinatorial structure of high-dimensional convex bodies. We shall concentrate this presentation on very recent results in Asymptotic Geometric Analysis. Time and Date: 5:00--6:00 p.m., Friday, December 1, 2006 Event: Egg Nog Party Invited: Everyone is Welcome Subject:Winter Holidays'' Location: MATX 1115 (Math Lounge) Time and Date: 12:30--1:30 p.m., Monday, December 4, 2006 Event: UBC SCAIM Seminar Speaker: Boaz Nadler, Weizmann Institute, Israel Subject:Statistical data analysis and stochastic dynamical systems - a two way street'' Location: ICICS/CS 238 Abstract: In this talk we present an interesting connection between various algorithms from the field of machine learning and statistical data analysis and the theory of stochastic processes. In particular we show that some common data mining algorithms, such as spectral clustering and kernel based semi-supervised learning can be analyzed by standard tools of applied mathematics, including asymptotic analysis and the theory of stochastic processes. Conversely, we also show that problems in the study of stochastic dynamical systems, such as dimensional reduction of high dimensional dynamical systems and estimation of effective macroscopic dynamics, can be analyzed by applying data analysis tools inspired by spectral clustering. Time and Date: 4:00--5:00 p.m., Monday, December 4, 2006 Event: Probability Seminar (Ander's seminar has been postponed.) Speaker: Alexander Holroyd, UBC Subject:Random Sorting Networks'' Location: WMAX 216 Abstract: See http://www.math.ubc.ca/~holroyd/sort for pictures. Joint work with Omer Angel, Dan Romik and Balint Virag. Sorting a list of items is perhaps the most celebrated problem in computer science. If one must do this by swapping neighbouring pairs, the worst initial condition is when the n items are in reverse order, in which case n choose 2 swaps are needed. A sorting network is any sequence of n choose 2 swaps which achieves this. We investigate the behaviour of a uniformly random n-item sorting network as n -> infinity. We prove a law of large numbers for the space-time process of swaps. Exact simulations and heuristic arguments have led us to astonishing conjectures. For example, the half-time permutation matrix appears to be circularly symmetric, while the trajectories of individual items appear to converge to a famous family of smooth curves. We prove the more modest results that, asymptotically, the support of the matrix lies within a certain octagon, while the trajectories are Holder-1/2. A key tool is a connection with Young tableaux. Time and Date: 3:30--4:30 p.m., Tuesday, December 5, 2006 Event: DG-MP-PDE Seminar Speaker: Adrian Butscher, U of Toronto Subject:New constructions of volume-critical submanifolds of the sphere'' Location: WMAX 110 Abstract: Constant mean curvature hypersurfaces in S^n are critical points of the (n-1)-volume functional subject to an enclosed-volume constraint whereas contact-stationary Legendrian (CSL) submanifolds of S^{2n+1} are n-dimensional submanifolds tangent to the contact distribution whose n-volume is critical amongst all Legendrian competitors. I will present new constructions of CMC and CSL submanifolds in spheres using gluing techniques and a good understanding of the isometries of the ambient sphere. I will also highlight some similarities between the world of CSL submanifolds and the world of CMC hypersurfaces. Time and Date: 3:30--4:30 p.m., Tuesday, December 5, 2006 Event: Discrete Mathematics Seminar Speaker: John Gimbel, University of Alaska Fairbanks Subject:Remarks on split graphs and related notions'' Location: WMAX 216 Abstract: A graph is split if its vertices can be covered by two sets A and B where A induces a complete graph and B induces an empty graph. This concept has many related notions. For example, the number of non-isomorphic set covers of a set of order n is the number of non-isomorphic split graphs of order n. We consider split graphs and three extensions: cochromatic number, split chromatic number and (j,k)-colorings. The cochromatic number of a graph is the minimum number of colors necessary to color the vertices so that each color class induces a complete or empty graph. The split chromatic number is the minimum number of colors used to color the vertices so that each color class induces a split graph. We focus our attention on (j,k)-colorings. A (j,k)-coloring of a graph is a covering of the vertex set using j+k parts where j parts induce complete graphs and k parts induce empty graphs. We consider a simple extremal problem: given j and k, what is the largest n so that every n-graph has a (j,k)-coloring. We also consider some results on computational complexity. Time and Date: 3:00--4:00 p.m., Wednesday, December 6, 2006 Event: Algebra/Topology Seminar Speaker: Jesper Grodal, Department of Mathematics, University of Chicago and University of Copenhagen Subject:Homotopical group theory II: p-local finite groups'' Location: WMAX 110 Time and Date: 4:00--5:00 p.m., Wednesday, December 6, 2006 Event: Probability Seminar Speaker: Mathieu Merle, UBC Subject:Introduction to Brownian snakes'' Location: WMAX 216 Abstract: Discrete models for an evolving population - such as branching random walks - arise in a variety of different contexts. In such models, individuals undergo both a branching phenomenon and a spatial displacement. Superprocesses are obtained as the weak continuous limits of such discrete models. Hence, it is not surprising that their genealogical evolution should be coded by some kind ofcontinuous branching structure. In a first part of the talk, we will define this structure by introducing real trees. We will then see that the random real tree underlying a superprocess descended from one single individual can be coded by a Brownian excursion under the Ito measure. We will then attach to this random continuous branching structure a random spatial displacement. This will lead to the definition of the Brownian snake. We will finally see that superprocesses (and also, as a consequence, the ISE) can be described in terms of the excursion measure of the Brownian snake. Time and Date: 1:00--1:50 p.m., Thursday, December 7, 2006 Event: SFU/UBC Number Theory Seminar (Note unusual time of day for Thursday's seminar.) Speaker: David Boyd, UBC Subject:Mahler's measure and L-functions of elliptic curves evaluated at s=3'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: The logarithmic Mahler measure M(P) of a polynomial P in n variables is the average of log P over the product of n circles. A few years ago, we conjectured infinitely many formulas evaluating the Mahler measure of certain two-variable polynomials as rational multiples of L(E,2)\pi^2, where L(E,s) is the L-function of a suitable elliptic curve. A finite number of these formulas have now been proved by Rodriguez-Villegas and more recently by Brunault. In this talk, we will present some experimentally discovered conjectural formulas for some three-variable polynomials as rational linear combinations of L(E,3)/\pi^4, \zeta (3)/\pi^2, and various classical dilogarithms. For example, to 40-decimal-place accuracy, m((x-1)^3+(x+1)(y+z))=(21/2)L(E,3)/\pi^4=6L'(E,-1), where E is an elliptic curve of conductor 14. So far, none of these formulas have been proved. Time and Date: 2:10--3:00 p.m., Thursday, December 7, 2006 Event: SFU/UBC Number Theory Seminar Speaker: Erick Wong, UBC Subject:Combinatorial properties of {x^2+ky^2}'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: For a fixed k>0, consider S(k), the set of integers representable as x^2+ky^2. Answering a question of M. Rosenfeld, we consider the problem of determining the maximum number of consecutive terms of this sequence, as well as the spacing between terms. We will show that there are infinitely many k for which the set S(k) contains infinitely many 5-tuples of consecutive integers, and that this length is best possible. Similarly, we show that for all k>0 not divisible by 4, the set S(k) contains infinitely many pairs of consecutive elements exactly d apart for every d>0. Time and Date: 3:30--4:30 p.m., Tuesday, December 12, 2006 Event: DG-MP-PDE Seminar Speaker: Alexis Vasseur, U of Texas Subject:Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation'' Location: WMAX 110 Abstract: The critical dissipative quasi-geostrophic equation was proposed by several authors as a toy model to study the regularity of solutions to 3D Navier-Stokes equations. In this work, in collaboration with L. Caffarelli, we prove that drift-diffusion equatons with L2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L2 data and critical diffusion (-\Delta)^{1/2}, are locally smooth for any space dimension. Time and Date: 3:30--4:30 p.m., Tuesday, December 12, 2006 Event: Probability Seminar Speaker: Nathan Clisby, University of Melbourne Subject:Self-avoiding walk enumeration via the lace expansion'' Location: TBA Abstract: We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion combined with another algorithmic improvement which we call the two step method. We have been able to significantly extend series for the simple cubic lattice from 26 to 30 terms, and dramatically extend series for hypercubic lattices for all dimensions greater than three. This is joint work with Richard Liang and Gordon Slade.