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##### Past 2008 Seminars

 2008 Seminars Time and Date: 3:00--4:00 p.m., Monday, January 7, 2008 Event: Joint IAM Seminar Series/Mathematics Colloquium Speaker: Yoichiro Mori, Postdoctoral Fellow, Department of Mathematics & PIMS, UBC Subject: A Three-Dimensional Model of Cellular Electrical Activity'' Location: LSK 301, Leonard S. Klinck Bldg. Note: Refreshments will be served before the seminar in the IAM Lounge, Room 306 (please bring your own mug). Time and Date: 12:30--2:00 p.m., Tuesday, January 8, 2008 Event: UBC SCAIM Seminar Speaker: Yoichiro Mori, Department of Mathematics & PIMS, UBC Subject:Convergence Proof of a Stokes Flow Immersed Boundary Method'' Location: WMAX 216 (PIMS) Abstract: The immersed boundary method is a popular method for computations in fluid-structure interaction problems. It is characterized by the use of an Eulerian grid for the fluid domain and a Lagrangian grid for the elastic structure, and the use of regularized dirac delta functions to establish communication between the two grids. In this talk, I will outline a convergence proof for a stationary Stokes flow immersed boundary problem. Computational results are presented to demonstrate that the error estimates obtained are close to optimal. I will end with a discussion of open problems. Time and Date: 2:00--3:00 p.m., Thursday, January 10, 2008 Event: Mathematical Biology Seminar Speaker: Nick Hill, University of Glasgow Subject:Abdominal Aortic Aneurysms'' Location: WMAX 216 (PIMS) Abstract: This is the first mathematical model to account for the evolution of the abdominal aortic aneurysm. The artery is treated as a two-layer, cylindrical membrane using nonlinear elasticity and a physiologically realistic constitutive model. It is subject to a constant systolic pressure and a physiological axial prestretch. The development of the aneurysm is assumed to be a consequence of the remodelling of its material constituents. Microstructural recruitment and fibre density variables for the collagen are introduced into the strain energy density functions. This enables the remodelling of collagen to be addressed as the aneurysm enlarges. An axisymmetric aneurysm, with axisymmetric degradation of elastin and linear differential equations for the remodelling of the fibre variables, is simulated numerically. Using physiologically determined parameters to model the abdominal aorta and realistic remodelling rates for its constituents, the predicted dilations of the aneurysm agree with those observed in vivo. An asymmetric aneurysm with spinal contact is also considered, and the stress distributions are consistent with previous studies. Additionally, the dynamic properties of the AAA are calculated for different stages in its development, and the evolution of clinically measurable mechanical properties compare well with published physiological data. Watton, P.N., Hill, N.A. & Heil, M. "A mathematical model for the growth of the abdominal aortic a neurysm." Biomechanics and Modeling in Mechanobiology, 3, pp. 98-113, 2004 Watton, P.N. & Hill, N.A. "Evolving mechanical properties of a model of abdominal aortic aneurysm." Biomechanics and Modeling in Mechanobiology, 2007, DOI: 10.1007/s10237-007-0115-9 Time and Date: 3:00 p.m., Thursday, January 10, 2008 Event: Specialized Mathematics Seminar Speaker: Prof. Juncheng Wei, Chinese University of Hong Kong Subject:Pattern Formation in the Diblock Copolymer System'' Location: WMAX 110 (PIMS) Abstract: We consider the lamellar and droplet phases in the Ohta-Kawasaki density functional theory of diblock copolymers. First, using \Gamma-convergence, the existence and stability of K-interface solutions in 1D are characterized. Then these solutions extend trivially to 2D and 3D to become perfect lamellar solutions. The stability of these lamellar solutions is completely characterized by asymptoticaly calculating the spectrum of the linearized problem. Consequently we find that they are stable, i.e. are local minimizers in space, only if they have sufficiently many interfaces. Interestingly the 1-D global minimizer is near the borderline of 3-D stability. Using bifurcation analysis, we find wriggled lamellar solutions of the Euler-Lagrange equation of the total free energy. They bifurcate from the perfect lamellar solutions. The stability of the wriggled lamellar solutions is reduced to a relatively simple finite dimensional problem, which may be solved accurately by a numerical method. Our tests show that most of them are stable. The existence of such stable wriggled lamellar solutions explains why in reality the lamellar phase is fragile and it often exists in distorted forms. Next we study the droplet patterns in a nonlocal free boundary problem modleing interface motion for a diblock copolymer. In a proper range of the block composition parameter and the nonlocal interaction parameter, an equilibrium pattern of many droplets is proved to exist in a general planar domain. A sub-range of the parameters is identified where the multiple droplet pattern is stable. This stable droplet pattern models the cylindrical phase in the diblock copolymer morphology. Each droplet is close to a round disc. The boundaries of the droplets satisfy an equation that involves the curvature of the boundary and a quantity that depends nonlocally on the whole pattern. The locations of the droplets are determined via a Green's function of the domain. In constructing the droplet pattern we overcome three obstacles: interface oscillation, droplet coarsening, and droplet translation. (joint work with X. Ren) Time and Date: 3:00--4:30 p.m., Friday, January 11, 2008 Event: Mathematics Colloquium Speaker: Prof. Juncheng Wei, Chinese University of Hong Kong Subject: Nonlinear Schrodinger Equation, Allen-Cahn Equation and Toda System'' 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, January 14, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Richard Baraniuk, Electrical and Computer Engineering Department, Rice University Subject: Compressive Signal Processing'' Location: Room 301, LSK Bldg. Abstract: Sensors, signal processing hardware, and algorithms are under increasing pressure to accommodate larger and higher-dimensional data sets; faster capture, sampling, and processing rates; lower power consumption; communication over more difficult channels; and radically new sensing modalities. This talk overviews our recent research on "Compressive Sensing", an emerging field based on the revelation that a small number of linear projections of a compressible signal contain enough information for signal reconstruction and statistical signal processing. The implications of compressive sensing are promising for many applications and enable the design of new kinds of analog-to-digital converters, imaging systems and cameras, and radar systems. Time and Date: 3:00--4:30 p.m., Monday, January 14, 2008 Event: Algebraic Geometry Seminar Speaker: Masoud Kamgarpour, University of Chicago Subject:Stacky abelianization of algebraic groups'' Location: WMAX 110 (PIMS) Abstract: Let X be a one-dimensional character sheaf on a connected algebraic group G. We will see that it is NOT true that the restriction of X to the commutator subgroup is trivial. To remedy the situation, we propose to think of a certain etale group cover of [G,G] as the "true commutator" of G. The quotient stack of G by the true commutator will be the universal Picard stack to which G maps". Preprint: http://arxiv.org/abs/0711.3023 Time and Date: 4:00 p.m., Monday, January 14, 2008 Event: Mathematics Colloquium Speaker: Akos Magyar, University of Georgia Subject: Geometric patterns in dense subsets of \Z^n'' Location: MATH 100 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Tuesday, January 15 , 2008 Event: DG-MP-PDE Seminar Speaker: Akos Magyar, University of Georgia Subject:Polynomial configurations in difference sets'' Location: WMAX 110 Abstract: Suppose A is a subset of the integers of positive density. We prove a quantitative result on the existence of linearly independent polynomial configurations in the difference set of A. Our approach is based on first establishing a higher dimensional analogue of a theorem of Sórközy and Furstenberg, and then applying a simple lifting argument. This is joint work with Neil Lyall. Time and Date: 12:00--1:00 p.m., Wednesday, January 16, 2008 Event: Complex Fluids Seminar Speaker: Xiaoyu Luo, University of Glasgow Subject:The cascade structure of linear stability in collapsible channel flows'' Location: CHBE 204 (Chemical and Biological Engineering Bldg., 2360 East Mall, UBC) Note: This is the new location and time for this term for the Complex Fluids Seminar. Abstract: Flow in collapsible tubes has been extensively studied in the last few decades, not only for its relevance to physiological applications, but also for its rich dynamic behaviour. In this talk, I will focus on the linear stability of flows in a collapsible channel. This is studied using both the full unsteady numerical ALE approach and the eigenvalue analysis for the Navier-Stokes equations coupled with two dimensional large deformation small strain elastic beam equations. It is found that the neutral stability of this system appears in a cascade structure consisting of different response modes. The cascade structure shows that in the Reynolds number-wall stiffness space, depending on the inlet boundary condition, the system may first lose stability to mode-1 or mode-2 perturbations as the wall stiffness is lowered to a critical value. However, as the wall stiffness is further reduced, the system is surprisingly re-stabilized, before going through a sequence of higher mode unstable zones. Extensive comparisons are made with earlier analytical models, and differences are discussed. A possible physical interpretation of the cascade structure is proposed. Although this study applies to two-dimensional collapsible channel flows, it is expected that similar cascade structures exist in possibly many other slender body fluid-structure interactive problems. Time and Date: 3:00 p.m., Wednesday, January 16, 2008 Event: Mathematics Colloquium Speaker: Young-Heon Kim, University of Toronto Subject: Curvature and continuity of optimal transport'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 4:15 p.m., Wednesday, January 16, 2008 (Note unusual time and location.) Event: Probability Seminar Speaker: Mathieu Merle, Department of Mathematics, UBC Subject:Scaling limit of the invasion percolation cluster on a regular tree'' Location: MATH 105 Abstract: We consider invasion percolation on a regular tree. Recent work of Angel, Goodman, den Hollander and Slade showed a structural representation of the invasion percolation cluster (IPC) as an infinite backbone from which emerge independent subcritical Galton-Watson trees. This representation allows a better understanding of the similarities and differences between the (IPC) and the incipient infinite cluster (IIC) on a regular tree. We will first exhibit the scaling limit of the (IIC) as a warm-up for our study. We then use the structural representation of (IPC) to show that the (IPC), when suitably rescaled, converges to continuous tree. Coding functions of the limiting continuous tree can be expressed in terms of the solution of a certain (SDE). Moreover, the limit can be used to deduce asymptotic properties of the (IPC). Time and Date: 4:15--5:15 p.m., Wednesday, January 16, 2008 Event: Algebra/Topology Seminar Speaker: Laurent Meersseman, Universite de Bourgogne Subject:Real quadrics in C^n, complex manifolds and convex polytopes'' Location: WMAX 110 Abstract: This is a joint work with Frederic Bosio (Poitiers, France). We investigate the topology of a large class of non-Kahler compact complex manifolds called LV-M manifolds. These manifolds are diffeomorphic to real quadrics in C^n of a special form, so we forget the complex structures and work with this model. On the other hand, LV-M manifolds admit a smooth torus action whose quotient is a simple convex polytope. In this talk, I will explain how complicated is the topology of LV-M manifolds by making a reduction to combinatorics of convex polytopes. In particular, I will give a combinatorial formula for the homology with coefficients in Z of LV-M manifolds. This uses cohomological results of Buchstaber and Panov. I will also resolve an associated wall-crossing problem by studying a set of surgeries defined on simple convex polytopes. Finally, I will discuss some consequences for compact complex manifolds. In particular, I will prove that there exist affine compact complex manifolds (that is manifolds with an atlas whose changes of charts are affine biholomorphisms of C^n) with arbitrary complicated homology groups. This contrasts with the Kahler case : affine Kahler compact complex manifolds are covered by a complex torus. Time and Date: 2:00--3:00 p.m., Thursday, January 17, 2008 Event: Mathematical Biology Seminar Speaker: Ryan Gutenkunst, Cornell University Subject:Sloppiness in biochemical modeling and evolution'' Location: WMAX 216 Abstract: The dynamics of complex biochemical networks typically depend on many parameters (e.g. reaction rate constants). I show that mathematical models of such networks exhibit a universal "sloppy" pattern of parameter sensitivities; their dynamics are exponentially more sensitive to changes in some combinations of parameters than others. For model builders this suggests that predictions will be much more efficiently constrained by fitting parameters than by directly measuring them. I also explore the evolutionary consequences of sloppiness in the context of Fisher's geometrical model. Sloppiness has little affect on the first step in an adaptive walk, but it may substantially slow the long-term pace of adaptation. Time and Date: 3:30--4:30 p.m., Thursday, January 17, 2008 Event: DG-MP-PDE Seminar Speaker: Young-Heon Kim, University of Toronto Subject:Determinants of Laplacians as functions on spaces of metrics'' Location: WMAX 110 Abstract: The determinant of the Laplacian is a global Riemannian invariant which is defined formally as the product of the nonzero eigenvalues of the Laplacian of a given Riemannian metric. It gives a continuous function on the space of Riemannian metrics. In this talk we are interested in the case of compact surfaces with boundary and will discuss the properness of the determinant function on the moduli space of hyperbolic surfaces with geodesic boundary and on the moduli space of flat surfaces with boundary of constant geodesic curvature. We will also discuss an application to the following isospectral compactness problem: On a given compact surface with boundary, consider the set of all smooth flat metrics having the same Dirichlet Laplacian spectrum. Is it compact in C^\infty topology? Time and Date: 3:00 p.m., Friday, January 18, 2008 Event: Mathematics Colloquium Speaker: Grigory Mikhalkin, University of Toronto Subject: Tropical and Real Geometry'' 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, January 21, 2008 Event: IAM Seminar Series Speaker: Michael Ward, UBC Subject:Self-Replicating Localized Spot Patterns for Reaction-Diffusion Models in Two-Dimensional Spatial Domains'' Location: Room 301, LSK Bldg. Abstract: There are many interesting problems related to the dynamics and instabilities of localized patterns, such as vortices, spots, and defects, in time-dependent partial differential equations. In this talk, we analyze the dynamical behavior of multi-spot solutions in a two-dimensional domain \Omega for certain two-component reaction-diffusion models in the singularly perturbed limit of small diffusivity \varepsilon for one of the two components. Such models, which include the Gray-Scott, Gierer-Meinhardt, and Schnakenburg systems, typically have no variational structure. In the limit \varepsilon \ra 0, a quasi-equilibrium spot pattern in the region away from the spots is constructed by representing each localized spot as a logarithmic singularity of unknown strength S_j for j=1,..., K at unknown spot locations x_j\in \Omega for j=1,..., K. A formal asymptotic analysis, which has the effect of summing infinite logarithimic series in powers of –1/log (\varepsilon ), is then used to derive a differential algebraic system of ODE's for the collective coordinates S_j and x_j for j=1,..., K, which characterizes the slow dynamics of a spot pattern. By numerically examining the stability thresholds for a single spot solution, a specific criterion in terms of the source strengths S_j for j=1,..., K is then formulated to theoretically predict the initiation of spot-replication events. The analytical theory is illustrated for spot patterns in the unit disk and the unit square, and is compared with full numerical results computed using an adaptive mesh finite-difference method. Time and Date: 3:00--4:30 p.m., Monday, January 21, 2008 Event: Algebraic Geometry Seminar Speaker: Grigory Mikhalkin, University of Toronto Subject:Tropical Geometry: Rules of the Game'' Location: WMAX 110 (PIMS) Abstract: This will be an introductory level talk describing basic notions and techniques of Tropical Geometry. We will look at similarities and distinctions of Tropical and Classical Geometries and outline a technique providing correspondence between them. Time and Date: 3:30--4:30 p.m., Tuesday, January 22, 2008 Event: Probability Seminar Speaker: Omer Angel, University of Toronto Subject:Symmetry and infinite exclusion'' Location: WMAX 110 Abstract: A fundamental result on asymmetric exclusion processes says that under certain starting conditions a particle will have an asymptotic speed that is uniformly distributed on [-1,1]. A natural generalization allows every particle to have a random speed, but the speeds are not independent. I will present a recently discovered symmetry of the exclusion process with infinitely many classes. As a consequence of the symmetry we are able to extract significant information on the joint density of the speeds, extending some results of Ferrari-Goncalves-Martin. No background will be assumed. Time and Date: 4:00-5:00 p.m., Tuesday, January 22, 2008 Event: Teaching Seminar Speaker: Mark MacLean, UBC Subject:Discussion, Chapter 1, Alan Schoenfeld's, Mathematical Problem Solving'' Location: MATX 1102 Time and Date: 12:00--1:00 p.m., Wednesday, January 23, 2008 Event: Complex Fluids Seminar Speaker: Paul Krochak, UBC Subject:The Effect of Fiber-Fiber Interactions in a Linearly Contracting Channel Flow'' Location: CHBE 204 (Chemical and Biological Engineering Bldg., 2360 East Mall, UBC) Abstract: The orientation state of papermaking fibers in a headbox is one of the principal components in determining the strength properties of paper. Despite the longstanding use of headboxes to create plane liquid jets, there are still many unanswered fundamental questions on the relationship between the operating state and the final paper properties. One of the essential difficulties is the incomplete understanding of the long range hydrodynamic fiber-fiber interactions and the interaction between the flow field and the orientation state of the suspension. In this work, a numerical model for predicting the effect of fiber-fiber interactions on the orientation state of a semi-dilute fiber suspension in a linear contracting channel is presented. An orientation distribution function is used to describe the local orientation state of the suspension and its evolution is governed by a Fokker-Plank equation where fiber-fiber interactions are modeled using the approach outlined by Folgar and Tucker (J. Reinforced Plastics and Composites 3:98, 1984). The flow field is fully coupled with the orientation state of the suspension and the effect on each is examined. Experiments were performed to measure the rotary diffusion coefficient, which effectively closes the model and comparison is made between the numerical predictions and experimental observations. Time and Date: 3:00 p.m., Wednesday, January 23, 2008 Event: Mathematics Colloquium Speaker: Omer Angel, University of Toronto Subject: Local limits of graphs'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 12:30 p.m., Thursday, January 24, 2008 Event: Graduate Student Seminar Speaker: Alex Duncan, Department of Mathematics, UBC Subject:Continued Fraction Arithmetic'' Location: MATH 203 Abstract: I will discuss Bill Gosper's method for arithmetic with continued fractions. Before his work, calculations with continued fractions "in place" was considered intractable. "Contrary to everybody," as stated in the abstract of his original paper, "...continued fractions are not only perfectly amenable to arithmetic, they are amenable to perfect arithmetic." Time and Date: 2:00--3:00 p.m., Thursday, January 24, 2008 Event: Mathematical Biology Seminar Speaker: Babak Pourbohloul, B.C. Centre for Disease Control Subject:Emerging Infectious Disease, Pandemic Preparedness and Mathematical Models: How to Prepare When We Don't Know the Enemy?'' Location: WMAX 216 Abstract: The underlying contact structure among individuals that determines the pattern of disease transmission and the progression in time of this pattern are two crucial elements in understanding and controlling communicable disease spread within a social setting. Mathematical models of infectious disease that are in principle analytically tractable, have taken two general approaches in incorporating these elements. The first approach, generally known as compartmental models, addresses the time evolution of disease spread at the expense of simplifying the pattern of transmission. On the other hand, the second approach - contact networks - incorporates detailed information of underlying contact structure among individuals. While providing accurate estimates on the final size of outbreak/epidemics, this approach in its current formalism, loses track of the time progression of outbreaks. So far, the only alternative to integrate both aspects of disease spread simultaneously, has been to abandon the analytical approach and rely on computer simulations. Although, powerful modern computers can perform an enormous amount of simulations at an incredibly rapid pace, the complex structure of realistic' contact networks along with the stochastic nature of disease spread pose a serious challenge to the ability of the computational techniques to the robust analysis of disease spread in large populations in real time. An analytical alternative to this approach is lacking. We offer a new analytical framework, which incorporates both complexity of contact network structure and time progression of disease spread. Furthermore, we demonstrate that this framework works equally effective for finite- and infinite'-size networks. Time and Date: 3:00--4:00 p.m., Thursday, January 24, 2008 Event: PIMS-MITACS Math Finance Seminar Speaker: Michael Ludkovski, University of Michigan Subject:Financial Hedging of Operational Flexibility'' Location: WMAX 110 Abstract: We extend the framework of real options to value the compound timing option owned by a manager of an industrial asset. The operator has control over the production modes, but faces operational constraints which introduce path-dependency. Moreover, the operator is only able to imperfectly hedge her income on the futures market. Using an exponential indifference valuation approach we construct a combined stochastic control formulation that merges the problems of optimal switching and indifference pricing in incomplete markets. We then present an iterative scheme for valuing operational flexibility which in particular shows additivity of indifference value over time. After discussing details of numerical implementation, we illustrate our results with several numerical examples and comparative statics and show how the model can be extended to cover other applications of interest, such as gas storage valuation. Time and Date: 3:00 p.m., Friday, January 25, 2008 Event: Mathematics Colloquium Speaker: Michael Ludkovski, University of Michigan Subject: Optimal Stopping and Optimal Switching for Hidden Markov Models'' 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, January 28, 2008 Event: IAM Seminar Series Speaker: Ivar Ekeland, Department of Mathematics and Department of Economics, UBC Subject:When Optimization Becomes Irrelevant: Time-Inconsistency and Its Consequences'' Location: Room 301, LSK Bldg. Abstract: In optimal control, one traditionally discounts the future at a constant rate: a gain u occurring at time t>0 is valued today at u exp(-rt), where r is the discount rate. If non-constant discount rates are used, as they should be for many reasons, then time-inconsistency occurs: policies that seem optimal at time t=0 will no longer seem optimal when the time to apply them comes. This has many interesting mathematical consequences, including an integral equation which generalizes the classical Hamilton-Jacobi equation, and which, in a simple case, reduces to an implicit differential equation. Time and Date: 3:00--4:30 p.m., Monday, January 28, 2008 Event: Algebraic Geometry Seminar Speaker: Jonathan Wise, Brown University Subject:Enumerative geometry of hyperelliptic curves in CP^2'' Location: WMAX 110 (PIMS) Abstract: We will discuss the relationship between the enumerative geometry of hyperelliptic curves in CP^2 and the orbifold Gromov-Witten invariants of the stack, [Sym^2 CP^2]. In particular, we will see how to determine the number of hyperelliptic curves of genus g and degree d passing through 3d + 1 points in generic position recursively from the Gromov-Witten invariants. No prior knowledge of Gromov-Witten invariants or stacks will be assumed. Time and Date: 4:00 p.m., Monday, January 28, 2008 Event: Mathematics Colloquium Speaker: Sujatha Ramdorai, Tata Institute Subject: Old and New Themes in Number Theory'' Location: MATH 100 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, January 29, 2008 Event: UBC SCAIM Seminar Speaker: Yogi Ahmad Erlangga, Earth and Ocean Sciences, UBC Subject:(Algebraic) Multilevel Krylov Method'' Location: WMAX 216 (PIMS) Abstract: Projections used in this method are constructed in a similar way as in deflation, but shifts small eigenvalues to the largest one instead of to zero. In contrast with deflation, however, the convergence rate of a Krylov method combined with this new projection method is insensitive to the inaccurate solve of the Galerkin matrix, which with some particular choice of deflation subspaces is closely related to the coarse-grid solve in multigrid or domain decomposition methods. Such an insensitivity allows the use of inner iterations to solve the Galerkin problem. An application of a Krylov subspace method to the associated Galerkin system with the projection preconditioner leads to a multilevel, nested Krylov iteration. In this multilevel projection Krylov subspace method, information of small eigenvalues to be projected is contained implicitly in the Galerkin system associated with the matrix of the linear system to be solved. These small eigenvalues, from a Krylov method point of view, are responsible for slow convergence. In terms of projection methods, this is conceptually similar to multigrid, but different in the sense that in multigrid the projection is done by the smoother. Furthermore, with the only condition that the deflation matrices are full rank, we have in principle more freedom in choosing the deflation subspace. Intergrid transfer operators used in multigrid are some of the possible candidates. During the talk, convergence results for problems with symmetric, nonsymmetric and indefinite matrix of coefficients will be presented. This is a joint and on-going work with Reinhard Nabben from Institute of Mathematics, TU Berlin, Germany. Time and Date: 3:30--4:30 p.m., Tuesday, January 29, 2008 Event: Probability Seminar Speaker: Sebastien Roch, Microsoft Research Subject:Cascade Processes in Social Networks'' Location: WMAX 216 Abstract: Social networks are often represented by directed graphs where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or word-of-mouth effects on such a graph is to consider a stochastic process of "infection'': each node becomes infected once an activation function of the set of its infected neighbors crosses a random threshold value. I will prove a conjecture of Kempe, Kleinberg, and Tardos which roughly states that if such a process is "locally'' submodular then it must be "globally'' submodular on average. The significance of this result is that it leads to a good algorithmic solution to the problem of maximizing the spread of influence in the network--a problem known in data mining as "viral marketing". This is joint work with Elchanan Mossel. Time and Date: 3:30--4:20 p.m., Tuesday, January 29, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Sujatha Ramdorai, Tata Institute Subject:Root numbers and Selmer groups of elliptic curves'' Location: UBC Campus, Room WMAX 110 Note: There will be a welcome reception with refreshments at PIMS from 3:00--3:30 p.m. before the first talk. Abstract: The theory of root numbers predicts when elliptic curves over number fields have rational points of infinite order. In this talk, we shall discuss results which bring together the root numbers and non-commutative Iwasawa theory. It is joint work with Coates, Fukaya and Kato, and has connections to some recent work of Rohrlich and T. Dokchitser and V. Dokchitser. Time and Date: 4:40--5:30 p.m., Tuesday, January 29, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Katherine Stange, Brown University Subject:Elliptic nets'' Location: UBC Campus, Room WMAX 110 Abstract: Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. I'll give the background on these and present a higher-dimensional analogue over arbitrary fields. Suppose E is an elliptic curve over a field K, and P_1, ..., P_n are points on E defined over K. To this information we associate an n-dimensional array of values of K satisfying a complicated nonlinear recurrence relation. These are called elliptic nets. All elliptic nets arise from elliptic curves in this manner. I'll explore some of the properties of elliptic nets and the geometric information they contain, including a connection to generalised Jacobians and the Tate and Weil pairings on the elliptic curve. Time and Date: 12:00--1:00 p.m., Wednesday, January 30, 2008 Event: Complex Fluids Seminar Speaker: John Gosline, Department of Zoology, UBC Subject:Bio-inspired Materials Design Oozes out of Hagfish Slime'' Location: CHBE 204 (Chemical and Biological Engineering Bldg., 2360 East Mall, UBC) Abstract: Hagfish are renowned for their ability to produce huge masses slime when they are disturbed. The slime is extremely dilute (ca. 40 ppm polymer in sea water) and is reinforced with by unusual protein threads. Initially, we thought of the slime as an ultra-dilute, fibre-reinforced hydrogel, but on closer analysis we realized that it is actually a fibre-reinforced liquid. Its function in nature is primarily as a predator defense from fish, and we have shown that the slime is likely able to suffocate fish that attack them, largely because the slime threads and adherent mucins clog the fish's gills. The threads have formed the main focus of our research. They exhibit exceptional extensibility and toughness, properties that play a key role in their function in the slime. The threads are constructed from intermediate filament (IF) proteins that self-assemble from alpha-helical, coiled-coil IF dimers into macroscopic fibres. When stretched, these threads undergo an alpha-helix to beta-sheet transformation that results in the creation of a beta-sheet crystal-reinforced polymer network, a network that is functionally similar to the network in spider's dragline silk. We are attempting to create silk-like biomaterials based on hagfish IF proteins, and in addition our studies provide insights into the mechanics of IFs in living cells. Time and Date: 3:00 p.m., Wednesday, January 30, 2008 Event: Mathematics Colloquium Speaker: Sebastien Roch, Microsoft Research Subject: Reconstructing the Tree of Life: Building Large Trees from Short Sequences'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 12:30 p.m., Thursday, January 31, 2008 Event: Graduate Student Seminar Speaker: Bruno L'Esperance, Department of Mathematics, UBC Subject:Optimal Transportation and Equilibrium in Hedonic Markets'' Location: MATH 203 Abstract: In the first part of this talk, I expect to introduce some notions of basic economic theory. In the second part, I present a mathematical model for the equilibrium in hedonic markets and show how such problem is related to a specific optimal transportation problem. Finally, I show some of the steps of the proofs, an extension of this model and an application to labor markets. There is no need to know any economic theory, everything needed will be introduced in the first part of the talk. This presentation is mainly based on work done by Dr. Ivar Ekeland. Time and Date: 2:00--3:00 p.m., Thursday, January 31, 2008 Event: Mathematical Biology Seminar Speaker: Xiaoyu Luo, Department of Mathematics, UBC and University of Glasgow Subject:Mitral heart valve modelling'' Location: WMAX 216 Abstract: The dynamic behaviour of a novel chorded mitral prosthesis is studied using an immersed boundary model. To investigate the mechanical behaviour of the mitral design under physiological flow conditions without having to model the left ventricle, we make use of in vivo magnetic resonance images of the left ventricle. The relative motion of the mitral annulus and the papillary muscle regions of the ventricle determined from these MRI images is then used as a prescribed boundary condition for the chorded mitral valve in a dynamic cycle. Results show that without the proper functioning of the papillary muscle, the mitral prosthesis can suffer from an intolerable over-stretch during systole compared with laboratory tests in which the mitral chordae are fixed in space. This turns out to be the key weakness of the current design. The mechanical performance of the prosthesis is compared with recent studies of native porcine valves; differences in mechanical behaviour are observed. Potential improvements for the design and future research projects are also discussed. Time and Date: 3:30--4:30 p.m., Thursday, January 31, 2008 Event: Discrete Mathematics Seminar Speaker: Abraham Flaxman, Microsoft Research Subject:Fluctuating Frugality: VCG Path Auction in the Giant Component'' Location: MATH 104 Abstract: Packet routing in the Internet is a natural application area for algorithmic mechanism design. It appeared as an example application in the seminal work of Nissan and Ronen, and has been the subject of on-going study ever since. The present paper investigates a simple game-theoretic model of routing in a graph, where a selfish agent controls each edge, and the goal is to route a packet between vertices s and t along the shortest path. The Vickery-Clarke-Groves (VCG) mechanism is a well-known auction protocol which obtains a minimum length (s, t)-path by inducing truthful behavior in selfish agents. Previous work has shown that the ratio of the VCG payment to the shortest path length may be arbitrarily large. In real-world graphs, however, the observed frugality ratio has not been too large (around 1.3). This was partially explained by Mihail, Papadimitriou, and Saberi, who provided bounds on frugality ratio in the Erdos-Renyi graph G_{n,d/n}. If F denotes the expected overpayment ratio, then the previous work shows that 1 + Omega(1/d) \leq F \leq 0(1). I will describe my recent work with Bruce Reed, in which we obtain a more precise bound on the overpayment ratio, and show that, as a function of d, G_{n,d/n} has lim inf (F-1) = Theta(1/d) and lim sup (F-1) = Theta(1). This requires deriving very precise bounds on the average length of the shortest path and the "second shortest" path between vertices in a sparse random graph. Time and Date: 3:00 p.m., Friday, February 1, 2008 Event: Mathematics Colloquium Speaker: Abraham Flaxman, Microsoft Research Subject: Average-case analysis of combinatorial problems (with emphasis on random spanning trees)'' 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 4, 2008 Event: IAM Seminar Series Speaker: Dinesh K. Pai, Department of Computer Science, UBC Subject:Simulation of Human Movement with Contact and Constraints'' Location: Room 301, LSK Bldg. Abstract: I will describe ongoing work in my lab towards developing mathematical and computational models of the musculoskeletal system, its neural control, and its interaction with the environment. First, I will describe a new approach to constructing detailed physical models of neuro-musculo-skeletal systems, using fiber-like 3D elastic elements we call "strands". The strand model offers some of the efficiency of line-based muscle models and a more realistic handling of neural control and mechanical constraints. I will describe the model and algorithms for its efficient numerical simulation. I will give specific examples of modeling and simulation of the oculomotor system and the hand, using data from MRI and other imaging modalities. Finally, I will describe simulation of frictional contact between rigid and deformable objects, and connections to convex optimization. This is important for modeling interaction with the environment. Time and Date: 3:00--4:30 p.m., Monday, February 4, 2008 Event: Algebraic Geometry Seminar Speaker: Dave Anderson, University of Michigan Subject:Chern class formulas for G_2 degeneracy loci'' Location: WMAX 110 (PIMS) Abstract: Let V be a vector bundle of rank n on a variety X, with subbundles E and F of respective ranks e and f. The locus of points of X where the fibers of E and F intersect in dimension more than e+f-n is a basic example of a degeneracy locus, and it is useful to have formulas for the cohomology classes of such loci in terms of the Chern classes of E, F, and V. Many variations are possible: there should be one for each Lie type, and for each element of the corresponding Weyl group. For classical types, formulas were given by Giambelli-Thom-Porteous, Kempf-Laksov, Harris-Tu, and Fulton. In this talk, I will give formulas corresponding to exceptional type G_2. Along the way, I'll discuss octonion bundles, and describe the G_2 flag variety in concrete, linear-algebraic terms. Preprint available at http://arxiv.org/abs/0712.2641. Time and Date: 3:00 p.m. , Monday, February 4, 2008 (pls note unusual day and location) Event: Probability Seminar Speaker: Davar Khoshnevisan, University of Utah Subject:Brownian sheet in critical dimension does not have multiple points'' Location: MATH 104 Abstract: I will describe some on-going work with R. Dalang, E. Nualart, D. Wu, and Y. Xiao, where we derive a decoupling formula for the Brownian sheet. That formula has the following consequence: An N-parameter Brownian sheet in d dimensions has k-multiple points if and only if k(d-2N) Time and Date: 4:00 p.m., Monday, February 4, 2008 Event: Mathematics Colloquium Speaker: Jing-Rebecca Li, INRIA Paris, Rocquencourt Research Centre Subject: Fast computation of time convolutions: the heat equation and applications'' Location: MATH 100 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, February 5, 2008 Event: UBC SCAIM Seminar Speaker: Jing-Rebecca Li, INRIA Subject:Fast computation of time convolutions: solution of the heat equation and extensions to other applications'' Location: WMAX 216 (PIMS) Abstract: I will describe a fast method to compute time convolutions, with the goal of numerically solving diffusion-type equations in a way that is computationally efficient in time and memory. In this talk, I will describe in some detail two aspects of this Fourier-based method. One is the choice of quadrature nodes and weights for the Fourier integral representation of the heat kernel and the extension of the discrete Fourier approximation to fractional powered convolution kernels. The second aspect is the evaluation of heat layer potentials on moving boundaries, which is challenging because time quadrature techniques can be prone to slow convergence due to certain properties of the geometry, even at fine discretizations. I will discuss this problem and our proposed solutions. Time and Date: 4:00-5:00 p.m., Tuesday, February 5, 2008 Event: Teaching Seminar Speaker: General Discussion Subject:What is good pedagogy in Mathematics?'' Location: MATX 1102 Time and Date: 12:00--1:00 p.m., Wednesday, February 6, 2008 Event: Complex Fluids Seminar Speaker: Thomas Seon, Department of Mathematics, UBC Subject:From Turbulent Mixing to Gravity Currents in Confined Geometry'' Location: CHBE 204 (Chemical and Biological Engineering Bldg., 2360 East Mall, UBC) Abstract: The present experimental work studies mixing between fluids of different density by buoyancy induced flow in the confined geometry of a tilted tube. The front velocity variations as a function of the control parameters (density contrast \delta\rho/\rho <<1 between the fluids, viscosity \nu , tube diameter d and tilt angle \theta from vertical) has allowed to identify 3 different flow regimes as a function of \theta: near horizontal, a viscous counterflow without mixing; for intermediate angles, an inertial regime with a weak transverse mixing without effect on the front velocity, then determined by \delta \rho, and, finally, near vertical, a more efficient mixing regime controlling the full flow volume. In this one, the longitudinal spreading of the mixing zone is macroscopically diffusive. The relevant dimensionless numbers for the front velocity and the diffusion coefficient, and the corresponding scaling laws have been determined. Time and Date: 12:00--1:00 p.m., Wednesday, February 6, 2008 Event: Mathematical Biology Seminar Speaker: Angela Reynolds, University of Pittsburgh Subject:Mathematical Models of Acute Inflammation'' Location: MATX 1101 Abstract: Acute inflammation involves both pro- and anti- inflammatory components. The balance between these responses is key to the survival of an insult. In severe cases, unbalance can result in multiple organ dysfunction (MODS). MODS is characterized by sequential organ failure caused by an overactive immune system that persists despite treatment of the initial insult. In order to explore treatments for MODS we have developed multiple models of acute inflammation. These models were constructed through a modular approach where the dynamics of multiple subsystems were analyzed. The subsystems were then merged to form the full model. This approach ensures that known dynamical features of component interactions, such as bistability, excitability, and bifurcation structures, are present in the model dynamics. We will consider three models accounting for various aspects of acute inflammation. The first will focus on the dynamics between pro- and anti-inflammation. The second models the communication between the tissue and blood, which is essential in mounting a successful response to pathogen. The third models acute inflammation in the lung and its effects on gas exchange. Creating these models is the first step in simulating the spread of inflammation between organs. Time and Date: 3:30--4:30 p.m., Wednesday, February 6, 2008 Event: Algebra/Topology Seminar Speaker: Jeff Smith, UBC Subject:Commutative cochains in finite characteristic'' Location: WMAX 110 Time and Date: 12:30 p.m., Thursday, February 7, 2008 Event: Graduate Student Seminar Speakers: David Kohler and Simon Rose, Mathematics, UBC Subjects:Algebraic geometry for operation research'' and A clever, if obvious, application of a famous theorem'' Location: MATH 203 Abstracts: Solving integer programs in operation research may be done by using tools from algebraic geometry, namely Grobner basis. I'll present both sides of the problem and show the nice relationship linking these two areas of mathematics. by David Kohler. Given a ruler and a protractor, I can do a reasonable job of computing the area of a rectangle. Maybe even a triangle or two. But before the advent of computers, how did one go about computing the area of more exotic shapes? In this talk I will discuss a few such methods, of varying degrees of cleverness, focusing on an explanation of how the Compensating Planimeter works its magic. by Simon Rose. Time and Date: 2:00--3:00 p.m., Thursday, February 7, 2008 Event: Mathematical Biology Seminar Speaker: Matthew Onsum, AstraZeneca Subject:Analysis of immune cell chemotaxis and signal integration'' Location: WMAX 216 Time and Date: 3:30--4:30 p.m., Thursday, February 7, 2008 Event: DG-MP-PDE Seminar Speaker: Michael Greenblatt, University at Buffalo, State University of New York Subject:Newton Polyhedra and Sharp Estimates for Oscillatory Integrals'' Location: WMAX 110 Abstract: Varchenko described how one can obtain sharp estimates for scalar oscillatory integrals when the Newton polyhedron of the phase satisfies a certain nondegeneracy condition. These estimates can be described in a nice geometric way in terms of this Newton polyhedron. We will describe how these estimates still hold under weaker conditions; the proof uses resolution of singularities methods. We then will describe a class of functions for which the weaker conditions can not be weakened further. Further generalizations will also be discussed. Time and Date: 3:00--3:50 p.m., Thursday, February 7, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Stephen Choi, SFU Subject:An extension to the Brun-Titchmarsh theorem'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: The Siegel-Walfisz theorem states that for any B>0, we have \Sigma_{p\leq x,p\cong d(mod v)} 1\sim x/\varphi (v) log(x) for v\leq log^B(x) and (v,d)=1. This only gives an asymptotic formula for the number of primes in an arithmetic progression for quite a small modulus v compared to x. However, if we are concerned only with an upper bound, the Brun-Titchmarsh theorem says that for any 1\leq v\leq x, we have \Sigma_{p\leq x, p\cong d(mod v)} 1 << x/\varphi (v)log (x). In this talk, we will discuss an extension to the Brun-Titchmarsh theorem that concerns the number of integers with exactly s distinct prime factors in an arithmetic progression. This is joint work with Kai Man Tsang and Tsz Ho Chan. Time and Date: 4:10--5:00 p.m., Thursday, February 7, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Ronald van Luijk, SFU Subject:TBA'' Location: SFU Campus, Room ASB 10900 (IRMACS) Time and Date: 3:00 p.m., Friday, February 8, 2008 Event: Mathematics Colloquium Speaker: Michael Greenblatt, SUNY at Buffalo Subject: Resolution of Singularities and Analysis'' 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, February 11, 2008 Event: Mathematical Biology Seminar Speaker: Pik-Yin Lai, National Central University, Taiwan Subject:Synchronized Bursting and Growth of cultured neuronal network: experiments and model'' Location: WMAX 216 Abstract: Synchronized bursting is observed in cortical neuronal cultures in vitro when the neuronal network is incubated for a sufficiently period of time. The synchronized bursting frequency of the network is found to be much slower than the characteristic time scale of a neuron and increases with the network connectivity. We present a detailed analysis and theoretical growth models to account for the experimental data on the growth of cortical neuronal networks. The bursting frequency (f) during SF of the networks is found to be an increasing function of k. In particular, the special form of P(k)~ exp(-k/ko) gives the experimental observed result that f is characterized by a critical age tc and a critical frequency (fc) as: f = fc + fo log(t/tc). The growth of the network is consistent with the model of an early enhanced growth of connection, but followed by a retarded growth once the synchronized cluster is formed. Our electrophysiological measurements using double-patch techniques reveal that even though the bursting frequencies are synchronized, the intra-burst spikes are not. We present a mean field model of the neural network that combines a Fitz-Hugh Nagumo (FHN) model with an additional dynamic variable. This new variable is slower than those in the FHN model. It enables the neuron firing to be inhibited and generates inter-spike intervals (ISI) with long time scales resulting in bursting. Time and Date: 3:00--4:00 p.m., Monday, February 11, 2008 Event: IAM Seminar Series Speaker: Michael Friedlander, Department of Computer Science, UBC Subject:Algorithms for Large-Scale Sparse Reconstruction'' Location: Room 301, LSK Bldg. Abstract: Many signal processing applications seek to approximate a signal as a linear combination of only a few elementary atoms drawn from a large collection. This is known as sparse reconstruction. The theory of compressed sensing allows us to pose the sparse reconstruction problem as a structured convex optimization problem. I will discuss the role of duality in revealing some unexpected and useful properties of these problems, and will show how they can lead to practical, large-scale algorithms. I will also describe some applications of these algorithms. Time and Date: 3:00--4:30 p.m., Monday, February 11, 2008 Event: Algebraic Geometry Seminar Speaker: Ronald van Luijk, SFU/UBC/PIMS Subject:K3 surfaces with Picard number one and infinitely many rational points'' Location: WMAX 110 (PIMS) Abstract: Not much is known about the arithmetic of K3 surfaces in general. We still do not know of a single K3 surface whose set of rational points has been proved to be neither empty, nor Zariski dense. Once the Picard number, which is the rank of the Neron-Severi group, is high enough, more structure is known and more can be said. Computing the Picard number of a given K3 surface is in general not easy. Although a general K3 surface has Picard number 1, until a couple of years ago, there was not a single K3 surface, defined over a number field, known to have Picard number one over the complex numbers. We will give examples of such surfaces that are defined over the rationals, and prove that they indeed have Picard number one over the complex numbers. Time and Date: 12:30--2:00 p.m., Tuesday, February 12, 2008 Event: UBC SCAIM Seminar Speaker: Paul Milewski, University of Wisconsin-Madison Subject:Solitary Capillary-Gravity Waves'' Location: WMAX 216 Abstract: When the effects of capillarity and gravity are balanced, which occurs at length scales of approximately 1 cm. in water, localized solitary surface waves have been found in model equations and in the full Euler equations in all the usual wave regimes: both in two- and three-dimensions and from shallow water to infinite depth. In shallow water there have been several studies, based on model Korteweg-de Vries and Kadomtsev-Petviashvilli-type equations, of the dynamics of such waves. In the more relevant deep water regime little has been done to study the stability and dynamics of these waves, in part because of the lack of good models. We present some new models for this limit together with results on stability and dynamics within these models, and some comparisons with the full Euler equations. This is joint work with my PhD student Ben Akers. Time and Date: 12:00--1:00 p.m., Wednesday, February 13, 2008 Event: Complex Fluids Seminar Speaker: Mariana Carrasco-Teja, Department of Mathematics, UBC Subject:Primary Cementing of Nearly Horizontal Oil Wells'' Location: CHBE 204 Abstract: We consider laminar displacement flows in narrow eccentric annuli, oriented horizontally, between 2 fluids of Herschel-Bulkley type. This situation is modeled via a Hele-Shaw approach. The main application is the primary cementing of nearly horizontal wells. Whereas slumping and stratification would be expected in the absence of any imposed flow rate, for a displacement flow we show that there are often steady state traveling wave solutions in this displacement. Surprisingly these may exist even at large eccentricities and for large density differences between the fluids. When heavy fluids displace light fluids, annular eccentricity opposes buoyancy and steady states are more prevalent than when light fluids displace heavy fluids. For large ratios of buoyancy forces to viscous forces we derive a lubrication-style displacement model. This simplification allows us to find necessary and sufficient conditions under which a displacement can be steady, which can be expressed conveniently in terms of a consistency ratio. It is interesting that buoyancy does not appear in the critical conditions for a horizontal well. Instead a competition between fluid rheologies and eccentricity is the determining factor. Buoyancy acts only to determine the axial length of the steady state profile. Time and Date: 3:00 p.m., Wednesday, February 13, 2008 Event: Mathematics Colloquium Speaker: Paul Milewski, University of Wisconsin-Madison Subject: Mathematics of Stability, Breaking and Mixing for Waves in Shallow Fluids'' Location: MATH 104 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Wednesday, February 13, 2008 Event: Algebra/Topology Seminar Speaker: Adam Clay, Department of Mathematics, UBC Subject:The space of left orders of the braid groups'' Location: WMAX 110 Abstract: As pointed out by Sikora in recent years, the set of all left-orders of a group admits a natural topology under which this set becomes a compact metric space. This space has recently been used to find elegant solutions to two long-standing open problems, yet very little is known about the structure of the space in general. In this talk, we investigate the braid groups, whose space of orders has especially interesting properties, and use the Dehornoy ordering of the braid groups (and some elementary topology) to show the existence of uncountably many left orders on the braid groups, all of which are well-orders when restricted to positive braids. This work is joint with Dale Rolfsen. Time and Date: 2:00--3:00 p.m., Thursday, February 21, 2008 Event: Mathematical Biology Seminar Speaker: Richard Allen, University College, London UK Subject:Modelling the Endothelial Cell Response to Fluid Flow'' Location: WMAX 216 Abstract: Following the onset of shear stress due to fluid flow endothelial cells polarize and elongate in the direction of flow. How the mechanical signal is transformed into an organised and directed response is poorly understood. A multi-scale cellular Potts model promises to aid investigation of this question. A 3D virtual cell defines the fluid flow via a boundary integral representation, solution of which gives the force over the surface of the cell. A framework of how to link this to models of Rho GTPase interaction, actin filament alignment and Arp2/3 induced actin polymerisation will be described. Time and Date: 3:00--4:00 p.m., Monday, February 25, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Joseph Pedlosky, Department of Physical Oceanography, Woods Hole Oceanographic Institution Subject:Theories of the General Ocean Circulation'' Location: Room 301, LSK Bldg. Abstract:The general circulation of the ocean is a global phenomenon in which many geographically localized structures have long attracted scientific attention. This lecture will survey some of these and emphasize the connection between them. The connection between western boundary currents, such as the Gulf Stream, and the oceanic interior circulation will be discussed. The vertical density structure of the broad interior of the ocean, the thermocline, will be shown to be connected to the equatorial current system, in particular the Equatorial Undercurrent (EUC). The possibility that the strength of the global meridional overturning circulation (MOC), so important to the climate system, is related to the detailed boundary layer structure joining the base of the thermocline to the abyssal ocean will be reviewed. Time and Date: 3:00--4:30 p.m., Monday, February 25, 2008 Event: Algebraic Geometry Seminar Speaker: Yan Soibelman, Kansas State University Subject:Motivic Donaldson-Thomas invariants for Calabi-Yau categories'' Location: WMAX 110 (PIMS) Abstract:I am going to discuss a joint work with Maxim Kontsevich which is devoted to mathematical structures underlying count of BPS states in topological string theory. Our approach is based on a version of Bridgeland's theory of stability structures as well as on the ideas of motivic integration. As a by-product of this approach we offer a new wall-crossing formula for the generalized Donaldson-Thomas invariants. Time and Date: 4:00 p.m., Monday, February 25, 2008 Event: PIMS Colloquium Speaker: Narcisse Blood, Kainai Studies Program, Department of Education, University of Lethbridge and International Indigenous Studies Department, University of Calgary Subject: Science, Math and Traditional Knowledge: working together towards a better way of managing our natural resources'' Location: WMAX 110, PIMS Facility, 1933 West Mall, UBC Abstract:Traditional Knowledge is an important element in ecological monitoring and research because of its nature as a bridge for understanding environmental processes over time. Academic knowledge has its role as does traditional knowledge in understanding environmental changes. Narcisse Blood will discuss how Science and Traditional Knowledge can complement each other to provide a better insight into ways of managing natural resources. Narcisse's background: Narcisse Blood (Ki'naksaapo'p), a member of the Kainai Nation, currently teaches for the Kainai Studies program, the Department of Education at the University of Lethbridge, and the International Indigenous Studies Department at the University of Calgary. Previously he was a Coordinator of the Kainai Studies program at Red Crow College, where he is recognized as an Eminent Scholar. He has served as Chair for the Mookaakin Cultural and Heritage Foundation of the Blood Tribe and on the Blood Tribe Chief and Council. Narcisse served as Speaker for the State of the Nations Symposium, where he gave a lecture titled "Defending Rights: An Indian World View on the Environment." He has principal transfer rights in the Niitsitapi (Blackfoot) knowledge disciplines of Iitskinaiksi (Horn Society) and Ninnaimsskaiksi (Bundle Owner). Time and Date: 12:30 p.m., Tuesday, February 26, 2008 Event: Math Dept. Presentation Event Speaker: Gary Walsh, on the new Cryptological Research Institute, Ottawa Subject:The Cryptologic Research Institute'' Location: WMAX 110 (PIMS first floor) Abstract:The Communications Security Establishment is furthering its commitment to research in Mathematics and Computer Science by initiating and sponsoring a new research institute in Ottawa. The Cryptologic Research Institute will be comprised of full-time research employees, and will also have part-time involvement from contractors/consultants from the academic community. We will discuss many aspects of the Cryptologic Research Institute, including the role of its members from the academic community. Time and Date: 3:30--4:30 p.m., Tuesday, February 26, 2008 Event: DG-MP-PDE Seminar Speaker: Yuxin Ge, Paris 12 and University of Washington Subject: Regularity of optimal transportation maps'' Location: WMAX 110 Abstract: Given a couple of smooth positive measures of same total mass on a compact Riemannian manifold M, we look for a smooth optimal transportation map G, pushing one measure to the other at a least total squared distance cost. The recent local C2 estimate of Ma--Trudinger--Wang enabled G. Loeper to treat the standard sphere case. In this talk, we discuss this topic on manifolds with curvature sufficiently close to 1 in C2 norm. This is a joint work with P. Delanoe. Time and Date: 12:00--1:00 p.m., Wednesday, February 27, 2008 Event: Complex Fluids Seminar Speaker: Peter Palffy-Muhoray, Liquid Crystal Institute, Kent State University Subject: Liquid Crystal Elastomers'' Location: CHBE 204 Abstract: Liquid Crystal Elastomers (LCEs) are orientationally ordered rubbers, characterized by a remarkable responsivity to excitations. The salient feature of these 'solid' liquid crystals is coupling between orientational order and elastic strain. Stretching an LCE sample, for example, changes the order parameter and the physical properties that depend on it, and conversely, changing the order parameter can result in dramatic changes in sample shape. In this talk, I will give an overview of these novel materials, review their history, discuss the physics underlying their behavior, present some intriguing experimental observations, describe modeling efforts and challenges, and consider practical applications. Time and Date: 3:00-4:00 p.m., Wednesday, February 27, 2008 Event: Probability Seminar Speaker: Timo Seppalainen, University of Wisconsin-Madison Subject: Current fluctuations in the asymmetric simple exclusion process'' Location: MATH 225 Abstract: The variance of the net particle current across the characteristic in the stationary asymmetric simple exclusion process is of the order t^{2/3}. This result is proved with couplings that control the motion of a second class particle. This is joint work with Marton Balazs from the Budapest University of Technology and Economics. Time and Date: 3:30--4:30 p.m., Wednesday, February 27, 2008 Event: Algebra/Topology Seminar Speaker: Kate Peterson, Queens University Subject:Character Varieties of Twist Knots'' Location: WMAX 110 Abstract: Character varieties associated to finite volume hyperbolic 3-manifolds with non-empty boundary encode much topological data, but are difficult to compute. I'll discuss the construction of explicit defining equations for the character varieties of an infinite family of knot complements which includes the twist knots, and discuss several consequences. This is joint work with M. Macasieb and R. van Luijk. Time and Date: 2:00--3:00 p.m., Thursday, February 28, 2008 Event: Mathematical Biology Seminar Speaker: Raibatak Das, Department of Mathematics, UBC Subject:The motion of cell-surface receptors examined with a hidden Markov model'' Location: WMAX 216 Abstract: Single particle tracks of tagged cell-surface proteins frequently show deviations from random Brownian diffusion. Such deviations are usually transient, and variously attributed to membrane heterogeneities, the presence of rigid obstacles, or interaction with other membrane-bound or cytosolic proteins. We examine the dynamics of a diffusing cell-surface protein that interacts with a homogeneously distributed binding partner, such as the cytoskeleton, such that the binding slows down its diffusion. The system is described by 2D diffusion coefficients of the protein in its free and bound states, and transition probabilities between the two states. The tracks of single protein molecules are then the outcome of a hidden Markov model, whose underlying state sequence (free or bound) is hidden, while the particle position at each observation time is recorded. In this formulation, the likelihood of the observed sequence of displacements in a track is a function of the four model parameters. We maximize this likelihood function with respect to the model parameters to estimate their best-fit values and assign statistical error bounds to these estimates. Thus, our analysis can reveal important biophysical details of the underlying physical system that are not easily discernible with a traditional single particle tracking analysis. We apply our analysis to experimentally observed tracks of the adhesion molecule LFA-1 on the surface of T cells. Time and Date: 3:00--3:50 p.m., Thursday, February 28, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Kate Peterson, Queens University Subject: Primitive roots and the Euclidean algorithm'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: An integer s is called a primitive root modulo a prime p if the multiplicative set generated by s surjects all non-zero residue classes modulo p. Artin's primitive root conjecture states that all integers s other than -1 or squares are primitive roots modulo infinitely many primes. I'll discuss a generalization of Artin's primitive root conjecture to number fields and connections this has to the Euclidean Algorithm problem. This is joint work with R. Murty. Time and Date: 4:00--5:00 p.m., Thursday, February 28, 2008 Event: Specialized Mathematics Seminar Speaker: Rustum Choksi, Associate Professor and PIMS SFU Site-Director, Department of Mathematics, Simon Fraser University Subject: Intrinsic Length Scales and Structure in Nonlocal Variational Problems'' Location: MATH 204 Abstract: We consider natural nonlocal perturbations of the well-studied Cahn-Hilliard and isoperimetric problems, focusing on certain analytical methods for capturing characteristics of minimizers. In particular, we describe the proofs of a series of uniform bounds on the distribution of the energy of any minimizer, and we show how these bounds permit one to draw certain ansatz-free conclusions about global minimizers. We also discuss small volume fraction regimes of these problems via a two-stage/scale Gamma-limit: the highest order to a local energy on dirac masses and the next order to a Coulomb-like interaction energy. This is joint work with 1) G. Alberti (Pisa) and F. Otto (Bonn) and 2) M.A. Peletier (Eindhoven University of Technology). Time and Date: 4:10--5:00 p.m., Thursday, February 28, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Erick Wong, Department of Mathematics, UBC Subject: Eigenvalues of random matrices and not the Riemann Hypothesis'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: Random matrix theory has been a hot topic in number theory, particularly since the Rudnick and Sarnak landmark work on the spacing of consecutive zeros of L-functions. This highly accessible talk has a far more elementary flavour, focusing on eigenvalues of random integer matrices instead of the Gaussian Unitary Ensemble. For a fixed n, consider a random n x n integer matrix with entries bounded by the parameter k. I'll give a simple proof that such a matrix almost certainly has no rational eigenvalues (as k increases). Then we'll delve into more detail on the exact eigenvalue distribution of the 2 x 2 case. Along the way we'll rediscover a forgotten determinant identity and tackle some quadruple sums. This is joint work with Greg Martin. Time and Date: 3:00 p.m., Friday, February 29, 2008 Event: Mathematics Colloquium Speaker: Rustum Choksi, Mathematics, SFU Subject: Mathematical and Physical Paradigms for Periodic Pattern Formation'' 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, March 3, 2008 Event: IAM Seminar Series Speaker: Kevin Lyons, Department of Forest Resources Management, UBC Subject:Overspecified Boundary Conditions: An Alternative to Saint Venant's Problem'' Location: Room 301, LSK Bldg. Abstract: Saint Venant’s problem is a classical problem in elastostatics, where a right cylinder is loaded on its plane ends. In Saint Venant’s solution, the condition of a fixed base is replaced by a stress field that maintains equilibrium, thus the mixed problem is replaced by a traction problem. The stress fields on the plane ends are further replaced by resultant loads (forces and moments). Various authors have extended solutions to anisotropic and heterogeneous materials with an interesting result: the plane sections remain plane for loads independent of the axial coordinate and the stresses in the plane of the transverse cross section are zero. This result is significant for natural materials, such as wood, that are weaker in the radial and tangential directions than in the axial direction. In this presentation, I will discuss my work on the mixed problem, particularly my attempts to determine whether the zero in-plane stress result from Saint Venant’s solution is due to characterizing the mixed problem as a traction problem. I will consider the elastodynamic problem of a right cylinder with a rigidly fixed base subject to time-dependent loads on the free end. First I deduce the stress field that satisfies pointwisethe boundary conditions for a rigidly fixed base; however, since the rigidly fixed base prescribes both the displacements and strains (overspecified boundary conditions) a proof of existence is required. The mixed elastodynamic problem spawns an equilibrium problem that I will use to make some observations on the differences between Saint Venant’s solution and the mixed problem. Time and Date: 3:00--4:30 p.m., Monday, March 3, 2008 Event: Algebraic Geometry Seminar Speaker: Bumsig Kim, Korea Institute for Advanced Study Subject:A Compactification of the space of Maps from Curves'' Location: WMAX 110 (PIMS) Abstract: We will present a new compactification of the moduli space of maps from pointed nonsingular complex projective stable curves to a nonsingular complex projective variety with prescribed ramification indices at the points. It will be explained that the compactification is a proper DM-stack equipped with a natural virtual fundamental class. This is joint work with A. Kresch and Y.-G. Oh. Time and Date: 3:30--4:30 p.m., Tuesday, March 4, 2008 Event: DG-MP-PDE Seminar Speaker: Tetsu Mizumachi, Kyushu University Subject:Asymptotic stability of lattice solitons in the energy space'' Location: WMAX 110 Time and Date: 12:00--1:00 p.m., Wednesday, March 5, 2008 Event: Complex Fluids Seminar Speaker: Diwen Zhou, Dept. of Chemical and Biological Engineering, UBC Subject:Simulation of Selective Withdrawal in Viscoelastic Fluids Systems'' Location: CHBE 204 Abstract: This talk reports my numerical work about selective withdrawal in fluid-gas system. The term "selective withdrawal" originated from drawing a fluid from a container holding stratified layers of immiscible fluids. In more recent literature, it refers to the flow in the neighborhood of a fluid-fluid or fluid-gas interface induced by suction through a tube. The results of my simulation in Newtonian system has been compared with previously work. Meanwhile, the effect of polymer to the selective withdrawal also has been investigated. In my simulation, the viscoelastic fluid is specified by the Giesekus model. Time and Date: 3:00-4:00 p.m., Wednesday, March 5, 2008 Event: Probability Seminar Speaker: Paul Joyce, Department of Mathematics, University of Idaho Subject:A General Extreme Value Theory Model for the Adaptation of DNA Sequences Under Strong Selection and Weak Mutation'' Location: MATH 225 Abstract: Adaptive evolution refers to a genetic change that confers a strong selective advantage to individuals that inherit this change. Examples include genetic changes that make microbes drug-resistant, or insects pesticide-resistant. Recent theoretical studies of the adaptation of DNA sequences assume that the distribution of fitness effects among new beneficial mutations is exponential. This has been justified by using extreme value theory and, in particular, by assuming that the distribution of fitnesses belongs to the so-called Gumbel domain of attraction. However, extreme value theory shows that two other domains of attraction are also possible: the Frechet and Weibull domains. Distributions in the Frechet domain have right tails that are heavier than exponential, while distributions in the Weibull domain have right tails that are truncated. To explore the consequences of relaxing the Gumbel assumption, we generalize previous adaptation theory to allow all three domains. We find that, while the shape of the distribution of selection coefficients among beneficial mutations can vary dramatically across the domains of attraction, previous Gumbel-based predictions about the first step of adaptive walks are remarkably robust. Time and Date: 3:30--4:30 p.m., Wednesday, March 5, 2008 Event: Algebra/Topology Seminar Speaker: Ryan Budney, University of Victoria Subject:An update on spaces of embeddings'' Location: WMAX 110 Abstract: The Cerf-Morlet comparison theorem states that the group of diffeomorphisms of the compact n-ball which is the identity on the boundary is an (n+1)-fold loop space, whose (n+1)-fold de-looping is the homotopy-quotient of the group of the PL-homeomorphisms of R^n by the smooth homeomorphisms of R^n. In 2002 I observed that this Cerf-Morlet iterated loop space structure generalizes to an iterated loop space structure on the space of embeddings of R^j in R^n which are standard outside of a fixed ball and equipped with a trivialization of a tubular neighbourhood. This talk will be about the homotopy-type of these embedding spaces, viewed as iterated loop-spaces. I've been able to make the most progress in the case (j,n)=(1,3), which I will describe in detail. My most recent work on this has to do with a realization problem' associated to the (j,n)=(1,3) case which boils down to a study of the symmetry groups of a certain family of hyperbolic links in S3 together with a family of natural representations of these symmetry groups. Time and Date: 12:30 p.m., Thursday, March 6, 2008 Event: Graduate Student Seminar Speaker: Warren Code, Department of Mathematics, UBC Subject:Impulsive Differential Equations via Measures'' Location: MATH 203 Abstract: Think of a bouncing ball. It is possible to model its motion by ignoring the deformation of the ball on impact, and simply treat it as a rigid object whose vertical velocity is reversed (and maybe diminished slightly) from down to up at the instant of impact. One way of building this sort of behaviour into a dynamical system is to introduce a measure as part of the dynamics, which permits discontinuities ("jumps") in the state trajectory (in the above case, the velocity of the ball). I will discuss the basic ideas as well as other physical systems where this type of analysis appears to be useful. Assumed background will be an elementary knowledge of dynamical systems (like \dot{x}(t) = f(x(t)) ) and measures. Time and Date: 2:00--3:00 p.m., Thursday, March 6, 2008 Event: Mathematical Biology Seminar Speaker: Geoff Wasteneys, Department of Botany, UBC Subject:Dynamic Properties of Microtubules in Plant Cells, with Implications for Spatial Organization, Growth and Development'' Location: WMAX 216 Abstract: Microtubules are dynamic polymers found in all eukaryotic organisms that build the cellular machines that separate chromosomes, polarize the cytoplasm, direct expansion and divide cells. Interestingly, plant cells lack the central microtubule-organizing centres common in animal cells but still manage to organize microtubules into complex arrays. The research in my laboratory explores how the dynamic properties of microtubules, which we can now quantify in live cells using fluorescent reporter proteins, help to determine the spatial organization of microtubule arrays, and how these arrays in turn control the growth, morphology and performance of plants. I will outline how genetic approaches to identify key accessory proteins that modulate microtubule dynamics are generating experimental tools for understanding the mechanisms that drive organization of the microtubule arrays. Comparing the dynamic behaviour of microtubules in mutant lines that are defective in one or more of these accessory proteins enables us to test models of the molecular mechanisms that drive microtubule organization. We are currently using this knowledge to explore the role microtubules play in the mechanical properties of the cellulosic cell wall, the helical handedness of elongating organs, and even the polar transport of the hormone auxin. Time and Date: 3:30--5:00 p.m., Thursday, March 6, 2008 Event: PIMS Lecture Series, entitled, The abelian/nonabelian correspondence in Gromov-Witten theory Note: Ionut Ciocan-Fontanine, U of Minnesota and Bumsig Kim, Korea Institute for Advanced Study will give the four lectures in this series. Speaker: Ionut Ciocan-Fontanine, University of Minnesota (Lecture 1) Subject:The abelian/nonabelian correspondence in Gromov-Witten theory I'' Location: WMAX 110 (PIMS Facility) Abstract: Given a "good" action of a reductive complex algebraic group G on a projective manifold X, the abelian/nonabelian correspondence refers to a precise relation that exists between topological invariants (cohomology, K-theory) of the Geometric Invariant Theory quotients X//G and X//T, where T is a maximal abelian subgroup in G. In this series of talks, we will explain how to extend this relation to the (genus zero) Gromov-Witten theories of the two quotients, based on joint works with Aaron Bertram and Claude Sabbah. Time and Date: 3:00 p.m., Friday, March 7, 2008 Event: Mathematics Colloquium Speaker: Patrick Brosnan, UBC Subject: Hodge theory and the Hodge conjecture'' 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, March 7, 2008 Event: Joint Distinguished UBC SCAIM-SFU CSC Seminar Speaker: Margot Gerritsen, Department of Energy Resources Engineering, Stanford University Subject:Giving the physics a chance: how to reduce the impact of numerical errors on solutions for flow and transport in porous media'' Location: UBC Robson Square, C100, Downtown Vancouver Abstract: Numerical errors are generally a bother, but in the case of adverse mobility ratio flows, such as those encountered when injecting water or gas (CO2) in oil reservoirs, they can be a real nuisance. In this talk we discuss the well-known grid orientation effect, which causes solutions to be very different depending on the orientation of the grid with respect to the general flow direction. It is not possible to completely remove this effect without introducing unacceptable levels of numerical damping. However, careful analysis of numerical errors in some popular discretization methods for the governing transport equations gave us two ideas to reduce their impact. The first is a correction of the solution in the critical near-well region, which can be applied to any discretization and gridding method. The second idea amounts to augmentation of existing schemes to render the numerical error that causes most problems isotropic. Time and Date:3:00--4:00 p.m., Monday, March 10, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Howard A. Stone, Harvard University Subject:Manipulating Thin-Film Flows: From Patterned Substrates to Evaporating Systems'' Location: Room 301, LSK Bldg. Abstract: Here we describe two variants of thin-film flows, one involving wetting and the other involving evaporation. First, we describe the spreading of mostly wetting liquid droplets on surfaces decorated with assemblies of micron-size cylindrical posts arranged in regular arrays. We obtain a variety of deterministic final shapes of the spreading droplets, including octagons, squares, hexagons and circles. Dynamic considerations provide a "shape" diagram and suggest rules for control. Second, we consider evaporation of volatile liquid drops. Using experiments and theory we show how the sense of the internal circulation depends on the ratio of the liquid and substrate conductivities and how it controls the deposition patterns. Time and Date: 3:00--4:30 p.m., Monday, March 10, 2008 Event: Algebraic Geometry Seminar Speaker: Dagan Karp, U.C. Berkeley Subject:Chern-Simons/Gromov-Witten duality'' Location: WMAX 110 (PIMS) Abstract: In this talk I hope to introduce Large N duality relating Chern-Simons gauge theory and Gromov-Witten theory. I will discuss some conjectures and theorems surrounding this subject and joint work with Sergiy Koshkin. Time and Date: 12:30--2:00 p.m., Tuesday, March 11, 2008 Event: UBC SCAIM Seminar Speaker: Brian Wetton, UBC Subject:Asymptotic Error Analysis of Finite Difference Methods'' Location: WMAX 216 (PIMS) Abstract: When computing approximations to PDE problems with smooth solutions using regular grids, the error has additional structure. For second order methods applied to elliptic or parabolic problems, an expansion for the error can be constructed that is regular in the grid spacing. This expansion can be used to justify convergence for nonlinear problems, and is an easy way to see why convergence with higher regularity is observed (a phenomena sometimes called superconvergence in the FE community). When artificial boundary conditions are introduced for higher order finite difference methods, numerical boundary layers result. Identifying the types of errors that are generated by a given scheme and the order at which they occur can be called Asymptotic Error Analysis. Several examples of the technique and its uses will be given. This will be an overview talk also with some material useful to anyone trying to implement "unusual" boundary conditions for PDE problems. Time and Date: 3:30--4:30 p.m., Tuesday, March 11, 2008 Event: DG-MP-PDE Seminar Speaker: Ivar Ekeland, UBC Subject:Systems of HJB equations'' Location: WMAX 110 Time and Date: 4:00-5:00 p.m., Tuesday, March 11, 2008 Event: Teaching Seminar Speaker: General Discussion Subject:Teaching Proof.'' Location: MATX 1102 Time and Date: 12:00--1:00 p.m., Wednesday, March 12, 2008 Event: Complex Fluids Seminar Speaker: Teodor I. Burghelea, Department of Mathematics, UBC Subject:The solid-fluid transition in a physical gel'' Location: CHBE 202 (Please note unusual location, not the regular meeting room.) Abstract: We present an experimental investigation of the solid-fluid transition in a yield stress shear thinning physical gel (Carbopol 940) under shear. Upon a gradual increase of the external forcing ,we observe three distinct flow regimes: an elastic solid like regime (characterized by a linear stress-strain dependence), a solid-fluid phase coexistence regime (characterized by a competition between destruction and reformation of the gel) and a viscous regime (characterized by a power law stress-strain dependence). The competition between destruction and reformation of the gel is investigated via systematic measurements of the dynamic elastic moduli as function of both stress amplitude and temperature. The transition from solid behavior to fluid behavior displays a clear hysteresis upon increasing and decreasing values of the external forcing. We find that the deformation power corresponding to the hysteresis region scales linearly with the rate at which the material is being forced. Based on these experimental findings, we suggest an analogy between the solid-fluid transition and a first order phase transition, e.g. the magnetization of a ferro-magnet where irreversibility and hysteresis emerge as a consequence of a phase coexistence regime. In order to get further insight into the solid-fluid transition, our experimental findings are complemented by a simple kinetic model that qualitatively describes the structural hysteresis observed in our rheological experiments. The model is fairly well validated against oscillatory flow data, by partial reconstruction of the Pipkin space. Time and Date: 3:30--4:30 p.m., Wednesday, March 12, 2008 Event: Algebra/Topology Seminar Speaker: Denis Sjerve, UBC Subject:Moduli for Hyperelliptic Curves'' Location: WMAX 110 Abstract: A hyperelliptic curve is a connected Riemann surface which admits a 2-fold branched covering over the 2-sphere. They can be described by quadratic equations (Riemann's approach), and then their moduli space is given by certain configuration spaces. They can also be described through uniformization (Poincare's approach). Using this approach I will explain how the moduli space can be related to right angled pentagons and Thurston's notion of simple earthquakes. This is joint work with Sadok Kallel. Time and Date: 2:00--3:00 p.m., Thursday, March 13, 2008 Event: Mathematical Biology Seminar Speaker: Paul Tian, College of William and Mary Subject:Mathematical Study of Brain Tumor Therapies'' Location: WMAX 216 Abstract: Glioma is the most serious malignant brain tumor. In order to improve the efficacy of therapies, it is important to understand its progression with therapies and its genesis. In this talk, I will first present our effort in understanding of glioma progression with different therapies in terms of mathematical models. The first model is about virotherapy of glioma, which is a free boundary problem with five nonlinear partial differential equations. Virotherapy is a promising treatment for malignant solid tumors, and it is now in animal experimental stage. In order to treat human glioma by virotherapy, it is critical to understand all factors involved in the therapy. Our model finds an important factor burst size of virus, and the effect of immunosuppression drug cyclophosphamide in animal experiments. The model prediction has been verified by experimental results. The second model is about radiotherapy plus chemotherapy after surgical resection, which is a two-component free boundary problem. After surgery, the tumor progression depends on the degree of resection and radiation, and a particular drug. We use human data to estimate parameter values, and the model can predict the mean survival times of patients who undergo different protocols of treatments. Time and Date: 3:00-4:00 p.m., Thursday, March 13, 2008 Event: Probability Seminar Speaker: Gabor Pete, Microsoft Research Subject:The scaling limits of dynamical and near-critical percolation and the minimal spanning tree'' Location: MATH 102 Abstract: Let each site of the triangular lattice, with small mesh \eta, have an independent Poisson clock with a certain rate r(\eta)=\eta^{3/4+o(1)} switching between open and closed. Then, at any given moment, the configuration is just critical percolation; in particular, the probability of a left-right open crossing in the unit square is close to 1/2. Furthermore, because of the scaling, the expected number of switches in unit time between having a crossing or not is of unit order. In joint work with Christophe Garban and Oded Schramm, we prove that the limit (as \eta \to 0) of the above process exists as a Markov process, and it is conformally covariant: if we change the domain with a conformal map \phi(z), then time has to be scaled locally by |\phi'(z)|^{3/4}. The same proof yields a similar result for near-critical percolation, and it also shows that the scaling limit of (a version of) the Minimal Spanning Tree exists, it is invariant under translations, rotations and scaling, but not under general conformal maps. Time and Date: 3:00--3:50 p.m., Thursday, March 13, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Cecilia Busuioc, Boston University Subject:The Steinberg symbol and special values of L-functions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: In this talk, we will describe a construction of Eisenstein classes in the parabolic cohomology of \gamma _0 (M) with values in Milnor's K_2-group of the ring of S-integers of the cyclotomic extension \boldmath{Q} (\mu _M). In the case where p is an irregular prime, we will explain a congruence between certain projections of Steinberg symbols of p-units and L-values of level-1 cusp forms congruent to an Eisenstein series mod p, a result that was predicted by a conjecture of R. Sharifi. Time and Date: 3:30--5:00 p.m., Thursday, March 13, 2008 Event: PIMS Lecture Series (Lecture 2) Speaker: Bumsig Kim, Korea Institute for Advanced Study Subject:The abelian/nonabelian correspondence in Gromov-Witten theory II'' Location: WMAX 110 (PIMS) Abstract: Given a "good" action of a reductive complex algebraic group G on a projective manifold X, the abelian/nonabelian correspondence refers to a precise relation that exists between topological invariants (cohomology, K-theory) of the Geometric Invariant Theory quotients X//G and X//T, where T is a maximal abelian subgroup in G. In this series of talks, we will explain how to extend this relation to the (genus zero) Gromov-Witten theories of the two quotients, based on joint works with Aaron Bertram and Claude Sabbah. Time and Date: 4:00--5:00 p.m., Thursday, March 13, 2008 Event: PIMS-MITACS Math Finance Seminar Speaker: Rocio Sotomayor, Georgia State University Subject:Explicit Solutions of Consumption-Investment Problems in Financial Markets with Regime Switching'' Location: WMAX 216 Abstract: We consider a financial market with different regimes that are modeled through an observable continuous-time finite-state Markov chain. The rates of returns and volatilities of the market investing assets, the bank interest rate and the investors' utility of consumption are dependent on the regime of the financial market. Under these settings, an investor taking decisions continuously in time has to select a consumption-investment policy to maximize his expected total discounted utility of consumption until bankruptcy. Using techniques of classical stochastic control adapted to regime switching, we derive the Hamilton-Jacobi-Bellman equation for the problem and obtain explicit optimal consumption and investment policies for specific HARA utility functions. We analyse as well the impact of the regime shifts in the investor's optimal decision. Time and Date: 4:10--5:00 p.m., Thursday, March 13, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Melissa Macasieb, Department of Mathematics, UBC Subject:Character Varieties of Hyperbolic Knot Complements'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: To every hyperbolic 3-manifold M with nonempty boundary, one can associate a pair of related algebraic varieties X(M) and Y(M) called the character varieties of M. These varieties carry much topological information about M, but are in general difficult to compute. In the case that M is a knot complement, X(M) and Y(M) are defined over Q. In this talk, I will discuss how properties of these varieties reflect the topology of M in the case M is a hyperbolic knot complement. I will also show how to obtain explicit equations for the the character varieties associated to a bi-infinite family of hyperbolic knots K(m,n) and discuss consequences of these results related to the existence of integral points on these curves. This is joint work with Kate Petersen and Ronald van Luijk. Time and Date: 3:00 p.m., Friday, March 14, 2008 Event: Mathematics Colloquium Speaker: Gabor Pete, Microsoft Research Subject: Noise sensitivity and the Fourier spectrum of critical percolation'' 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, March 17, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Boris N. Kholodenko, Department of Pathology, Anatomy, and Cell Biology, Jefferson Medical College, Thom as Jefferson University Subject:Cell Signalling Dynamics in Time and Space'' Location: Room 301, LSK Bldg. Abstract: The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dy namics of downstream signalling networks. Computational models provide insights into the intricate relationships between stimuli and r esponses and reveal mechanisms that enable networks to amplify signals, reduce noise and generate discontinuous bistable dynamics or o scillations. These temporal dynamics are coupled to precipitous spatial gradients of signalling activities, which guide pivotal intrac ellular processes. Trafficking of endosomes and kinase-scaffold complexes driven by molecular motors propagate signals from the plasma membrane to the nucleus. Rapid survival signals in neurons might be transmitted by waves of protein modification. Time and Date: 2:00--3:00 p.m., Tuesday, March 18, 2008 Event: Mathematical Biology Seminar Note: Special day. Speaker: Vered Rom-Kedar, Weizmann Institute of Science Subject:Novel strategies for G-CSF support of severe prolonged neutropenia'' Location: WMAX 216 Abstract: We develop, in an axiomatic fashion, structurally stable mathematical equations that describe the G-CSF -neutrophil dynamics (the majority of the white blood cells are neutrophils. G- CSF is a factor that may be injected to help patients produce more neutrophils). We then show that a variant of this model adequately describes the neutrophils dynamics after chemotherapy treatments with various support protocols. A grading for neutropenia (the dangerous drop in the neutrophil's level) and corresponding tailored G-CSF treatments are proposed and are shown to be robust to parameter variability. Our results clarify and revise the current American Society of Clinical Oncology recommendations for G-CSF administration in neutropenia following intensive chemotherapy regime ns. As all our recommendations correspond to clinically available protocols, a framework for a prospective randomized clinical trial i s proposed. Time and Date: 3:30--4:30 p.m., Tuesday, March 18, 2008 Event: DG-MP-PDE Seminar Speaker: Eduard Kirr, University of Illinois at Urbana-Champaign Subject:Asymptotic stability of ground states in 3D subcritical nonlinear Schroedinger equation'' Location: WMAX 110 Abstract: The talk will start with an overview of asymptotic stability results for NLS. By definition, the ground states are stable if a solution starting nearby decomposes into a part convergent to a ground state and a part radiating away. For ma ny years the theory covered only the supercritical (large power) nonlinearities mainly because a large power of a small perturbation a round a ground state is very small and easily dispersed by the Schroedinger type operator given by the linearization at the ground sta te. Recently results for critical nonlinearities have been obtained. The second part of the talk will focus on a new apprach which giv es asymptotic stability results even for subcritical (low power) nonlinearities. It relies on linearizing the equation along a one par ameter family of ground states. By continuously adapting the linearization to the actual evolution of the solution we are able to capt ure the correct effective potential induced by the nonlinearity into a time dependent Schroedinger type operator. The dispersive estim ates we prove for this operator allow us to control the remaining nonlinear terms and obtain the asymptotic stability results. Time and Date: 12:00--1:00 p.m., Wednesday, March 19, 2008 Event: Complex Fluids Seminar Speaker: Anthony Wachs, Institut Francais du Petrole Subject:Direct Numerical Simulation of Particulate Flows with Collisions'' Location: CHBE 204 Abstract: The comprehension of fluid/solid interactions in moderately to highly concentrated particulate flows is still limited even if the fluid is Newtonian and particles are assumed to be ideal spheres (or circular cylinders in 2D modelling). M ost of the complexity relies on the various scales in the process: from the particle to the flow domain, and the corresponding momentu m transfers. As the solid fraction exceeds a certain critical value (which lies in the range 5 to 8%), the probability of collisions b etween particles grows non-negligible and a proper treatment of all multi-body collisions is required in the modelling of the system. Here, we present an original numerical approach to address particulate flows with collisions based on the coupling of a Discrete Eleme nts method for the solid part and a standard Finite Elements solver for the fluid part. Coupling is achieved by a Distributed Lagrange Multiplier/Fictitious Domain method. Our numerical strategy highlights some promising ^M capabilities to survey a large number of particulate flow problems without any restriction on the size, the shape (which is constraine d to be at least convex) or the polydispersity of the suspension as well as the rheological properties of the suspending fluid. Result s on the 2D sedimentation of isometric polygonal particles in a Newtonian fluid as well as new 3D results give a flavour of what can b e expected from this type of approach. Time and Date: 3:30--4:30 p.m., Wednesday, March 19, 2008 Event: Algebra/Topology Seminar Speaker: Hendryk Pfeiffer, Department of Mathematics, UBC Subject:Invariants of 3-dimensional Kirby calculus and representation theory'' Location: WMAX 110 Abstract: Just as the Jones polynomial can be constructed from the Kauffman bracket, the coloured Jones polynomia l can be obtained from a coloured version of the Kauffman bracket, known as Temperley-Lieb recoupling theory'. If the bracket is eval uated at a suitable root of unity, it not only yields an invariant of framed tangles, but also an invariant of 3-dimensional Kirby cal culus and thereby an invariant of (smooth) compact oriented 3-manifolds. Algebraically speaking, the root-of-unity evaluated bracket d efines a modular tensor category. Ever since Reshetikhin and Turaev invented this notion, there has been the question of whether these categories are representation categories of suitable algberas with extra structure. In this talk, I present the answer to this questi on and describe the algebras and their additional structure in terms of ribbon diagrams. Time and Date: 12:30 p.m., Thursday, March 20, 2008 Event: Graduate Student Seminar Speaker: Jennifer Hubbarde, Department of Mathematics, UBC Subject:Development of a Burst-Death Model for Experimental Evolution'' Location: MATH 203 Abstract: Estimating the fixation probability of an initially rare beneficial mutation is fundamental to our unde rstanding of adaptation. Such estimates are critical to studies of evolution under controlled laboratory conditions, and are also ess ential for predicting the rate of adaptation of natural populations - for example the rate of adaptation in response to environmental change, or the rate of emergence of novel, or drug resistant, pathogens. Recent work has emphasized that fixation probabilities are e xtremely sensitive to the underlying life history model. In this talk, I will develop a "burst-death" life history model, in analogy to the well-studied birth-death process, in which lifetimes are exponentially-distributed, and when an individual reproduces, a "burst " of a fixed number of offspring is produced. Using this model, we can gain new estimates of the fixation probability of a beneficial mutation in a virus population. Time and Date: 3:30--4:30 p.m., Thursday, March 20, 2008 Event: Algebra/Topology Seminar Note: unusual day and location. Speaker: Jack Morava, The Johns Hopkins University Subject:Classical mechanics in tree space'' Location: MATH 105 Abstract: The space of rooted trees with n leaves has a surprisingly natural structure as a compact, smooth (thou gh non-orientable, if n>3) closed manifold of dimension n-2. It is moreover aspherical, with a fundamental group that shares a surpris ing number of features with the group of braids on n strands. These spaces are of great practical importance in computational biology and phylogenetics, but the study of dynamical systems (ie, of interesting flows) on such spaces is only beginning. The papers posted a t arXiv:math/0507514 and arXiv:math/0702515 give some idea of the breadth and interest of the subject. Time and Date: 3:30--4:30 p.m., Thursday, March 20, 2008 Event: DG-MP-PDE Seminar Speaker: Rugang Ye, U. California, Santa Barbara Subject:Entropy functionals and the Ricci flow'' Location: WMAX 110 Abstract: In this talk I'll present my recent results on the log entropy functional and the Sobolev inequalities along the Ricci flow, including their applications to the Ricci flow with surgery. I'll also present the extension of these results to noncompact manifolds. Time and Date: 4:00-5:00 p.m., Tuesday, March 25, 2008 Event: Teaching Seminar Speaker: General Discussion Subject:What is 'student engagement' in a Mathematics Class'' Location: MATX 1102 Time and Date: 3:00-4:00 p.m., Wednesday, March 26, 2008 Event: Probability Seminar Speaker: Zhen-Qing Chen, Department of Mathematics, University of Washington, Seattle Subject:A strong limit theorem for Dawson-Watanabe Superprocesses'' Location: MATH 225 Abstract: In this talk I will discuss some recent progress on scaling limit theorems for Dawson-Watanabe superprocesses. We will show that weak limit theorem can be established for a large class of superprocesses when the underlying spatial processes are symmetric Hunt processes. When the underling process is a symmetric diffusion with C1_b-coefficients or a symmetric L\'evy process on \R^d whose L\'evy exponent \Psi (\eta ) is bounded from below by c |\eta|^\alpha for some c>0 and \alpha \in (0, 2) when |\eta| is large, a stronger almost sure limit theorem can be established for the superprocess. Our approach uses the principal eigenvalue and the ground state for some associated Schrodinger operator. The limit theorems are established under the assumption that an associated Schrodinger operator has a spectral gap. Time and Date: 4:00--5:00 p.m., Wednesday, March 26, 2008 Event: The Ivan and Betty Niven Distinguished Lectures, Student/Public Lecture Speaker: Ram Murty, Queen's University Subject:What are transcendental numbers?'' Location: MATH 105 Note: Refreshments will be served in the Math Faculty Lounge (MATX 1115) at 3:45 p.m. Abstract: After defining transcendental numbers, we will discuss several open questions regarding them. We will focus on the question whether Euler's constant is transcendental. Time and Date: 2:00 p.m., Thursday, March 27th, 2008 Event: Math Biology Seminar Speaker: Jessica Conway, Northwestern University Subject: "Superlattice Patterns in Oscillatory Systems Forced at Multiple Resonant Frequencies" Location: WMAX 216 Abstract: Superlattice patterns and quasipatterns have been well-studied in waves on the surface of vertically vibrated viscous fluids (Faraday waves). We show that such patterns, comprised of 4 or more Fourier modes at different orientation, can also be obtained in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations if they are exposed to a spatially homogeneous forcing with judiciously chosen time dependence with frequencies near the 1:1-, 1:2-, and 1:3-resonance. For weak forcing such systems can be described by a suitably extended complex Ginzburg-Landau equation with time periodic coefficients. Using Floquet theory and weakly nonlinear analysis we obtain the amplitude equations for simple patterns (comprised of 1, 2, or 3 modes) as well as superlattice patterns comprised of more modes. Exploiting spatiotemporal resonances we stabilize subharmonic 4- and 5-mode patterns. We confirm our analysis through direct numerical simulations of the Ginzburg-Landau equation. We also show the possibility of such complex patterns in the laboratory setting by using system parameters reported for experiments on the oscillatory Belousov-Zhabotinsky reaction and explicitly demonstrating that the forcing parameters can be tuned such that 4-mode patterns are the preferred patterns. Time and Date: 3:00--3:50 p.m., Thursday, March 27, 2008 Event: The Ivan and Betty Niven Distinguished Lectures, 2nd Lecture, joint with PIMS/SFU/UBC Number Theory Seminar Speaker: Ram Murty, Queen's University Subject:Effective Equidistribution of Hecke Eigenvalues'' Location: UBC Campus, Room WMAX 110 (PIMS Facility) Note: 3:50--4:10 p.m. tea break Abstract: For a fixed prime p, we consider the space S(N,k) of cusp forms of weight k and level N, with N coprime to p. In 1995, J.-P. Serre proved the existence of a measure u_p with re spect to which the eigenvalues of the p-th Hecke operator acting on S(N,k) are equidistributed as k+N tends to infinity . We will derive an effective version of Serre's theorem and apply it to study the factorization of J_0(N) into simple abelian varieties . Our methods can also be applied to study the variation of eigenvalues of the Frobenius automorphism acting on a family of curves mod p and the variation of eigenvalues of adjacency matrices of regular graphs. (This is joint work with Kaneenika Sinha.) Time and Date: 3:30--5:00 p.m., Thursday, March 27, 2008 Event: PIMS Lecture Series (Lecture 3) Speaker: Ionut Ciocan-Fontanine, University of Minnesota Subject:The abelian/nonabelian correspondence in Gromov-Witten theory III'' Location: MATH 102 Abstract: Given a "good" action of a reductive complex algebraic group G on a projective manifold X, the abelian/nonabelian correspondence refers to a precise relation that exists between topological invariants (cohomology, K-theory) of the Geometric Invariant Theory quotients X//G and X//T, where T is a maximal abelian subgroup in G. In this series of talks, we will explain how to extend this relation to the (genus zero) Gromov-Witten theories of the two quotients, based on joint works with Aaron Bertram and Claude Sabbah. Time and Date: 4:10--5:00 p.m., Thursday, March 27, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Vishaal Kapoor, UBC Subject:Characters and things'' Location: UBC Campus, Room WMAX 110 (PIMS Facility) Abstract: In this expository talk, I'll be discussing the work of Granville and Soundararajan on sums of multiplicative functions in arithmetic progression. Time and Date: 12:00--1:00 p.m., Friday, March 28, 2008 Event: The Ivan and Betty Niven Distinguished Lectures, 3rd Lecture, joint with Mathematics Departmental Colloquium Speaker: Ram Murty, Queen's University Subject:Are e and pi algebraically related?'' Location: MATH 100 Note: Refreshments will be served at 11:45 a.m. (MATX 1115, Math Lounge). Abstract: Though e and pi are transcendental numbers, it is unknown if e+pi and e pi are transcendental. It is conjectured that they are. In fact, there is a general conjecture due to Scha nuel that implies that e and pi are algebraically independent. We will discuss this conjecture and its implication to special values of L-series as well as present some new results on the transcendence of certain infinite series. (This is joint work with S. Gun and P. Rath.) Time and Date: 3:00 p.m., Friday, March 28, 2008 Event: Mathematics Colloquium Speaker: Karoly Bezdek, Department of Mathematics and Statistics, University of Calgary Subject:From the Kneser-Poulsen conjecture to ball-polyhedra'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Abstract: A very fundamental geometric problem on finite systems of spheres was independently phrased by Kneser (1955) and Poulsen (1954). According to their well-known conjecture if a finite set of balls in Euclidean space is repositioned so that the distance between the centers of every pair of balls is decreased, then the volume of the union (resp., intersection) of the balls is decreased (resp., increased). In the first half of the talk we survey the state of the art of the Kneser-Poulsen conjecture in Euclidean, spherical as well as hyperbolic spaces with the emphases being on the Euclidean case. Based on that it seems very natural and important to study the geometry of intersections of finitely many congruent balls from the viewpoint of discrete geometry in Euclidean space. We call these sets ball-polyhedra. In the second half of this paper we survey a selection of fundamental results known on ball-polyhedra. Besides the obvious survey character of the talk we want to emphasize our definite intention to raise quite a number of open problems to motivate further research. Time and Date: 3:00--4:00 p.m., Monday, March 31, 2008 Event: IAM Seminar Series Speaker: Amir Moradifam, Ph.D. Student, Department of Mathematics, UBC Subject: Iterative Methods for Solving Sparse Linear Systems'' Location: Room 301, LSK Bldg. Abstract: Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations, we propose new templates for solving large non-symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well-known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill-conditioned and highly non-symmetric systems. Time and Date: 3:30--4:30 p.m., Tuesday, April 1, 2008 Event: Discrete Mathematics Seminar Speaker: Ole Warnaar, University of Melbourne Subject: A gentle introduction to Macdonald polynomials'' Location: WMAX 216 Abstract: In this talk I will present a gentle introduction to the beautiful world of Macdonald polynomials. These polynomials were introduced in 1988 by Macdonald as a generalisation of the well-known Schur functions, and have since found numerous applications in many fields of mathematics, such as algebra, geometry and mathematical physics. Time and Date: 12:00--1:00 p.m., Wednesday, April 2, 2008 Event: Complex Fluids Seminar CANCELLED as of March 31/08 10:20 a.m. Speaker: Vahid Bazargan, Dept. of Mechanical Engineering, UBC Subject: Formation of Temporary Separating Walls in Microfluidic Devices'' Location: CHBE 204 Abstract: Not yet available. Time and Date: April 3-5, 2008 Event: Mathematical Biology Seminar - Disease Dynamics 2008 See http://www.pims.math.ca/science/2008/08disdyn/schedule.html for details. Location: PIMS, Rooms 200-220, 1933 West Mall, UBC Time and Date: 3:00 p.m., Friday, April 4, 2008 Event: Mathematics Colloquium Speaker: Ole Warnaar Subject: The Selberg integral'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge) Abstract: In the 1940s, Atle Selberg discovered an n-dimensional generalisation of the Euler beta integral. At the time, Selberg was almost dismissive of his result and only reluctantly published a proof in a Norwegian mathematical magazine, mainly read by high school teachers. Now, more than 60 years later, the Selberg integral is widely recognised as one of the most important known integral evaluations, with applications to geometry, representation theory, combinatorics, number theory and more. this talk will cover the very early history of the Selberg integral (starting with Wallis and Euler), Selberg's work of the 1940s, the amazing story of the rediscovery of the integral by Dyson, Mehta and Bombieri, as well as some very recent developments related to representation theory. Time and Date: 2:00--3:00 p.m., Monday, April 7, 2008 Event: Special PIMS-MITACS Math Finance Seminar Speaker: Chris Rogers, Cambridge University Subject:Contracting for optimal investment under risk management constraints'' Location: WMAX 216 (PIMS) Abstract: The theory of risk measurement has been extensively developed over the past ten years or so, but there has been comparatively little effort devoted to using this theory to inform portfolio choice. One theme of this paper is to study how an investor in a conventional log-Brownian market would invest to optimize expected utility of terminal wealth, when subjected to a bound on his risk, as measured by a coherent law-invariant risk measure. Results of Kusuoka lead to remarkably complete expressions for the solution to this problem. The second theme of the paper is to discuss how one would actually manage (not just measure) risk. We study a principal/agent problem, where the principal is required to satisfy some risk constraint. The principal then proposes a compensation package to the agent, who then optimises selfishly ignoring the risk constraint. The principal can pick a compensation package that induces the agent to select the principal's optimal choice. Time and Date: 3:00--4:00 p.m., Monday, April 7, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Yasumasa Nishiura, Laboratory of Nonlinear Studies and Computation, Research Institute for Electronic Science, Hokkaido University, Japan Subject:Particle Patterns in Dissipative Systems'' Location: Room 301, LSK Bldg. Abstract: Particle patterns mean any spatially localized structures sustained by the balance between inflow and outflow of energy/material, which arise in the form of chemical blobs, discharge patterns, morphological spots, or binary convection cells. These are typically modeled by three-component reaction-diffusion systems or a couple of complex GL equations with a concentration field. They collide with each other, interact with defects and experience large deformation and/or basin-switching of dynamics in the form of merging, annihilation, rebound, and pinning to the defect created by heterogeneities. A new viewpoint based on a network of hidden saddles is presented to reveal the skeletal structure of those complex transient dynamics. Time and Date: 3:00--4:30 p.m., Monday, April 7, 2008 Event: Algebraic Geometry Seminar Speaker: Anthony Joseph, Weizmann Institute Subject:Slices for some non-reductive coadjoint actions'' Location: WMAX 110 (PIMS) Abstract: Two classes of subalgebras of semisimple Lie algebras share some of the remarkable properties of semisimple Lie algebras with respect to the structure of the algebra of (semi)-invariants and the geometry of co-adjoint orbits. The first are biparabolic subalgebras, the second centralizer subalgebras. In many cases the (semi)-invariant subalgebra is polynomial. Moreover the number and degrees of the generators is given by a simple combinatorial procedure, which satisfy a sum formula similar to the semisimple case. Again it is often the case that the variety of (almost) all regular coadjoint orbits admits a slice. The proof involves finding an "adapted pair" which replaces the use of a regular s-triple in the semisimple case. Furthermore additional hypotheses can be satisfied to recover "Toda-lattice" behaviour. Time and Date: 3:00 p.m., Wednesday, April 9, 2008 Event: Mathematics Colloquium Speaker: Daniel K. Nakano, University of Georgia Subject: Bridging Algebra and Geometry via Cohomology'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30 p.m., Thursday, April 10, 2008 Event: Graduate Student Seminar Speaker: Amy Goldlist, Department of Mathematics, UBC Subject:Density of Maximal Divisors of Certain Quartic Recurrences'' Location: MATH 203 Abstract: We will look at what linear recurrences are, and develop an algebraic statement to describe when primes divide consecutive terms. On the way, we will look at how primes split in various extensions, and what that tells us about them. Using some simple sums, we will find the density of maximal divisors of a particular sequence. Time and Date: 3:00--3:50 p.m., Thursday, April 10, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Nathan Ng, University of Lethbridge Subject:Lower bounds for discrete moments of the Riemann zeta function'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: Assuming the Riemann Hypothesis, we establish lower bounds for moments of the derivative of the Riemann zeta-function averaged over the non-trivial zeros of zeta. Our proof is based upon a method of Rudnick and Soundararajan that provides analogous bounds for moments of L-functions at the central point. This is joint work with Milinovich. Time and Date: 3:30--4:30 p.m., Thursday, April 10, 2008 Event: Algebra/Topology Seminar Note: unusual day for seminar. Speaker: Daniel K. Nakano, University of Georgia Subject:Lie Superalgebras: Geometry and Cohomology'' Location: WMAX 110 Abstract: Let g be a simple classical Lie superalgebra. In this talk, we will construct subalgebras which "detect" the relative cohomology of g with respect to g_0 through the use of invariant theory. This will allow us the define rank varieties and develop a theory of support varieties for modules over the Lie superalgebra. Later in the talk, we will indicate how these varieties provide a geometric interpretation of the combinatorial description of the "defect" of g and the "atypicality" of simple g-modules due to Kac and Wakimoto. Time and Date: 4:10--5:00 p.m., Thursday, April 10, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Habiba Kadiri, University of Lethbridge Subject:A bound for the least prime ideal in the Chebotarev density problem'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: A classical theorem due to Linnik gives a bound for the least prime number in an arithmetic progression. Lagarias, Montgomery and Odlyzko gave a generalization of this result to any number field. Their proof relies on some results on the distribution of the zeros of the Dedekind zeta function (zero-free regions, Deuring-Heilbronn phenomenon). In this talk, I will present some new results about these zeros. As a consequence, we are able to prove an effective version of the theorem of Lagarias et al. Time and Date: 3:00 p.m., Friday, April 11, 2008 Event: Mathematics Colloquium Speaker: Eric Friedlander, Northwestern University and Univ. of Southern California Subject: Elementary representation theory'' Location: MATX 1100 Note: Refreshments will be served at (MATX 1115, Math Lounge). Time and Date: 3:00--4:30 p.m., Monday, April 14, 2008 Event: Algebraic Geometry Seminar Speaker: Paul Horja, Department of Mathematics, UBC Subject:Triangulated categories and toric varieties, II'' Location: WMAX 110 (PIMS) Abstract: Toric varieties have traditionally provided good examples for testing proposals in algebraic geometry. In this talk, some results about the structure of their categories of coherent sheaves will be presented. Certain implications of these ideas for homological mirror symmetry and the mirror monodromy transformations will also be discussed. This is joint work with Lev Borisov. Time and Date: 3:30--4:30 p.m., Tuesday, April 15, 2008 Event: Discrete Mathematics Seminar Speaker: Jonathan Jedwab, Department of Mathematics, SFU Subject:Multiple dimensions are more natural: Golay complementary sequences and arrays'' Location: WMAX 216 Abstract: Golay complementary sequences have been used since the 1950s in diverse areas of digital information processing, including multislit spectrometry, optical time domain reflectometry, and power control for multicarrier wireless transmission. In 1999 Jim Davis and I demonstrated an unexpected connection with the classical Reed-Muller codes, which accounted for all known Golay sequences of length 2^m over binary, quaternary, and higher-order alphabets. But in 2005 Li and Chu discovered an additional 1024 length 16 Golay quaternary sequences. I shall explain how these additional sequences arise, and describe a new approach to the construction and enumeration of Golay sequences in which Golay sequences are viewed as projections of a multi-dimensional Golay array. This simplifies previous approaches, by separating the construction of Golay arrays from the enumeration of all possible projections of these arrays to lower dimensions. It accounts, in particular, for all quaternary Golay sequences spawned by Li and Chu’s examples. The talk will not assume any prior knowledge. (Joint work with Frank Fiedler and Matthew Parker) Time and Date: 3:30--4:30 p.m., Wednesday, April 16, 2008 Event: Algebra/Topology Seminar Speaker: Daniel Juan-Pineda, Universidad Nacional Autonoma de Mexico Subject:Nil phenomena in algebraic K theory'' Location: WMAX 110 Abstract: I will present how Nil groups appear in algebraic K theory, some vanishing results in lower K theory and surprising contrasting results in higher K theory. Time and Date: 3:00 p.m., Friday, April 18, 2008 Event: Mathematics Colloquium Speaker: Jean-Pierre Bourguignon, CNRS-IHES Subject: Geometry of Spaces of Measures'' Location: West Mall Annex 110 (PIMS Facility) Note: Refreshments will be served beforehand over at PIMS. Time and Date: 3:00-4:00 p.m., Wednesday, April 23, 2008 Event: Probability Seminar Speaker: Burgess Davis, Purdue U. Subject:Reinforced Random Walk'' Location: MATH 225 Abstract: Reinforced random walks are nearest neighbor random walks on graphs which leave a trace that increases the chance of revisiting visited territory. For example, the walk on the two dimensional integer lattice, which jumps across a bond with probability equal to the weight of the bond divided by sum of the weights of the four possible bonds it could jump across, where the weight of a previously crossed bond is two and that of an uncrossed bond is one, is a reinforced random walk. I will discuss several reinforced walks and some connections to standard, unreinforced, random walks. Time and Date: 3:00--4:30 p.m., Monday, April 28, 2008 Event: Algebraic Geometry Seminar Speaker: Jim Carrell, UBC Subject:Schubert varieties and Bruhat intervals'' Location: WMAX 110 (PIMS) Abstract: This talk is partly a prequel to Steve Mitchell's talk in the fall on Schubert varieties in loop Grassmannians and partly survey of a new result of Bjorner and Eckdahl (On the shape of Bruhat intervals) which will appear in the Annals. Their result verifies a conjecture that Dale Peterson and I made in the 90s about the Poincar\'e polynomial of a Schubert variety in G/B. Time and Date: 3:30-4:30 p.m., Tuesday, April 29, 2008 Event: DG-MP-PDE Seminar Speaker: Pengzi Miao, Monash University Subject:On the size of the outermost minimal surface in a compact 3-manifold with a spherical boundary'' Location: WMAX 110 Abstract: Let M be a compact three dimensional Riemannian manifold with a non-empty boundary. Suppose S is a boundary component of M such that its mean curvature vector points inward. Assume S_H is a closed minimal surface in M which has the properties that S_H and S bounds a region \Omega in M and there is no other closed minimal surfaces in \Omega . Assuming that M has nonnegative scalar curvature, we are interested in estimating the area of S_H from above by the geometry data of S. A result of this type could be viewed as a localized statement of the Riemannian Penrose Inequality in general relativity. In this talk, we derive such an inequality under the additional assumption that S is metrically a round sphere. Time and Date: Time Changed to 11:00 a.m. -- 12:00 p.m., Wednesday, April 30, 2008 Event: Complex Fluids Seminar Speaker: Tom Peacock, MIT Subject:Two Experiments at Low Reynolds Number'' Location: CHBE 204 Abstract: We present the result of two interesting experiments that both happen to take place at low Reynolds number. First, we present new results on the often controversial topic of unsteady flow separation. In these experiments we clearly demonstrate that fixed separation can occur in an unsteady flow and that the location of separation is well predicted by a recent kinematic theory. Time permitting, we will then present some insight into the mechanisms by which asymmetric objects are spontaneously propelled when floating in a density stratification. Time and Date: 3:00 p.m., Friday, May 2, 2008 Event: Mathematics Colloquium Speaker: Barbara Keyfitz, Fields Institute Subject: Hyperbolic conservation laws: the next generation'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:30 p.m., Monday, May 5, 2008 Event: Algebraic Geometry Seminar Speaker: Anthony Joseph, Weizmann Institute Subject: Graded injectivity -- or can one circumvent Grauert-Riemanschneider?'' Location: MATX 1102 Time and Date: 2:00 p.m., Thursday, May 15, 2008 Event: Probability Seminar Speaker: Craig A. Tracy, UC Davis Subject: Integral Formulas for the Asymmetric Simple Exclusion Process'' Location: MATX 1102 Abstract: The asymmetric simple exclusion process (ASEP) is a much studied interacting particle model for nonequilibrium phenomena. ASEP on the integer lattice Z is a continuous time Markov process \eta_t where \eta_t(x) = 1 if x is occupied at time t and \eta_t(x) = 0 if x is vacant at time t. Particles move on Z according to two rules: (1) A particle at x waits an exponential time with parameter one, and then it chooses y with probability p(x, y); (2) If y is vacant at that time it moves to y, while if y is occupied it remains at x. The adjective "simple" refers to the fact that allowed jumps are only one step to the right with probability p or one step to the left with probability q = 1 - p. Assuming an initial configuration that is bounded below (as for example in the step initial configuration of particles located at Z+), we derive exact formulas for the distribution of the mth left-most particle at time t. Our methods are motivated from integrable systems, e.g. Bethe Ansatz. (But there is no Ansatz in our proof!) In the case of the T(totally)ASEP our formulas reduce to known results of Johansson. This is joint work with Harold Widom. Time and Date: 4:00 p.m., Thursday, May 15, 2008 Event: Special PIMS Colloquium Speaker: Richard Askey, University of Wisconsin Subject: Ptolemy's theorem and extensions'' Location: WMAX 216 (PIMS Facility, 1933 West Mall, UBC) Abstract: Ptolemy's theorem is where serious trigonometry starts, although it is chords of circles rather than right triangles which are the building blocks. Ptolemy's theorem deals with cyclic quadrilaterals, their sides and the diagonals. In Ptolemy's book, both the statement and the proof seem to come out of nowhere. I will start with the motivation for the theorem, give Ptolemy's beautiful proof and then give some other proofs and an extension to a general quadrilateral. The proof for a general quadrilateral which I will give combines one idea from Ptolemy's proof and of a proof Euler gave of a different extension of Ptolemy's theorem. All of this can be understood with a knowledge of high school mathematics, so students are encouraged to attend. Time and Date: 11:00 a.m. -- 12:00 p.m., Friday, May 23, 2008 Event: Special Mathematics Seminar Speaker: Sebastien Ferenczi, Luminy Subject:Induction and combinatorics for interval-exchange transformations'' Location: MATX 1102 Time and Date: 4:00 p.m., Monday, May 26, 2008 Event: PIMS Distinguished Lecture Speaker: Jean-Pierre Serre, College de France Subject:Variation with p of the number of solutions mod p of polynomial equations'' Location: MATH BLDG. 100 Lecture Hall Note: Refreshments will be served at 3:00 p.m. onwards in MATX 1115, Math Lounge. Last week's announcement included MATX 1100 as the location and this has since been changed to MATH 100. About the Speaker: : Jean-Pierre Serre is one of the leading mathematicians of our time. He has made fundamental contributions in algebraic geometry, number theory and topology. He has received many awards, including the Fields Medal in 1954 and the Abel Prize in 2003. Time and Date: 3:00 p.m., Thursday, May 29, 2008 Event: UBC SCAIM Seminar Speaker: Sivan Toledo, Computer Science, Tel Aviv University, (on leave currently at MIT Computer Science and Artificial Intelligence Lab) Subject:Support preconditioners for finite-elements problems'' Location: MATX 1102 Abstract: The talk will focus on two new paradigms for constructing so-called support (or combinatorial) preconditioners for linear systems arising in finite-elements problems. The first paradigm is based on approximating most of the element matrices with diagonally-dominant approximate elements, assembling the approximations, and sparsifying the global approximation using a graph algorithm. This paradigm was invented by Boman, Hendrickson, and Vavasis; my students and I extended it theoretically and constructed the first practical solver based on it. The second paradigm, called fretsaw preconditioning, is based on combinatorially sparsifying the dual graph of the finite-elements mesh, a graph in which edges represent continuity relations. This paradigm was developed by Shklarski and I; Spielman and Daitch recently used it to develop provably-efficient preconditioners for two-dimensional problems in linear elasticity. I will also mention more recent results in the solution of least-squares problems. Time and Date: 2:00--3:15 p.m., Monday, June 9, 2008 Event: PIMS Lecture Series Speaker: Prof. Yiming Long, Nankai University, China Subject:Index theory for symplectic matrix paths with applications I'' Location: WMAX 110 Abstract: The fundamental solution of a linear Hamiltonian system is a symplectic matrix path started from the identity matrix. The study on the index theory of symplectic paths aims on understanding properties of solutions of nonlinear Hamiltonian systems via its linearizations. My lectures on this topic will contain three parts: (1) An introduction on the index theory of symplectic matrix paths. (2) The index iteration theory of symplectic paths. (3) Applications of the index iteration theory to the studies of closed orbits of Hamiltonian systems and closed geodesics on Finsler and Riemannian spheres. Time and Date: 2:00--3:15 p.m., Thursday, June 12, 2008 Event: PIMS Lecture Series Speaker: Prof. Yiming Long, Nankai University, China Subject:Index theory for symplectic matrix paths with applications II'' Location: WMAX 110 Note: Lectures will continue on June 23 and 26th. Time and Date: 4:00--5:00 p.m., Thursday, June 12, 2008 Event: CRM-Fields-PIMS 2008 Prize Lecture Speaker: Prof. Allan Borodin, University of Toronto Subject:Why Simple Algorithms can be Complex: Toward a Systematic Study of Algorithms?'' Location:GEOG 100, UBC Campus Note: Refreshments will be served at 3:30 p.m. in the PIMS 1st floor lounge before the lecture. Abstract: Richard Karp has called Computer Science the systematic study of algorithms. This raises the question as to how much the design and analysis of algorithms is a systematic study or science as opposed to say an art form as suggested by the title of Don Knuth's influential texts. For discrete computation, the well-accepted Church-Turing thesis provides a precise mathematical model for what is computable'' and hence (indirectly) for what can constitute an algorithm''. While there has been a rich and ongoing development of new and often surprising algorithms in diverse areas, conceptually simple algorithms are often used for expediency and sometimes even to obtain the best-known results for many fundamental problems. An ambitious (or perhaps naive) goal is to develop a theory for conceptually simple combinatorial algorithms'', starting off with greedy or myopic algorithms. I will review some of the history of previous efforts in this regard, some recent ideas and results, and my current thinking about the power and (provable) limitations of simple algorithmic paradigms. In particular, I will present the priority algorithm framework as a model for greedy-like optimization algorithms, and then discuss how this framework can be extended to model some common forms of simple dynamic programming, backtracking and primal dual algorithms. Time and Date: 11:00 a.m. -- 12:30 p.m., Wednesday, June 18, 2008 Event: Mathematics Seminar Speaker: Jonathan Jedwab, Simon Fraser University Subject:Can an undergraduate really conduct research in one summer?'' Location:MATX 1102 Abstract: Is it really possible for an undergraduate, in a single summer, to master the necessary technical background to tackle an open research problem, develop significant new results of publishable quality, and report on them fully? I shall describe two case studies that indicate the answer is a definite yes: the first was conducted with Kayo Yoshida in 2005, and the second with Denis Dmitriev in 2006. These studies, their accompanying journal publications, and the responses of other researchers, have significantly improved our understanding of the "peak sidelobe problem", a classical problem of digital sequence design that had seen no theoretical improvement for nearly forty years. No prior knowledge will be assumed. Time and Date: 2:00--3:15 p.m., Monday, June 23, 2008 Event: PIMS Lecture Series Speaker: Prof. Yiming Long, Nankai University, China Subject:Index theory for symplectic matrix paths with applications III'' Location: WMAX 110 Abstract: The fundamental solution of a linear Hamiltonian system is a symplectic matrix path started from the identity matrix. The study on the index theory of symplectic paths aims on understanding properties of solutions of nonlinear Hamiltonian systems via its linearizations. My lectures on this topic will contain three parts: (1) An introduction on the index theory of symplectic matrix paths. (2) The index iteration theory of symplectic paths. (3) Applications of the index iteration theory to the studies of closed orbits of Hamiltonian systems and closed geodesics on Finsler and Riemannian spheres. Time and Date: 3:30--4:30 p.m., Tuesday, June 24, 2008 Event: PIMS Lecture Speaker: Prof. Walter Schachermayer, Vienna University of Technology Subject:Optimal and better transport plans I'' Location: WMAX 110 Abstract: We consider the Monge-Kantorovick transport problem in a purely measure theoretic setting, i.e. without imposing continuity assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and possibly attain infinity. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions which are finite almost everywhere on an open set. In a previous paper Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish necessary and sufficient conditions on c-monotone transport plans to be strongly c-monotone. Note: The paper is on line at http://arxiv.org/abs/0802.0646 Time and Date: 3:30--4:30 p.m., Wednesday, June 25, 2008 Event: Algebra-Topology Seminar Speaker: Andres Navas-Flores, Universidad de Santiago, Chile Subject:Orderable groups and dynamics'' Location: WMAX 110 Time and Date: 2:00--3:15 p.m., Thursday, June 26, 2008 Event: PIMS Lecture Series Speaker: Prof. Yiming Long, Nankai University, China Subject:Index theory for symplectic matrix paths with applications IV'' Location: WMAX 110 Time and Date: 3:30--4:30 p.m., Thursday, June 26, 2008 Event: PIMS Lecture Speaker: Prof. Walter Schachermayer, Vienna University of Technology Subject:Optimal and better transport plans II'' Location: WMAX 110 Time and Date: 2:00--3:30 p.m., Friday, July 4, 2008 Event: PIMS Summer School in Probability Lecture Speaker: Yuval Peres, Microsoft Research, Redmond, USA Subject: Maximum overhang and the black cat problem'' Location: GEOG 100, 1984 West Mall, UBC Abstract: A black cat starts at the origin of the lattice Z^d. In each step you can give the cat a command to jump if it is at a specific vertex v, and then it will jump to a neighboring vertex, all choices being equally likely. You do not see the cat. How many such commands are needed to ensure that the cat is at distance greater than n from the origin with probability at least 1/2? We relate this question to the overhang problem: How many blocks are needed to build a stack that reaches distance n from the edge of a table? (This part is joint with Paterson, Thorup, Winkler and Zwick). In the second part of the talk (Joint with L. Levine), I will discuss the rotor-router model, a deterministic analogue of random walk proposed by Jim Propp. We prove that the asymptotic shape of this model in the Euclidean lattice is a ball, and discuss open problems on the patterns of directions of particle last exits and on the related abelian sandpile model. An open problem on the sandpile model brings us back to the black cat problem. Time and Date: 2:00 p.m., Thursday, July 24, 2008 Event: Probability Seminar Speaker: Carl Mueller, U. Rochester Subject:A representation for fractional Brownian motion in terms of SPDE, and an application'' Location: MATX 1102 Abstract: We give a new representation for fractional Brownian motion in terms of the stochastic heat equation driven by white noise or colored noise. There are various representations for fractional Brownian motion, but this one allows us to use the Markov property and time reversal. As an application, we give simple proofs of known results about hitting properties of fractional Brownian motion, and its double points. The latter result was first proved by Talagrand, and the difficulty of his papers is legendary among probabilists. Our proofs use some old ideas of Levy, which are not as well known as they should be. Time and Date: 3:30 p.m., Thursday, August 7, 2008 Event: Probability Seminar Speaker: Yuxiang Chong Subject: The roughness and smoothness of numerical solutions to the stochastic heat equation'' Location: MATX 1102 Abstract: The stochastic heat equation is the heat equation driven by white noise. Its solutions are Holder continuous with parameter one half minus epsilon in the space variable, and one quarter minus epsilon in the time variable. We show that the numerical solutions share this property in the sense that they have non-trivial limiting quadriatic variation in x and quartic variation in t. These variations are discontinuous functionals on the space of continuous functions, so it is not automatic that the limiting values exist, and not surprising that they depend on the exact numerical schemes used; it requires a very careful choice of scheme to get the correct limiting values. In particular, part of the folklore of the subject says that a numerical scheme with excessively long time-steps over-smooths the solution. We make this precise by showing exactly how the length of the time-steps affects the quadratic and quartic variations. Time and Date: 3:30 p.m., Thursday, August 7th, 2008 Event: Probability Seminar Speaker: Yuxiang Chong Subject: The roughness and smoothness of numerical solutions to the stochastic heat equation'' Location: MATX 1102 Abstract: The stochastic heat equation is the heat equation driven by white noise. Its solutions are Holder continuous with parameter one half minus epsilon in the space variable, and one quarter minus epsilon in the time variable. We show that the numerical solutions share this property in the sense that they have non-trivial limiting quadriatic variation in x and quartic variation in t. These variations are discontinuous functionals on the space of continuous functions, so it is not automatic that the limiting values exist, and not surprising that they depend on the exact numerical schemes used; it requires a very careful choice of scheme to get the correct limiting values. In particular, part of the folklore of the subject says that a numerical scheme with excessively long time-steps over-smooths the solution. We make this precise by showing exactly how the length of the time-steps affects the quadratic and quartic variations. Time and Date: 2:00 p.m., Wednesday, August 27, 2008 Event: Mathematical Biology Seminar Speaker: Seido Nagano, Reitsumeikan University, Japan Subject:Receptors as a master key for synchronization of rhythms-amoebae know the strategy of the crystal growth?'' Location: Math Annex 1102, UBC Campus Time and Date: 2:30--3:30 p.m., Tuesday, September 2, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics Speaker: Hendryk Pfeiffer, UBC Subject:Getting modular categories ready for categorification'' Location: WMAX 110 (first flr PIMS) Time and Date: 3:45--4:45 p.m., Tuesday, September 2, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics Speaker: Ezra Getzler, Northwestern University Subject:Two dimensional open/closed topological field theory'' Location: WMAX 110 Time and Date: 2:00--2:30 p.m., Wednesday, September 3, 2008 Event: Algebra/Topology Seminar Function: Organizational Meeting is to take place. Note:Future seminars TBA. Location: WMAX 110 (PIMS) Time and Date: 2:30--3:30 p.m., Wednesday, September 3, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics - continued Speaker: Richard Thomas, Mathematics, Imperial College London Subject: Smoothing nodal Calabi-Yau n-folds'' Location: WMAX 110 Time and Date: 3:45--4:45 p.m., Wednesday, September 3, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics Speaker: Eric Zaslow, Northwestern University Subject: Branes, Sheaves and T-Duality'' Location: WMAX 110 Time and Date: 2:30--3:30 p.m., Thursday, September 4, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics - continued Speaker: Jim Bryan, UBC Subject: The orbifold topological vertex and the Crepant Resolution conjecture for Donaldson-Thomas theory'' Location: WMAX 216, (2nd flr PIMS) Time and Date: 3:45--4:45 p.m., Thursday, September 4, 2008 Event: PIMS Workshop on Geometry, Algebra, and Physics Speaker: Kai Behrend, UBC Subject: Attempts at categorifying Donaldson-Thomas theory'' Location: WMAX 216, (2nd flr PIMS) Time and Date: 3:00--3:50 p.m., Thursday, September 4, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Thomas Stoll, University of Waterloo Subject: Coming across Newman's phenomenon, a good many times'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: Consider the sequence of the multiples of three written in base two, and reduce the sum of digits mod two. A well-known result of Newman (1969) says that the resulting sequence shows a surplus of 0s with respect to 1s. We investigate similar phenomena for rarefied sums of generalized Thue-Morse sequences. In particular, we find many (new) Newman-type phenomena for any even digital base and large classes of arithmetic progressions. This work sharpens and extends results by Dumont, Drmota, and Skalba. Time and Date: 3:00 p.m., Friday, September 5, 2008 Event: Mathematics Colloquium Speaker: Ezra Getzler, Northwestern Subject: Topological field theory in two dimensions and Teichmueller 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 8, 2008 Event: Institute of Applied Mathematics Seminar Speaker: Neil Balmforth, Department of Mathematics and Department of Earth and Ocean Sciences, UBC Subject: Continual Skipping on Water'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Skipping or skimming stones on water is a familiar pastime to many on the beach -- throwing a stone onto the water surface in such a way that the stone bounces as many times as possible before sinking. In this lecture I will describe whether it is possible to force an object to skip continually along the water surface by towing it at fixed speed. The fluid mechanics behind the phenomenon will be explored by building experimental and mathematical models. Along the way, we uncover connections to surfing, beach skimmers, seaplanes and bouncing bombs. Time and Date: 2:45-3:30 p.m., Wednesday, September 10, 2008 Event: PIMS Tea Location: West Mall Annex (WMAX), 1st Floor Lounge Graduate Students, Professors and Staff are cordially invited. Time and Date: 3:00-4:00 p.m., Wednesday, September 10, 2008 Event: Probability Seminar Speaker: Eugene Kritchevski, Department of Mathematics, UBC Subject: Poisson statistics of eigenvalues for random discrete Schrodinger operators'' Location: WMAX 216 (PIMS) Abstract: In this talk, I will consider random discrete Schrodinger operators of the form H= L+ c V acting on the Hilbert space l^2(X), where X is a given countable set endowed with a nice homogeneous structure: e.g. the lattice Z^d, a regular tree, or a hierarchical lattice. Here L is a given self-adjoint operator on l^2(X) e.g. the discrete or the hierarchical Laplacian, V is a random potential (Vf)(x)=v(x)f(x) with v(x) i.i.d. random variables, and c>0 is a coupling constant measuring the strength of the disorder. One is interested to understand the statistical behavior of the random eigenvalues of large finite volume approximations to H in the thermodynamic limit. In some cases it is possible to prove that, after a natural rescaling, the random eigenvalues behave as a Poisson point process. After reviewing the known results for the Anderson model on Z^d and for the regular tree, I will discuss my work on the hierarchical model. I will explain the mechanism responsible for Poisson statistics of eigenvalues and, if time permits, results on generic spectral localization. Time and Date: 3:00--4:00 p.m., Wednesday, September 10, 2008 Time of seminar has changed from 3:30 to 3:00 p.m. start. Event: Algebra/Topology Seminar Speaker: Jose Manuel Gomez, Department of Mathematics, UBC Subject:From fibered symmetric bimonoidal categories to Symmetric spectra, I'' Location: WMAX 110 (PIMS) Abstract: In this first talk of a two talk series I will explain the approach of Elmendorf and Mandell to the multiplicative theory of spectra. It is well known that for a permutative C, the classifying space BC is an E_\infty-space. In the case that C is a bipermutative category then BC is an E_\infty-ring space but situation is far more complicated. A new approach to this theory has been developed by Elmendorf and Mandell using the theory of multicategories. I will explain their construction. Time and Date: 3:00--3:50 p.m., Thursday, September 11, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Stephanie Treneer, University of Western Washington Subject: Arithmetic of the Fourier coefficients of modular forms'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: The Fourier coefficients of modular forms encode a wealth of arithmetic information. Techniques from the theory of modular forms have been used to prove the existence of linear congruences for the partition function and for several other arithmetic functions that are generated by weakly holomorphic modular forms. We will give general results about congruences for the coefficients of any weakly holomorphic modular form in a large class. We will also discuss weak Maass forms, and use them to derive new families of weakly holomorphic modular forms which encode information about the ranks of partitions. Time and Date: 4:10--5:00 p.m., Thursday, September 11, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Jonathan Bober, University of Michigan Subject: Integral ratios of factorials and related questions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: Motivated by the Beurling-Nyman criterion for the Riemann Hypothesis, Vasyunin studied the question of when certain linear combinations of floor functions are always nonnegative. This turns out to be equivalent to determining for which a_1...a_k and b_1...b_{k+1} the factorial ratio (a_1 n)!...(a_k n)! ----------------- (b_1 n)!...(b_{k+1} n)! is an integer for all n. I'll describe the complete classification of such a and b (there are 2 infinite families, and 52 sporadic solutions), and some related questions. The classification comes from the classification of monodromy groups for hypergeomtric functions, and also turns out to be related to the classification of cyclic quotient singularities. Time and Date: 2:45-3:00 p.m., Friday, September 12, 2008 Event: Mathematics Departmental Tea Location: Math Annex (MATX), 1115 Lounge Come join us for refreshments throughout the term before the 3:00 p.m. colloquium. Time and Date: 3:00 p.m., Friday, September 12, 2008 Event: Mathematics Colloquium Speaker: Prof. Chang-Shou Lin, Department of Mathematics, National Taiwan University Subject: Existence and uniqueness of solution to a mean field equation in two dimension at the critical parameter'' Location: MATX 1100 Time and Date: 3:00--4:00 p.m., Monday, September 15, 2008 Event: IAM Seminar Series Speaker: Paul Tupper, Department of Mathematics, SFU Subject: How Does Molecular Dynamics Work?'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: In computational physics, molecular dynamics refers to the computer simulation of a material at the atomic level. Given its scientific importance, there is very little rigorous justification of molecular dynamics. From the viewpoint of numerical analysis it is surprising that it works at all. The problem is that individual trajectories computed by molecular dynamics are accurate for only short time intervals, whereas researchers trust the results over very long time intervals. It has been conjectured that these long trajectories are accurate in some weak statistical sense. Another conjecture is that the numerical trajectories satisfy the shadowing property: that they are close to exact trajectories with different initial conditions. I will explain how these two views are actually equivalent to each other, after we suitably modify the concept of shadowing. Time and Date: 3:00--4:00 p.m., Monday, September 15, 2008 Event: Algebraic Geometry Seminar Speaker: Richard Thomas, Imperial College and Department of Mathematics, UBC Subject:Counting curves in threefolds'' Location: WMAX 110 (PIMS) Abstract: I will review 2 standard ways to count curves (in threefolds, mainly) -- Gromov-Witten theory and the Maulik-Nekrasov-Okounkov-Pandharipande count of subschemes -- and their defects. Then I'll explain a third way without these defects, and how it helps to define a fourth way -- the conjectural BPS counts of Gopakumar-Vafa. There is no fifth way. Joint work with Rahul Pandharipande. Time and Date: 12:30--2:00 p.m., Tuesday, September 16, 2008 Event: Scientific Computing and Applied & Industrial Mathematics Seminar Speaker: Robert Bridson, Computer Science, UBC Subject: Directly Solving Saddle Point Systems'' Location: WMAX 110 (PIMS) Abstract: Symmetric indefinite matrices continue to pose a challenge for linear solvers: how can the symmetric structure of the problem be exploited for higher efficiency and robustness? In this talk I'll look at an important class of such matrices, saddle-point (or KKT) problems that arise in a large number of applications: for example, constrained optimization, mixed finite elements, Stokes flow, constrained dynamics. In particular, I'll discuss a new strategy for directly solving such sparse systems using an LDL^T factorization, by introducing a simple a priori ordering constraint which can guarantee no need for numerical pivoting. This allows for highly efficient tools designed for positive definite matrices to be adapted to this more general class of problems. Time and Date: 3:30--4:30 p.m., Tuesday, September 16, 2008 Event: DG-MP-PDE Seminar Speaker: Yitzhak Weit, University of Haifa Subject: The mean value property of harmonic functions in weighted spaces'' Location: WMAX 110 Abstract: A class of radial measures mu on Rn is defined so that integrable harmonic functions f on Rn may be characterized as solutions of convolution equations f*mu = mu. In particular we show that f*exp(-x)= f is harmonic if and only if n<9. Time and Date: 2:45--3:15 p.m., Wednesday, September 17, 2008 Event: PIMS Afternoon Tea Location: WMAX, 1st Floor Lounge. Note: Refreshments including organic fruit and cookies will be served. Time and Date: 3:00-4:00 p.m., Wednesday, September 17, 2008 Event: Probability Seminar Speaker: Robert Masson, Department of Mathematics, UBC Subject: The growth exponent for loop-erased random walk'' Location: WMAX 216 (PIMS) Abstract: The loop-erased random walk is the process obtained by chronologically erasing loops from a random walk. The growth exponent for LERW is defined to be the number a such that the expected number of steps of a LERW from the origin to the circle of radius n grows like n^a. Using domino tilings to compute the number of uniform spanning trees of rectilinear regions in the plane, Rick Kenyon showed that the growth exponent for LERW on Z^2 is equal to 5/4. In this talk, I will give a new proof of this result using the convergence of LERW to SLE_2, valid for walks on more general lattices. I will then indicate how these techniques can be used to get estimates on the second moment of the number of steps and also give a sketch of an as yet incomplete argument showing the existence of the growth exponent in three dimensions. Time and Date: 3:00--4:00 p.m., Wednesday, September 17, 2008 Event: Algebra/Topology Seminar Speaker: Jose Manuel Gomez, Department of Mathematics, UBC Subject: From fibered symmetric bimonoidal categories to Symmetric spectra, II'' Location: WMAX 110 Abstract: It is well known that for a permutative C, the classifying space BC is an E_\infty-space. In the case that C is a bipermutative category then BC is an E_\infty-ring space but situation is far more complicated. A new approach to this theory has been developed by Elmendorf and Mandell using the theory of multicategories. I will explain their construction. Time and Date: 1:30--3:00 p.m., Thursday, September 18, 2008 Event: Seminar on Algebraic groups, Galois cohomology and related topics Speaker: Mark MacDonald, Department of Mathematics, UBC Subject: Introduction to Cohomological Invariants'' Location: MATX 1102 Time and Date: 2:00--3:00 p.m., Thursday, September 18, 2008 Event: Mathematical Biology Seminar Speaker: Gideon Ngwa, Department of Mathematics, University of Buea, Cameroon Subject: On the population dynamics of the malaria vector'' Location: WMAX 216 Abstract: A deterministic differential equation model for the population dynamics of the human malaria vector is derived and studied. Conditions for the existence and stability of a non-zero steady state vector population density are derived. These reveal that a threshold parameter, the vectorial basic reproduction number, exist and the vector can established itself in the community if and only if this parameter exceeds unity. When a non-zero steady state population density exists, it can be stable but it can also be driven to instability via a Hopf Bifurcation to periodic solutions, as a parameter is varied in parameter space. By considering a special case, an asymptotic perturbation analysis is used to derive the amplitude of the oscillating solutions for the full non-linear system. The present modelling exercise and results show that it is possible to study the population dynamics of disease vectors, and hence oscillatory behaviour as it is often observed in most indirectly transmitted infectious diseases of humans, without recourse to external seasonal forcing. In this communication, we derive and study a simple model for the dynamics of the human malaria vector based on the simple idea that the mosquito has a human biting habit. Since it is the mosquito that actively seeks and bites human beings, this assumption, which has been used successfully to model the dynamics of malaria transmission Ngwa et al. [1, 2, 3], may be seen as a restricted form of homogeneous mixing based on the idea that the mosquito has a human biting habit. The concept of the existence of a basic reproduction number, R0, in models has been addressed by Porphyre et al. [4], Diekmann et. al. [5]. In our formulation, R0 depends on a mass action contact rate tau* as well as on the probability of the mosquito obtaining a successful blood meal p in the sense that R0 goes to 0 whenever p goes to 0 or tau* goes to 0, and saturates to a positive non-zero value when p goes to 1 and tau* becomes infinite. [1] Ngwa, G.A., Modelling the dynamics of endemic malaria in growing populations. Discrete and Continuous Dynamical SystemsÐSeries B Vol 4 No. 4 (2004), 11731202. [2] Ngwa, G.A., Ngonghala, C. Ngeh and Sama Wilson, N.B, A model for endemic malaria with delay and variable populations. Journal of the Cameroon Academy of Sciences, Vol. 1 No. 3 (2001), 168-186. [3] Ngwa, G.A. and Shu, W.S., A mathematical model for endemic malaria with variable human and mosquito populations. Math. and Comp. Modelling, 32(7-8) (2000), 747763. [4] Porphyre T. Bicout D.J., Sabatier P., Modelling the abundance of mosquito vectors versus flooding dynamics. Ecological Modelling 183 (2005) 173-181. [5] Diekmann O., Heesterbeek J.A.P. and Metz J.A.J. On the definition and computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol. 28 (1990), 365-382. Time and Date: 3:00 p.m., Friday, September 19, 2008 Event: Mathematics Colloquium Speaker: Richard Thomas, Department of Mathematics, UBC Subject: Counting curves in threefolds'' 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 22, 2008 Event: IAM Seminar Series Speaker: Christoph Hauert, Department of Mathematics, UBC Subject: Spatial Dynamics of Ecological Public Goods'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Public goods model the production, consumption and exploitation of common resources ranging from extra-cellular products in microorganisms to global issues of climate change. Individuals can cooperate and sustain common resources at some cost or defect and exploit the resources without contributing. This generates a conflict of interest, which characterizes social dilemmas: individual selection favors defectors but for the community it is best if everybody cooperates. Traditional models of public goods do not take into account that benefits of the common resource enable cooperators to maintain higher population densities. This leads to a natural feedback between population dynamics and interaction group sizes as captured by 'ecological public goods'. Here we show that the spatial evolutionary dynamics of ecological public goods in 'reaction-diffusion' systems promotes cooperation based on different types of pattern formation processes. In spatial settings individuals can migrate (diffuse) in order to populate new territories. Slow diffusion of cooperators fosters aggregation in highly productive patches (activation), whereas fast diffusion enables defectors to readily locate and exploit these patches (inhibition). These antagonistic forces promote co-existence of cooperators and defectors in static or dynamic patterns, including spatial chaos of ever changing configurations. The local environment of cooperators and defectors is shaped by the production or consumption of common resources. Hence, diffusion-induced self-organization into spatial patterns not only enhances cooperation but also provides a simple mechanisms for the spontaneous generation of habitat diversity, which denotes a crucial determinant of the viability of ecological systems. Time and Date: 3:10--4:10 p.m., Monday, September 22, 2008 Event: Algebraic Geometry Seminar Speaker: Richard Thomas, Imperial College and Department of Mathematics, UBC Subject: Counting curves in threefolds - continued'' Location: WMAX 110 (PIMS) Abstract: I will review 2 standard ways to count curves (in threefolds, mainly) -- Gromov-Witten theory and the Maulik-Nekrasov-Okounkov-Pandharipande count of subschemes -- and their defects. Then I'll explain a third way without these defects, and how it helps to define a fourth way -- the conjectural BPS counts of Gopakumar-Vafa. There is no fifth way. Joint work with Rahul Pandharipande. Time and Date: 3:30--4:30 p.m., Tuesday, September 23, 2008 Event: DG-MP-PDE Seminar Speaker: Tobias Lamm, Department of Mathematics, UBC Subject: Superquadratic curvature functionals and approximation of the Willmore energy'' Location: WMAX 110 Abstract: Curvature functionals arise naturally in geometry, physics and biology. In this talk I will introduce the Willmore functional and supercritical modifications thereof. Then I will study the existence and regularity properties of the critical points of the supercritical functionals and I will show how one can use them to get a new proof of a result of Leon Simon on the existence of a minimizing Willmore torus. This is joint work with E. Kuwert and Y. Li. Time and Date: 2:45--3:15 p.m., Wednesday, September 24, 2008 Event: PIMS Afternoon Tea Location: WMAX, 1st Floor Lounge Time and Date: 3:00-4:00 p.m., Wednesday, September 24, 2008 Event: Probability Seminar Speaker: Shankar Bhamidi, Department of Mathematics, UBC Subject: Flows through Random Networks: Probabilistic and Statistical Problems'' Location: WMAX 216 (PIMS) Abstract: In the last few years with the availability of large amounts of data, there has been a lot of effort in coming up with Network models trying to explain "Real world" networks as well as in trying to model dynamic processes on these networks. In connection to the above consider the following 3 problems: 1. Edge flow problem: Given a connected network with edge costs, suppose each node sends a unit amount of flow to every other node via the least cost path. We are intersted in the amount of flow passing through various nodes and edges. What happens when the Network becomes large? Can we come up with a tractable math model giving us precise asymptotic information? 2. Price of Anarchy: Networks such as road networks, typically exhibit "selfish" behaviour in that there are a large number of agents each of whom try to move in the network maximizing their own utility, depending on the present congestion levels of the edges in the network. Suppose there was a central authority who could minimize some sort of global cost function and route traffic so that the "common good" is maximized. How much better of is the above central planning method compared to the selfish routing behavior? How can we make mathematical sense of the above problem? Further can we come up with some math model which gives us asymptotic results as the number of interacting agents becomes large? 3. Multicast tree problem: In a number of problems that arise from trying to discover the underlying structure of the Internet, often it is impossible to take direct measurements at the routers. We shall mention some initial progress in trying to reconstruct the "Multicast" tree using only "end-to-end " measurements. We shall give a brief overview of the above problems and state results from works in progress. In the last part of the talk we shall try to give the key probabilistic ideas that help us understand the edge flow problem in the model considered and the predictions for other locally tree like network models. Time and Date: 3:00--4:00 p.m., Wednesday, September 24, 2008 Event: Algebra/Topology Seminar Speaker: Jose Cantarero, Department of Mathematics, UBC Subject: Equivariant K-theory, groupoids and proper actions'' Location: WMAX 110 Abstract: The completion theorem of Atiyah and Segal relates the equivariant K-theory of a space with the K-theory of the Borel construction. In this talk, I will introduce a construction of equivariant K-theory for actions of Lie groupoids and show that there is a completion theorem under some circumstances. Some applications and examples will be given. Time and Date: 1:30--3:00 p.m., Thursday, September 25, 2008 Event: Seminar on Algebraic groups, Galois cohomology and related topics Speaker: Aurel Meyer, Department of Mathematics, UBC Subject: Introduction to cohomological invariants and essential dimension'' Location: MATX 1102 Time and Date: 2:00--3:00 p.m., Thursday, September 25, 2008 Event: Mathematical Biology Seminar Speaker: Heather Hardway, Department of Mathematics, Rice University Subject: Modeling Genetic Networks in the Fruit Fly'' Location: WMAX 216 Abstract: Over the past century, the Drosophila melanogaster (fruit fly) gene network has become one of the most studied and well understood. This is especially true of the genes involved in the anterior-posterior axis specification, the first step in spatially organizing the developing embryo. However, a new feature of this system was recently discovered: positional noise filtering. Gene products were shown to have high specificity with respect to positional location, despite receiving noisy information from upstream regulators. I will discuss reaction-diffusion models for this system and the results of a parameter search for such robust networks. In addition, I will present some unexpected nonlinear phenomenon possible in these gene networks, including tango waves in an activator-inhibitor system. Time and Date: 3:00--3:50 p.m., Thursday, September 25, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Tapani Matala-aho, University of Turku Subject: Arithmetic of q-series via Pade approximations'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: An interesting part of Number Theory is involved with a question of arithmetic nature of explicitly defined numbers. A brief report will be given to the linear independence question of q-series, taking the q-exponential function as a running example. Then we will discuss how the known explicit Padé approximants could be modified to produce sharp quantitative independence results. Time and Date: 4:10--5:00 p.m., Thursday, September 25, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Nils Bruin, SFU Subject: The congruent number problem for primes" Location: UBC Campus, WMAX 110 (PIMS) Abstract: Given an integer n, can we construct a right-angled triangle with rational sides that has exactly area n? This is a classical problem, which requires surprisingly deep mathematics. The problem was almost completely solved by work of Shimura and Tunnell. If we restrict to prime values for n, we can get some results via rather more elementary methods. I will explain how one can get these results and show how they can be extended. I will also discuss the limits of these generalizations. Time and Date: 4:00--5:00 p.m., Thursday, September 25, 2008 Event: Complex Fluids Seminar (Note special day and time, usual day/time is 12 p.m. Wednesdays) Speaker: Chul Park, Department of Mechanical and Industrial Engineering, University of Toronto Subject: Science and Technology of Microcellular Foaming'' Location: Chemical & Biological Engineering Bldg. Room 204 (CHBE, 2360 East Mall, UBC) Abstract: A continuous extrusion process for the manufacture of low-density microcellular polymers is presented. Microcellular polymers are foamed plastics characterized by a cell-population density greater than 10^9 cells/cm^3 and a fully grown cell size on the order of 10 microns. Microcellular polymers typically exhibit, if compared to non-foamed plastics, up to a five-fold higher impact strength, toughness, and fatigue life, as well as higher thermal stability, and lower thermal conductivity. The basic approach to the production of microcellular structures is to continuously form a polymer/gas solution, to nucleate a large number of bubbles using thermodynamic instability via a rapid pressure drop, to shape a nucleated polymer/gas solution under pressure, and to induce a volume expansion to a desired expansion ratio. Successful completion of these steps in extrusion will manufacture microcellular foamed plastics of a high cell-population density with superior mechanical properties. Several processing issues will be addressed in detail in the seminar: (a) the control of microcell nucleation in extrusion, (b) the control of cell growth to achieve a desired expansion ratio with CO_2 as a blowing agent, and (c) a strategy to prevent the deterioration of the cell population density via cell coalescence during expansion. The critical processing and materials parameters that affect the cellular morphology of microcellular foams will also be presented. By tailoring the processing conditions, microcellular foams with a cell-population density higher than 10^9 cells/cm^3 and a high volume expansion ratio up to 65 times have been successfully obtained from various polymeric materials. This research includes not only the basic science of the polymer/gas systems, but also the development of an industrially viable technology that exploits the full potential of the unique properties of microcellular plastics. Time and Date: 3:00 p.m., Friday, September 26, 2008 Event: Mathematics Colloquium Speaker: Eldad Haber, Department of Mathematics and Computer Science, Emory University, Atlanta, GA Subject:PDE constrained optimization'' 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 29, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Andrew Belmonte, Department of Mathematics, Pennsylvania State University Subject:Hydrodynamic Instabilities mediated by Active Interfaces'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Many fluid instabilities involving free surfaces are governed by interfacial forces - for instance surface tension. However, some materials have surface forces produced by active physical processes not present in the bulk fluid, such as forces due to the electric charge residing on the interface between conducting and insulating liquids. I will give an overview of these systems, and present recent experimental observations of instabilities due to such active or reactive interfaces: two Newtonian fluids which react to produce a fragile elastic material (during impact splashes or viscous fingering), and droplets of electrolyte solution in viscous nonconducting oil, for which oppositely charged drops do not always coalesce. Time and Date: 3:10--4:10 p.m., Monday, September 29, 2008 Event: Algebraic Geometry Seminar Speaker: Richard Thomas, Imperial College Subject:Counting curves in threefolds'' - continued Location: WMAX 110 (PIMS) Abstract: I will review 2 standard ways to count curves (in threefolds, mainly) -- Gromov-Witten theory and the Maulik-Nekrasov-Okounkov-Pandharipande count of subschemes -- and their defects. Then I'll explain a third way without these defects, and how it helps to define a fourth way -- the conjectural BPS counts of Gopakumar-Vafa. There is no fifth way. Joint work with Rahul Pandharipande. Time and Date: 12:30--2:00 p.m., Tuesday, September 30, 2008 Event: SCAIM Seminar Speaker: Kees van den Doel, Computer Science, UBC Subject:The Inverse Potential Problem'' Location: WMAX 110 Abstract: The inverse potential problem is to recover an electrical or gravitational source distribution on the interior of some domain from measurements of the potential on the boundary. This problem arises in electroencephalography (EEG), surface electromyography (sEMG), cardiology, and geophysics. This inverse problem is ill-posed, moreover an infinite number of solutions always exist, even under theoretically ideal conditions (infinite precision, complete boundary data, no data error). The problem thus needs to be regularized, and the choice of regularization selects the desired properties of the solution. In this talk I'll discuss applications to EMG and fast levelset methods for this problem. Time and Date: 2:00--3:00 p.m., Tuesday, September 30, 2008 Event: Discrete Mathematics Seminar Speaker: Joel Friedman, UBC Subject:Open Problems in Expanders'' Location: WMAX 110 Abstract: In this talk we will describe some of the main open problems in the field of expanding graphs, from the view point of eigenvalues of the graph's adjacency matrix. One of the main problems--are there (can one construct) d-regular Ramanujan graphs for any fixed d--has numerous interesting approaches. Time and Date: 12:00--1:00 p.m., Wednesday, October 1, 2008 Event: Complex Fluids Seminar Speaker: Chunfeng Zhou, Department of Chemical and Biological Engineering, UBC Subject:3D Phase-Field Simulations of Interfacial Dynamics in Newtonian and Viscoelastic Fluids'' Location: CHBE 204 (2360 East Mall) Abstract: We have developed a diffuse-interface algorithm for computing two-component interfacial flows of Newtonian and non-Newtonian fluids in 3D. An adaptive meshing scheme produces fine grid near the interface and coarse mesh in the bulk, and leads to accurate resolution of the interface at moderate computational cost. Another advantage of the method is that there is no need for manual intervention during topological changes of the interface such as rupture and coalescence. However, the fully implicit time-stepping results in a large matrix system for complex 3D flows, with high demands for memory and CPU speed. As validating examples, we discuss a drop spreading on a partially wetting substrate and drop deformation in Newtonian and viscoelastic fluids. The results show very good agreement with those from the literature and our own 2D axisymmetric simulations. Time and Date: 3:00-4:00 p.m., Wednesday, October 1, 2008 Event: Probability Seminar Speaker: Pierluigi Falco, UBC Subject:Extended Scaling Relations for the Eight Vertex and Ashkin Teller models'' Location: WMAX 216 (PIMS) Abstract: The critical, nonuniversal properties of the Eight Vertex, Ashkin-Teller and XYZ models are widely expected to be described by the quantum field theory obtained as a formal scaling limit. On the basis of this assumption, Kadanoff, Luther and Peschel conjectured universal scaling formulae that connect the nonuniversal critical indices. So far these conjectures have remained unproven. We present a constructive, renormalization-group approach that allows us to prove some of them under the condition of small coupling. Time and Date: 3:00--4:00 p.m., Wednesday, October 1, 2008 Event: Algebra/Topology Seminar Speaker: Dan Ramras, Vanderbilt University Subject:Periodicity in Deformation K-theory'' Location: WMAX 110 Abstract: The deformation K-theory spectrum K(G) of a discrete group G serves as a homotopy theoretical analogue of the ordinary representation ring R(G). In all known cases, K(G) is 2-periodic above some degree (when the classifying space BG is compact, these periodic groups often agree with complex K-theory of BG, but not always!). Work of Tyler Lawson relates this periodicity phenomenon to the topology of the stable moduli space of representations. I'll explain Lawson's results, and describe several examples of periodicity that can be derived using them. These include fundamental groups surfaces (where gauge theory also plays a key role), and, more generally, certain surface bundles over surfaces. Time and Date: 2:00--3:00 p.m., Thursday, October 2, 2008 Event: Seminar on Algebraic groups, Galois cohomology and related topics Speaker: Max Lieblich, Princeton University Subject:Recent progress on the period-index problem'' Location: WMAX 110 (Note: unusual location) Abstract: The period-index problem is a classical problem on the complexity of division algebras over fields (or, via the work of Brosnan, Reichstein, and Vistoli, on the essential dimensions of certain algebraic stacks). In the case of function fields, this problem has an appealing geometric avatar which ties it to the properties of moduli spaces of sheaves on Deligne-Mumford stacks (including the stacks of roots familiar from work of Cadman). I will review some of what is known about this problem and then discuss recent progress using geometric techniques. Time and Date: 2:00--3:00 p.m., Thursday, October 2, 2008 Event: Mathematical Biology Seminar Speaker: Caz Taylor, Centre for Wildlife Ecology, SFU Subject:Finding optimal behavior using decision rules in an individual-based model'' Location: WMAX 216 Abstract: We describe a modeling approach in which individuals are able to use information about their state and the environment to formulate behavioural rules that optimize fitness. We model the decision probability as a function of weighted input or state variables. We then use a search optimization algorithm (simulated annealing) to find the rule weights so that a series of decisions made by an individual maximize a known fitness function. The advantage of this individual rule-based approach is that we can optimize behaviour in an environment that includes complex interactions, such as density-dependence. We apply this approach to the migration behavior of Western Sandpipers (Calidris mauri), moving sequentially through a set of stopover sites along the North American Pacific coast and optimizing arrival time at the breeding grounds. The departure probability of each individual at each stopover site is a function of four state variables (i) whether or not the individual is on time, (ii) the individual fuel load, (iii) availability of food, and (iv) risk of predation. The latter two variables depend not only on the individual but on the density of conspecifics and therefore on the behavior of all other individuals. We investigate how different types of density dependence affects the patterns of migration. Time and Date: 3:00 p.m., Friday, October 3, 2008 Event: Mathematics Colloquium Speaker: Andreas Seeger, University of Wisconsin-Madison Subject:Radial Fourier multipliers and the wave equation'' 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 6, 2008 Event: IAM Seminar Series Speaker: Bernard Deconinck, Department of Applied Mathematics, University of Washington Subject:Stability of Stationary Periodic Solutions of Nonlinear Wave Equations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The stability of solitary wave solutions of nonlinear wave equations has been extensively studied over the last few decades. Recently, there has been increasing interest in studying the stability of the periodic counterparts of these solitary wave solutions. This has been facilitated by the development of new numerical techniques, as well as an improved understanding of the analysis required to approach these questions. Some of each will be discussed in this talk. I will discuss Hill's method, which is a numerical method to compute spectra of linear operators, and convergence results we have been able to prove for it. Then I will discuss the stability of periodic solutions of integrable equations such as the KdV and NLS equations, emphasizing the complete results that may be obtained. Time and Date: 3:10--4:10 p.m., Monday, October 6, 2008 Event: Algebraic Geometry Seminar Speaker: Ralph Cohen, Stanford University Subject:String Topology and its applications: a status report'' Location: WMAX 110 (PIMS) Abstract: As the title suggests, I'll talk about what's new in string topology, its relation to Floer theory and symplectic theory in general, and questions that remain. Time and Date: 2:00--3:00 p.m., Tuesday, October 7, 2008 Event: Discrete Maths Seminar Speaker: Thomas Prellberg, Queen Mary, University of London and Libra Visiting Professor of Diversity, University of Maine Subject:Walks in Wedges and Crossings of Matchings'' Location: WMAX 110 Abstract: We consider a model of partially directed walks from the origin in the square lattice confined to a symmetric wedge defined by Y = ±X. We derive a functional equation for the generating function of the model, and obtain an explicit solution using a version of the Kernel method. This solution shows that there is a direct connection with matchings of an 2n-set counted with respect to the number of crossings, and two bijective proofs have since been obtained. Time and Date: 3:00-4:00 p.m., Wednesday, October 8, 2008 Event: Probability Seminar Speaker: Vieri Mastropietro, University of Rome - Tor Vergata Subject:The Hubbard model on the square and honeycomb lattice by functional integral methods'' Location: WMAX 216 (PIMS) Abstract: We present some results on the planar Hubbard model on the square and the honeycomb lattice in the weak coupling regime. The Schwinger functions are expressed in terms of fermionic Grassmann integrals and analyzed by by constructive Renormalization Group methods. Time and Date: 3:00--4:00 p.m., Wednesday, October 8, 2008 Event: Algebra/Topology Seminar Speaker: Ian Hambleton, McMaster University Subject:Equivariant CW-Complexes and group actions on sphere'' Location: WMAX 110 Abstract: In the talk I will describe a general framework for studying an open problem: which finite groups of rank 2 can act on spheres with rank 1 isotropy? The idea is to construct periodic projective resolutions over the orbit category, based on work of Tom Dieck and Lueck, and then to prove a realization theorem to obtain a geometric action with prescibed isotropy. As an application, we show that the symmetric group G=S_5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups. (joint work with Semra Pamuk and Ergun Yalcin) Time and Date: 12:30--1:30 p.m., Thursday, October 9, 2008 Event: Graduate Seminar Speaker: Alex Duncan, UBC Subject:Cubic Surfaces'' Location: MATH 104 Note: Pizza and pop provided. Abstract: This will be a fairly informal exposition of smooth cubic hypersurfaces in space. These surfaces have many beautiful properties. They can always be described as a blow-up of six points (in "general position") on 2-dimensional projective space. Also, there are the famous 27 lines sitting inside the surface. The automorphisms of cubic surfaces are related to permutations of these lines and the Weyl group of E_6. The talk should be accessible to anyone, concepts like blow-ups and projective spaces will be introduced as needed. Time and Date: 1:30--3:00 p.m., Thursday, October 9, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Jean Fasel, Department of Mathematics, UBC Subject:Introduction to Witt rings'' Location: MATX 1102 Time and Date: 2:00--3:00 p.m., Thursday, October 9, 2008 Event: Mathematical Biology Seminar Speakers: Sally Otto and Rich FitzJohn, Department of Zoology, UBC Subject:Inferring the past for traits that alter speciation and extinction rates'' Location: WMAX 216 Abstract: We will describe work by ourselves and co-authors Wayne Maddison and Peter Midford to build a likelihood-based approach to infer how speciation and extinction rates depend on the state of a particular character. The phylogenetic tree of a group of species contains information about character transitions and about diversification: higher speciation rates, for example, give rise to shorter branch lengths. The likelihood method that we have developed uses all of the information contained in a phylogeny and integrates over all possible evolutionary histories to infer the speciation and extinction rates for species with different character states. Our method can be used to provide more detailed information than previous methods, allowing us to disentangle whether a particular character state is rare because species in that state are prone to extinction, are unlikely to speciate, or tend to move out of that state faster than they move in. Time and Date: 3:00--3:50 p.m., Thursday, October 9, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Michael Coons, SFU Subject:(Non)automaticity of number-theoretic functions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: Denote by \lambda(n) Liouville's function concerning the parity of the number of prime divisors of n. Using a theorem of Allouche, Mend\es France, and Peyri\ere, we prove that \lambda(n) is not k--automatic for any k\geq 2. This yields that \sum_{n=1}^\infty \lambda(n) z^n\in\mathbb{F}_p[[z]] is transcendental over \mathbb{F}_p(z) for any prime p. Similar results are proven (or reproven) for many common number--theoretic functions, including \varphi, \mu, \Omega, \omega, \rho, and others. Time and Date: 4:10--5:00 p.m., Thursday, October 9, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Jason Bell, SFU Subject:The dynamical Mordell-Lang problem'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: We look at the following problem: Let X be a quasi-projective complex variety and let \sigma be an endomorphism of X. If x\in X and Y is a subvariety of X, what can be said about the intersection of the orbit of x under \sigma with Y. As it turns out, it many cases we can infer that either the intersection must be either finite or Y has a subvariety that is stable under some iterate of \sigma. We apply this theorem in a few different settings. This is joint work with Dragos Ghioca and Tom Tucker. Time and Date: 3:00 p.m., Friday, October 10, 2008 Event: Mathematics Colloquium Speaker: Ozgur Yilmaz, UBC Subject: Sparse recovery via non-convex optimization'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m.(MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, October 14, 2008 Event: SCAIM Seminar Speaker: Hui Huang, Computer Science, UBC Subject:Efficient Reconstruction of 2D Images and 3D Surfaces" Abstract: The goal of this thesis is to gain a deep understanding of inverse problems arising from 2D image and 3D surface reconstruction, and to design effective techniques for solving them. Both computational and theoretical issues are studied and efficient numerical algorithms are proposed. The first part of this thesis is concerned with the recovery of 2D images, e.g., denoising and deblurring. We first consider implicit methods that involve solving linear systems at each iteration. An adaptive Huber regularization functional is used to select the most reasonable model and a global convergence result for lagged diffusivity is proved. Two mechanisms---multilevel continuation and multigrid preconditioning---are proposed to improve efficiency for large-scale problems. Next, explicit methods involving the construction of an artificial time-dependent differential equation model followed by forward Euler discretization are analyzed. A rapid, adaptive scheme is then proposed, and additional hybrid algorithms are designed to improve the quality of such processes. We also devise methods for more challenging cases, such as recapturing texture from a noisy input and deblurring an image in the presence of heavy noise. It is well-known that extending image processing methods to 3D triangular surface meshes is far from trivial or automatic. In the second part of this thesis we discuss techniques for faithfully reconstructing such surface models with different features. Some models contain a lot of small yet visually meaningful details, and typically require very fine meshes to represent them well; others consist of large flat regions, long sharp edges (creases) and distinct corners, and the meshes required for their representation can often be much coarser. All of these models may be sampled very irregularly. For models of the first class, we methodically develop a fast multiscale anisotropic Laplacian (MSAL) smoothing algorithm. To reconstruct a piecewise smooth CAD-like model in the second class, we design an efficient hybrid algorithm based on specific vertex classification, which combines K-means clustering and geometric a priori information. Hence, we have a set of algorithms that efficiently handle smoothing and regularization of meshes large and small in a variety of situations. Speaker: Zhenguo Pan, Mathematics, UBC Subject:Simulation and Analysis of Coupled Surface and Grain Boundary Motion'' Abstract: A coupled surface and grain boundary motion that arises in materials science is considered. A formulation that describes the coupled motion and preserves arc length parametrization up to scaling is proposed. Numerical results and other related topics are discussed as well. Location: WMAX 110 (PIMS) Time and Date: 2:00--3:00 p.m., Tuesday, October 14, 2008 Event: Discrete Maths Seminar Speaker: Paul Ottaway, Dalhousie University and Department of Mathematics, UBC Subject:A brief and selective history of combinatorial game theory'' Location: WMAX 110 Abstract: I will give a brief history of the study of games with a focus on the development of Combinatorial Game Theory (CGT) a la Conway. I will present the material with some mathematical interludes and conclude with a short selection of open problems in the field. Time and Date: 3:30--4:30 p.m., Tuesday, October 14, 2008 Event: DG-MP-PDE Seminar Speaker: Weiyong He, Department of Mathematics, UBC Subject:The space of volume forms'' Location: WMAX 110 Abstract: Donaldson introduced a metric and a geometric structure on the space of volume forms on any compact Riemannian manifold. The geodesic equation is a degenerate fully nonlinear elliptic equation. Also this equation is relevant to many interesting problems such as Namh's equation and some interesting free boundary equations. Also the space of volume forms coincides with the conformal class, the probability space. In this talk we try to solve the geodesic equation and its perturbation equation also. This is a joint work with X. Chen. Time and Date: 12:00--1:00 p.m., Wednesday, October 15, 2008 Event: Complex Fluids Seminar Speaker: Guillaume Carazzo, Department of Mathematics, UBC Subject:The catastrophic eruption of Mt Vesuvius (AD 79): how a little bit of fluid dynamics could have saved the inhabitants of Pompei'' Location: CHBE 204 (2360 East Mall) Abstract: Explosive volcanic eruptions are among the most powerful and dangerous turbulent flows on Earth. The outcome of such eruptions is particularly difficult to predict as a result of the unusual dynamics that allow the jet to form a high buoyant plume that may or may not collapse and create dense pyroclastic flows. Quantitative prediction of the behavior of explosive eruption columns is a major challenge for physical volcanology. Analyses of past and historical eruptions provide important constraints on theoretical models. The catastrophic eruption of Mount Vesuvius volcano (Italy) in AD79 is famously responsible for the destruction of Pompei, but it also represents an excellent example of the unsteady behavior of sustained explosive columns. After a brief review of the sequence of events that occurred during this eruption and their consequences, a simple theoretical model of a turbulent jet is proposed. The comparison of this model with field data suggests that the column collapse responsible for the death of 2,000 people could have been predicted at least 5 hours before the catastrophe. Time and Date: 3:00-4:00 p.m., Wednesday, October 15, 2008 Event: Probability Seminar Speaker: Xinghua Zheng, Department of Mathematics, UBC Subject:Critical Branching Random Walks and Spatial Epidemics'' Location: WMAX 216 (PIMS) Abstract: Watanabe's Theorem asserts that the measure-valued processes associated with a sequence of critical branching random walks, under suitable assumptions and after rescaling, converge to a super-Brownian motion \{X_t\}. There has been extensive study of the closed support of the measure X_t. In particular, it is known that when d \geq 3, for any fixed time t>0, the measure can be recovered from its support (Perkins(1989)) and the measure spreads its mass over the support in a fairly uniform manner (Perkins(1988)). We will discuss analogous results about branching random walks in 2 or higher dimensions via the study of the following occupation statistics: the maximal number of particles at a single site, the number of multiplicity-j sites, the number of particles at a typical'' site, and the number of occupied sites. We will then focus on the 2 or 3 dimensional case. We show that the local time processes associated with branching random walks, under suitable scaling, converge to the local time density process associated with the limiting super-Brownian motion. This establishes a conjecture due to Adler (1993). Finally we will talk about spatial SIR epidemics. In these models, finite populations of size N are situated at the sites of the integer lattice. Based on the local time convergence result, we show that the measure-valued processes associated with these epidemics, suitably scaled, converge, in the large-N limit, either to a standard Dawson-Watanabe process (super-Brownian motion) or to a Dawson-Watanabe process with density-dependent killing, depending on the size of the the initially infected set. Based on joint work with Steven Lalley. Time and Date: 3:00--4:00 p.m., Wednesday, October 15, 2008 Event: Algebra/Topology Seminar Speaker: Rick Jardine, Department of Mathematics, UWO Subject:Path categories and concurrency'' Location: WMAX 110 Abstract: The path category P(K) of a simplicial complex K is a category which is built from vertices (objects) and 1-simplices (morphisms), subject to commutativity conditions associated to the 2-simplices of K. This construction extends to a functor from simplicial sets to categories which is left adjoint to the nerve. Here is why one cares: path category morphisms specialize to execution paths in higher dimensional automata. These objects are geometric models for behaviour of parallel processing systems, and techniques are required to distinguish execution paths between states in such a system. This calculational problem is non-trivial, since the path category functor is not a standard homotopy invariant and produces categories with little extra structure. The known viable lines of attack arise from higher category theory and homotopy coherence theory. Time and Date: 4:00--5:00 p.m., Wednesday, October 15, 2008 Event: Algebra/Topology Seminar Speaker: Jesper Grodal, University of Copenhagen Subject:TBA'' Location: WMAX 110 Time and Date: 1:30--3:00 p.m., Thursday, October 16, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Jean Fasel, Department of Mathematics, UBC Subject:Gersten complexes'' Location: MATX 1102 Time and Date: 2:00--3:00 p.m., Thursday, October 16, 2008 Event: Mathematical Biology Seminar Speaker: Scott Grandison, John Innes Centre and University of East Anglia, Norwich Subject:It's tough at the tip: Mechanical models of polar growth'' Location: WMAX 216 Abstract: From cell morphogenesis to protein docking, shape and shape dynamics have a vital role to play in our understanding of biological systems. In this talk we will discuss a novel method for extracting important shape information based on image processing, minimum energy surfaces and the calculus of variations which allows us to infer some of the mechanical properties of a tip growing Arabidopsis root hair from time-lapse image data. We have developed a computer simulation, based on a network of interconnected springs which enable our formulation to be validated against further experimental data. Time and Date: 3:00 p.m., Friday, October 17, 2008 Event: Mathematics Colloquium Speaker: Yue-Xian Li, UBC Subject: Modeling Hormonal Rhythms in a Network of Endocrine Neurons'' 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 20, 2008 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Michael Shelley, Department of Mathematics, Center for Neural Science and the Courant Institute Applied Mathematics Laboratory, New York University Subject:Transport and Mixing in Complex Fluids'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Fluids with suspended microstructure – complex fluids – are common in micro- and biofluidics and can have fascinating dynamical behaviors. I will overview modeling and simulation studies of transport and mixing in complex fluids. These studies will illustrate how microscopic fibers can become random walkers by dint of their internal degrees of freedom, how intrinsic oscillations of a driven viscoelastic fluid can mix a fluid at low Reynolds number, and how hydrodynamically mediated interactions among many small swimmers can drive, or damp out, large-scale roiling flows. Time and Date: 3:10--4:10 p.m., Monday, October 20, 2008 Event: Algebraic Geometry Seminar Speaker: Eric Zaslow, Northwestern University Subject:The Fukaya Category and Microlocalization'' Location: WMAX 110 (PIMS) Abstract: Morse theory is a way of studying the topology of a manifold through the structure of gradient flow trajectories of a function. The Fukaya category can be thought of as Morse theory on the space of paths between Lagrangian submanifolds of a symplectic space such as a cotangent bundle. (The Lagrangian submanifolds are the objects of the category.) Morse theory is also instrumental in the study of the topology of a manifold through its constructible sheaves. In such a context, passing to the cotangent bundle and Lagrangian submanifolds is called "microlocalization." Thus microlocalization and Morse theory would appear to relate constructible sheaves to the Fukaya category. My aim in these talks is to describe two theorems. One (microlocalization) equates the Fukaya category of the cotangent bundle of a manifold to the category of constructible sheaves on the manifold. The other (T-duality) is an application of microlocalization to mirror symmetry for projective toric varieties. Time and Date: 3:00-4:00 p.m., Wednesday, October 22, 2008 Event: Probability Seminar Speaker: David Brydges, UBC Subject:A combinatorial generalisation of Cramer's rule'' Location: WMAX 216 (PIMS) Abstract: We review a result of G.X. Viennot, Lecture Notes in Mathematics, #1234, and comment on its significance for statistical mechanics: a ratio of generating functions for disjoint oriented loops in a finite graph can be expressed in terms of the generating function of a single path in the graph weighted according to loops in the path, where the loops are defined by the same algorithm as in loop erased random walk. The result is a generalisation of Cramer's formula for the inverse of a matrix. Time and Date: 12:30--1:30 p.m., Thursday, October 23, 2008 Event: Mathematics Graduate Seminar Speaker: David Kohler, Department of Mathematics, UBC Subject:The Strong Law of Small Numbers'' Location: MATH 104 Abstract: Introduced by Gardner in 1980 and then by Guy in 1988, the strong law of small numbers states that "there aren't enough small numbers to meet the many demands made of them". We will have a look at some of the many examples provided by Guy to illustrate the law, everyone will be asked wether the shown pattern persists or not. This talk is intended to be amusing and light, absolutely no technical knowledge will be needed, anyone is welcomed! Time and Date: 2:00--3:00 p.m., Thursday, October 23, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Mark MacDonald, Department of Mathematics, UBC Subject:Cohomological invariants of orthogonal groups'' Location: MATX 1102 Time and Date: 3:00--3:50 p.m., Thursday, October 23, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: John Garza, Kansas State University Subject:An optimal solution to a problem concerning the Mahler measure of polynomials'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: This talk concerns Lehmer's Mahler measure problem. It follows from results of Amoroso that the height of algebraic numbers different from zero and the roots of unity contained in dihedral extensions of the rationals is bounded below by 3^{-14}. I have identified the lowest Mahler measure amongst such numbers. I will discuss this result and propose some new problems. I will also discuss Charles Samuel's recent work concerning lower bounds on the projective heights of algebraic points and a possible improvement to his work. Time and Date: 4:10--5:00 p.m., Thursday, October 23, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Imin Chen, SFU Subject:Perfect powers expressible as sums of two cubes'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: Kraus showed that the equation x^3 + y^3 = z^p has no non-trivial primitive solutions for 17 <= p < 10^4 using a computational criterion based on the modular method. Together with work of Bruin and Dahmen, the exponents 3 <= p < 10^4 could be resolved. I will report on recent joint work with Siksek which show one can use Brauer-Manin type obstructions on an associated hyperelliptic curve to resolve, for instance, exponents p = 2,3 (mod 5). The ideas are based on previous work of Siksek and obstructions inspired from classical descent. Time and Date: 3:00 p.m., Friday, October 24, 2008 Event: Mathematics Colloquium Speaker: Eric Cytrynbaum, UBC Subject: Models of cell division in bacteria'' 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 27, 2008 Event: IAM Seminar Series Speaker: Eric Shea-Brown, Department of Applied Mathematics, University of Washington Subject:Dynamics of Correlation and Coding in Simple Neural Circuits'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Correlations among neural spike times are ubiquitous, and questions of how these correlations develop, and of the impact they have on the neural code, are central in neuroscience. Their analysis also poses rich applied mathematics problems. We address two of the most basic ones here. First, we ask: How do correlations among different neurons depend on the cells' operating range - their rate and regularity of spiking? We use both linear response calculations and in vitro experiments to show that correlations between pairs of neurons vary sharply with their firing rates, almost universally. We illustrate the consequences via Fisher information, which quantifies the accuracy of encoding. Next, we ask: How do correlations among different trials depend on architecture of neural circuits? (Here, the same stimulus is received by the circuit on each 'trial.') We take a first step toward the answer by identifying a surprising role for some, but not all, feedback connections in creating unreliable (and hence decorrelated) responses, a phenomenon which we quantify via Lyapunov exponents. This is joint work with Jaime de la Rocha, Brent Doiron, Kreso Josic, Kevin Lin, Alex Reyes, and Lai-Sang Young. Time and Date: 3:10--4:10 p.m., Monday, October 27, 2008 Event: Algebraic Geometry Seminar Speaker: Eric Zaslow, Northwestern University Subject:The Fukaya Category and Microlocalization II'' Location: WMAX 110 (PIMS) Abstract: Morse theory is a way of studying the topology of a manifold through the structure of gradient flow trajectories of a function. The Fukaya category can be thought of as Morse theory on the space of paths between Lagrangian submanifolds of a symplectic space such as a cotangent bundle. (The Lagrangian submanifolds are the objects of the category.) Morse theory is also instrumental in the study of the topology of a manifold through its constructible sheaves. In such a context, passing to the cotangent bundle and Lagrangian submanifolds is called "microlocalization." Thus microlocalization and Morse theory would appear to relate constructible sheaves to the Fukaya category. My aim in these talks is to describe two theorems. One (microlocalization) equates the Fukaya category of the cotangent bundle of a manifold to the category of constructible sheaves on the manifold. The other (T-duality) is an application of microlocalization to mirror symmetry for projective toric varieties. Time and Date: 12:30--2:00 p.m., Tuesday, October 28, 2008 Event: SCAIM Seminar Speaker: Jan Modersitzki, Department of Computing and Software, McMaster University Subject:A Numerical Perspective on Image Processing'' Location: WMAX 110 Abstract: Image registration is a central problem in image processing. The objective is to automatically establish correspondences between two images. Particularly in medical imaging, registration is essential to motion correction, treatment verification, navigation, or image fusion, the integration of information from different devices. Today's most general approaches are based on a variational setting that allows a combination of different building blocks like distance measures, regularizer, and constraints. Central problems in registration are the identification of application conform building blocks, its ill-posedness, the efficient numerical treatment, and the validation of results. The talk introduces to image registration and addresses the above problems exemplarily on a variety of real-life examples. Emphasis is given to numerical approaches that lead to high dimensional constrained optimization problems. Time and Date: 2:00--3:00 p.m., Tuesday, October 28, 2008 Event: Discrete Maths Seminar Speaker: Juanjo Rue, Universitat Politecnica de Catalunya, Barcelona Subject:A question of Sarkozy and Sos on bilinear forms and generalisations'' Location: WMAX 110 Abstract: This talk deals with a problem on combinatorial number theory. More concretely, we prove that if 2 <= k_1 <= k_2, then there is no infinite sequence A of positive integers such that the representation function r(n) = #{ (a, a') : n = k_1 a + k_ 2a': a, a' \in A} is constant for n large enough. This result completes previous work of Dirac and Moser for the special case k_1 = 1 and answers a question posed by Sarkozy and Sos. We present also an sketch of the proof for the related problem concerning the families k_1 A+....+k_n A with the natural condition (k_i,k_j)=\delta_{i,j}, k_i \neq 1. This is a joint work with Javier Cilleruelo, from Universidad Autonoma de Madrid. Time and Date: 3:30--4:30 p.m., Tuesday, October 28, 2008 Event: DG-MP-PDE Seminar Speaker: Nassif Ghoussoub, UBC Subject:On a MEMS model involving a fourth order elliptic equation'' Location: WMAX 110 Time and Date: 12:00--1:00 p.m., Wednesday, October 29, 2008 Event: Complex Fluids Seminar Speaker: Professor R. Sureshkumar, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis Subject:Flow-Induced Structure Transition in Surfactant Solutions'' Location: CHBE 204 (2360 East Mall) Abstract: It is well known that translucent solutions containing rodlike (length ~ 10 nm) surfactant micelles self-organize under flow to form viscoelastic gels. Flow-induced structure (FIS) formation has excited much fundamental research and pragmatic interest as a cost-effective manufacturing route for active nanomaterials. However, its practical impact has been very limited since to date all reported FIS transitions are reversible since the gel disintegrates within seconds after flow stoppage. Further, the gel-solution interface is highly unstable and often fluctuate chaotically. We will first summarize our recent work on reversible gelation (Vasudevan et al. J. Rheol. 2008). We will then present a novel microfluidics-assisted robust laminar process, which allows for the generation of extension rates many orders of magnitude greater than that is realizable in conventional devices, to produce purely flow-induced, i.e., without the addition of external agents, permanent nanogels. Atomic force microscopy of the gel reveals highly aligned micelles with short-range order. Experimental conditions under which gelation occurs compare well with the predictions of Turner and Cates (J. Phys: Condens. Matter, 4, 3719 (1992)). Time and Date: 3:00-4:00 p.m., Wednesday, October 29, 2008 Event: Probability Seminar Speaker: Eric Fusy, Department of Mathematics, UBC Subject:Probabilistic algorithms to estimate the cardinality of large multisets'' Location: WMAX 216 (PIMS) Abstract: A multiset is a set where each element can appear many times, its cardinality n is the number of distinct elements. The problem of computing n has many applications in computer science (e.g. estimate the number of distinct connections on a server), the difficulty being that the multiset is often too large to be stored. I will explain how probabilistic methods make it possible to precisely estimate n without storing the multiset and with very little auxiliary memory. Time and Date: 2:00 p.m., Thursday, October 30, 2008 Event: SCAIM Seminar (Note unusual day.) Speaker: Jie Shen, Department of Mathematics, Purdue University Subject:Modeling and simulation of multiphase incompressible flows using an energetic variational phase field model'' Location: WMAX 110 Abstract: I shall present an energetic variational phase field model for multiphase incompressible flows which leads to a set of coupled nonlinear system consisting a phase equation and the Navier-Stokes equations. I shall present efficient and accurate numerical schemes for solving this coupled nonlinear system, and show ample numerical results (drop formation and pitching-off, defect motion in liquid crystal flow, etc.) which not only demonstrate the effectiveness of the numerical schemes, but also validate the flexibility and robustness of the phase-field model. Time and Date: 2:00--3:00 p.m., Thursday, October 30, 2008 Event: Mathematical Biology Seminar Speaker: Jana Gevertz, Department of Mathematics, Princeton University Subject:Multi-scale Mathematical Modeling of Heterogeneous Tumor Growth'' Location: WMAX 216 Abstract: An in silico tool that can be utilized in the clinic to predict neoplastic progression and propose individualized treatment strategies is the holy grail of computational tumor modeling. As we have the long-term goal of developing such a simulation tool, we have worked over the years to address a number of tumor-related questions using variations of one theoretical model. In this talk, I will focus on both the implementation of, and the results drawn from, several of the model variants. Questions we have addressed through our modeling efforts include: 1. How do we develop a minimalistic quantitative model of tumor progression? 2. What effects do organ geometry and topology have on tumor size, shape and spread? 3. How does an evolving vasculature impact tumor dynamics? 4. What effects do genetic mutations have on patient prognosis? After looking at a set of model variants that allows us to answer each of these questions, I talk about recent efforts to merge these models into one comprehensive cancer simulation tool. I use the merged model to highlight biological features that must be considered in a clinically-relevant tumor growth algorithm and to test the impact of vascular-targeting treatment strategies. Time and Date: 3:00 p.m., Friday, October 31, 2008 Event: Mathematics Colloquium Speaker: Professor Jie Shen, Department of Mathematics, Purdue University Subject: Fast Spectral-Galerkin Method: Algorithms, Analysis and Applications'' 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 3, 2008 Event: IAM Seminar Series Speaker: Professor J.F. Williams, Department of Mathematics, SFU Subject:(In-)Stability of Finite-Time Singularities in the Harmonic Map Heat Flow'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behaviour of singularities arising in this heat flow. While blow-up is known to occur for radially symmetric equivariant solutions, we investigate stability for blow-up in a wider class. We also extend this asymptotic analysis to the case of the Landau-Lifshitz-Gilbert equation of micro-magnetics where we show that blow-up must occur but that it is unstable. This is joint work with Jan Bouwe van den Berg. Time and Date: 3:10--4:10 p.m., Monday, November 3, 2008 Event: Algebraic Geometry Seminar Speaker: Eric Zaslow, Northwestern University Subject:The Fukaya Category and Microlocalization III'' Location: WMAX 110 (PIMS) Abstract: Morse theory is a way of studying the topology of a manifold through the structure of gradient flow trajectories of a function. The Fukaya category can be thought of as Morse theory on the space of paths between Lagrangian submanifolds of a symplectic space such as a cotangent bundle. (The Lagrangian submanifolds are the objects of the category.) Morse theory is also instrumental in the study of the topology of a manifold through its constructible sheaves. In such a context, passing to the cotangent bundle and Lagrangian submanifolds is called "microlocalization." Thus microlocalization and Morse theory would appear to relate constructible sheaves to the Fukaya category. My aim in these talks is to describe two theorems. One (microlocalization) equates the Fukaya category of the cotangent bundle of a manifold to the category of constructible sheaves on the manifold. The other (T-duality) is an application of microlocalization to mirror symmetry for projective toric varieties. Time and Date: 12:30--2:00 p.m., Tuesday, November 4, 2008 Event: SCAIM Seminar Speaker: Christopher Batty, Computer Science, UBC Subject:A Variational MAC Method for Flows with Complex Boundaries'' Location: WMAX 110 Abstract: The classic MAC method established itself early on as an effective technique for simulating incompressible viscous flows, however its use was somewhat limited by the inability to handle boundaries that do not align with the underlying Cartesian grid. This talk will present progress towards overcoming this problem, by exploiting variational principles whose natural boundary conditions implicitly handle these difficult situations. This approach yields variational finite difference schemes that reproduce the traditional MAC stencils, with the exception that boundary conditions are expressed automatically by fractional volume weights on the stencils, rather than explicit special cases. We will discuss the pressure projection problem and the full unsteady Stokes problem, considering both solid and free surface boundaries, and present some preliminary convergence results. The method also simplifies solid-fluid coupling, allowing the simulation of fluid interactions with arbitrary kinematic and dynamic rigid bodies. Time and Date: 2:00--3:00 p.m., Tuesday, November 4, 2008 Event: Discrete Maths Seminar Speaker: Eric Fusy, UBC Subject:Decomposition and enumeration of planar graphs'' Location: WMAX 110 Abstract: I will review on a decomposition (described by Tutte in the book "Connectivity in Graphs") of a graph into 3-connected components. In the case of planar graphs, this decomposition yields, on one hand, an efficient exact enumeration procedure, and on the other hand (more recently), a precise asymptotic estimate for the number of planar graphs with n vertices. Time and Date: 3:30--4:30 p.m., Tuesday, November 4, 2008 Event: DG-MP-PDE Seminar Speaker: Mark Haskins, Imperial College Subject:Gluing Constructions of Special Lagrangians'' Location: WMAX 110 Time and Date: 12:00--1:00 p.m., Wednesday, November 5, 2008 Event: Complex Fluids Seminar Speaker: Vahid Bazargan, Dept. of Mechanical Engineering, UBC Subject:Micro Flow Control using Thermally Responsive Polymer Solutions'' Location: CHBE 204 (2360 East Mall) Abstract: Microfluidics refers to devices and methods for controlling and manipulating fluid flows at length scales less than a millimeter. Miniaturization of a laboratory to a small device, usually termed as lab-on-a-chip, is an advanced technology that integrates a microfluidic system including channels, mixers, reservoirs, pumps and valves on a micro scale chip and can manipulate very small sample volumes of fluids. While several flow control concepts for microfluidic devices have been developed to date, here flow control concepts based on thermally responsive polymer solutions are presented. In particular, flow control concepts base on the thermally triggered reversible phase change of aqueous solutions of the polymer Pluronic will be discussed. Selective heating of small regions of microfluidic channels, which leads to localized gel formation in these channels and reversible channel blockage, will be used to control a membrane valve that controls flow in a separate channel. This new technology will allow generating inexpensive portable bioanalysis tools where microvalve actuation occurs simply through heaters at a constant pressure source without a need for large external pressure control systems as is currently the case. Furthermore, a concept for controlled cross-channel transport of particles and potentially cells is presented that relies on the continuous regeneration of a gel wall at the diffusive interface of two co-streaming fluids in a microfluidic channel. Time and Date: 3:00-4:00 p.m., Wednesday, November 5, 2008 Event: Probability Seminar Speaker: Lung-Chi Chen, Department of Mathematics, UBC Subject:The limit distribution for long-range oriented percolation'' Location: WMAX 216 (PIMS) Abstract: In this talk, I will present the Fourier transform of the properly-scaled, normalized, two-point function for sufficiently spread-out long-range oriented percolation with index \alpha>0. The Fourier transform converges to e^{-C|k|^{\alpha\wedge2}} for some C\in(0,\infty) above the upper-critical dimension d_c\equiv 2(\alpha\wedge 2). Moreover, the constant C exhibits crossover at \alpha=2, which is a result of interactions among occupied paths. Time and Date: 3:00--4:00 p.m., Wednesday, November 5, 2008 Event: Algebra/Topology Seminar Speaker: Alejandro Adem, UBC and PIMS Subject:Commuting Matrices and Spaces of Homomorphisms'' Location: WMAX 110 Abstract: Let G denote a Lie group, and consider the space of all commuting n-tuples of elements in G. In this talk we will discuss basic topological properties of spaces such as these, and how they relate to bundle theory, group cohomology and other interesting topological invariants. Time and Date: 12:30--1:30 p.m., Thursday, November 6, 2008 Event: Mathematics Graduate Seminar Speaker: Mclean Edwards, Department of Mathematics, UBC Subject:Subverting the hassle of e-documents: Using Subversion to make your academic life easier!" followed by LaTeX tips and tricks'' Location: MATH 104 Abstract: Subversion is a popular revision control system that is installed and ready to use on some of our math servers. A revision control system is great because it keeps a history of all of the changes you make to a document in a central location, and allows you to revert to a previous version at any time from any location. Furthermore, it is designed to be used by many people concurrently, and can intelligently deal with multiple people editing something simultaneously. It does take some technical knowledge and has a small learning curve, so I'll be guiding you through getting started and using subversion on a day-to-day basis. If you use multiple computers and/or do collaborative research, you'll not want to miss this. A laptop that can ssh to math.ubc.ca (or a close friend with such a laptop) is necessary to get the most out of this seminar (you'll need to bring the laptop, possibly with friend attached). If you plan to come, please email me beforehand (mcleane) so I can setup an account. If you forget to email, don't worry, you'll just end up with a generic account name. Even if you use only one computer, Subversion is perfect for thesis writing. I use it myself every day and figure I save about 20 minutes weekly in time and worry because of it. For the second half, I'll present a couple of tips and tricks I find helpful and time-saving when writing LaTeX code. Then we'll open the floor and hear from you. Do you know of any LaTeX tips yourself? Please bring some along with you and share with the rest of us. We'd all love to hear them! Time and Date: 2:00--3:00 p.m., Thursday, November 6, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Masoud Kamgarpour, Department of Mathematics, UBC Subject:Understanding lower cohomology groups via monoidal categories'' Location: MATX 1102 Abstract: I will explain Grothendieck's dictionary relating central extensions and multiplicative torsors. This will provide us with a "new" interpretation of the second group cohomology. Time permitting, I will discuss an analogous interpretation of the third cohomology group. In a future lecture, we will apply these techniques to understand lower cohomology groups of algebraic groups. Familiarity with the notion of monoidal category will be helpful, though not necessary. Time and Date: 3:00 p.m., Friday, November 7, 2008 Event: Mathematics Colloquium Speaker: Greg Martin, UBC Subject: Prime number races'' 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 10, 2008 Event: IAM Seminar Series Speaker: Bernie Shizgal, Department of Chemistry, UBC Subject:The Resolution of the Gibbs Phenomenon'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The expansion of an analytic piecewise smooth function on a finite interval in a Fourier series leads to spurious oscillations at jump discontinuities. This result is known as the Gibbs phenomenon. The present talk describes a new method for the resolution of the Gibbs phenomenon which follows on the reconstruction method of Gottlieb and coworkers based on Gegenbauer polynomials. We refer to their approach as the direct method and to the new methodology as the inverse method. The direct method requires that certain conditions are met concerning \lambda in the weight function (1–x^2)^{\lambda – 1/2}, the number of Fourier coefficients, N, and the number of Gegenbauer polynomials, m. We show that the new inverse method can give exact results for polynomials independent of \lambda and with m = N. The paper presents several numerical examples applied to a single domain or to subdomains of the main domain so as to illustrate the superiority of the inverse method in comparison with the direct method. Image resolution in two dimensions will also be discussed and illustrated with several examples including resolution of the Shepp-Logan phantom image. Time and Date: 12:00--1:00 p.m., Wednesday, November 12, 2008 Event: Complex Fluids Seminar Speaker: Peng Gao, Dept. of Chemical and Biological Engineering, UBC Subject:Linear Stability of Flows with Wall Suction/Injection or Surfactants'' Location: CHBE 204 (2360 East Mall) Abstract: Effects of wall suction/injection and surfactants play an important role in the stability of flows involved in a wide range of engineering applications. In a majority of previous studies on these topics, the basic flow configuration is usually treated as a steady system or has only one interface. The present work consists of two parts. The first part is devoted to the linear stability of periodic flows with the suction/injection, including a Poiseuille flow modulated by oscillatory suction/injection and a flat Stokes layer with constant suction/injection. The second part is devoted to the effect of insoluble surfactants on the stability of a two-layer film and an oscillatory fluid layer. It is found that the influences of suction/injection and surfactants on the stability of these periodic or multiphase systems may be quite different with and even contrary to the simple steady cases. Time and Date: 3:00--4:00 p.m., Wednesday, November 12, 2008 Event: Algebra/Topology Seminar Speaker: Izak Grguric, Department of Mathematics, UBC Subject:Characteristic numbers and the geometry of \mathbb{Z}_4-equivariant bordism'' Location: WMAX 110 Abstract: Let G be a finite group. Divide the collection of closed, unoriented manifolds with G action into equivalence classes under the G-bordism relation: two G-manifolds are G-bordant if their disjoint union equals the boundary of another compact G-manifold. We might ask: given a specific G, what set of G-bordism invariants completely determines the G-bordism class of a given manifold? In the classical case (G trivial), we know what the answer is: the Stiefel-Whitney numbers. Historically, one of the first non-classical cases handled was that of the cyclic group of prime order. Here, the G-bordism type of a manifold turns out to be completely determined by the characteristic numbers of normal bundles to the fixed point set of the manifold. In this talk we will focus on the case when G is a cyclic group of 4 elements. This case is sufficiently rich so that the G-bordism class is not solely dictated by the normal bundles, and yet it is sufficiently simple so that various characteristic numbers carry interesting geometric interpretations. Time and Date: 2:00--3:00 p.m., Thursday, November 13, 2008 Event: Discrete Maths Seminar Speaker: Peter McNamara, Bucknell University and UC Berkeley Subject:Infinite log-concavity'' Location: WMAX 110 Abstract: We will begin by recalling what it means for a sequence of integers to be log-concave. While log-concavity has been widely studied in combinatorics, such sequences are also known to arise in algebraic geometry and algebra. In 2004, George Boros and Victor Moll introduced the concept of infinite log-concavity, and conjectured that the rows of Pascal's triangle are infinitely log-concave. We will show how a stronger version of log-concavity can be used to give a computer proof of their conjecture for the first 1450 rows. We will also discuss related questions for the columns of Pascal's triangle, q-analogues and, if time permits, symmetric functions and real-rooted polynomials. Including several easily-stated conjectures along the way, we hope to convince the audience that infinite log-concavity is a fundamental concept deserving of further attention. This is joint work with Bruce Sagan. Time and Date: 2:00--3:00 p.m., Thursday, November 13, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Masoud Kargampour, UBC Subject:Torsors, Gerbes, and Group Extensions'' Location: MATX 1102 Time and Date: 2:00--3:00 p.m., Thursday, November 13, 2008 Event: Mathematical Biology Seminar Speaker: Gareth Leng, Dept. of Biomedical Sciences, University of Edinburgh, UK Subject:Modeling a model system; bursts and pulses in neuroendocrine neurones'' Location: WMAX 216 Abstract: Peptides in the hypothalamus are not like conventional neurotransmitters; their release is not particularly associated with synapses, and their long half-lives mean that they can diffuse to distant targets. Peptides can act on their cells of origin to facilitate the development of patterned electrical activity, they can act on their neighbours to bind the collective activity of a neural population into a coherent signalling entity, and the co-ordinated population output can transmit waves of peptide secretion that act as a patterned hormonal analogue signal within the brain. At their distant targets, peptides can re-programme neural networks, by effects on gene expression, synaptogenesis, and by functionally rewiring connections by priming activity-dependent release. My lab has studied mainly the oxytocin and vasopressin neurones of the hypothalamus, these neurones fire in distinctive patterns that govern and in turn are governed by the peptide secretion that they induce. Oxytocin cells display remarkable synchronised bursts, that arise through emergent properties of an interactive network; vasopressin cells also burst, but asynchronously in a very different way and for very different reasons. In their different ways, these two neuronal systems have become important model systems in neuroscience; in this talk I will talk about modelling these model systems. (1) Leng G, Brown C, Sabatier N, Scott V (2008) Population dynamics in vasopressin neurons. Neuroendocrinology PMID: 18667805. (2) Leng G, Ludwig M (2008) Neurotransmitters and peptides: whispered secrets and public announcements. Journal of Physiology Oct 9. [Epub ahead of print]. (3) Rossoni E, Feng J, Tirozzi B, Brown D, Leng G, Moos F (2008) Emergent synchronous bursting of oxytocin neuronal network. PLoS Computational Biology Jul 18;4(7):e1000123.PMID: 18636098. (4) Leng G, Macgregor D (2008) Mathematical modelling in neuroendocrinology Journal of Neuroendocrinology 20: 713-718 PMID: 18513205. Time and Date: 3:00--3:50 p.m., Thursday, November 13, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Eyal Goren, McGill University Subject:The canonical subgroup: introduction, motivation and some new results'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: This is joint work with Payman Kassaei (King's College). The theory of the canonical subgroup for abelian varieties arises in the context of p-adic modular forms. I will explain what are p-adic modular forms, provide some historical and modern motivation for their study, and in that context motivate the study of the canonical subgroup as underlying the properties of the U operator. I will then explain the ingredients used in the approach Kassaei and I have for this problem, and announce some recent results, that improve on existing literature for the case of Hilbert modular varieties. Instead of talking about the many technical details of the proof, I will try and explain the deus-ex-machina and why we hope our method can be extended to many other Shimura varieties. Time and Date: 3:30--4:30 p.m., Thursday, November 13, 2008 Event: PIMS Biostatistics Lecture (joint with the Statistics Dept., UBC) Speaker: Jack Kalbfleisch, Department of Biostatistics, University of Michigan Subject:Statistical analysis of Illness Death and Semi-competing Risk Data'' Location: WMAX 110, West Mall, UBC Abstract: Semi-competing risks data frequently arise in clinical and observational studies. In these cases, the subject can experience both non-terminal and terminal events where the terminal event (e.g., death) censors the non-terminal event (e.g., relapse) but not vice-versa. Typically, the two events are correlated. An approach based on latent failure times has been advocated for the analysis of such data, where the joint survival function of two event times is assumed to follow a copula function over the positive quadrant with observation restricted to the upper wedge. We argue, that similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We consider an illness-death process which circumvents any need for latent times and provides for easy incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference, a simple iterative procedure is developed and needed asymptotic results are obtained. Simulation studies are conducted to assess the finite sample performance of the proposed estimators and the methods are illustrated in an analysis of data on nasopharyngeal cancer from a randomized clinical trial in Singapore. This is joint work with Jinfeng Xu, and Beechoo Tai, National University of Singapore. Time and Date: 4:10--5:00 p.m., Thursday, November 13, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Kevin Doerksen, SFU Subject:Characterization of genus two curves with (4,4)-split Jacobians'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: We say that a genus two curve C has a (n,n)-split Jacobian if its Jacobian is (n,n)-isogenous to the product of two elliptic curves. If C is a degree n cover of an elliptic curve E, then it has an (n,n)-split Jacobian. In this talk, we will characterize all genus 2 curves with (4,4)-split Jacobians. Time and Date: 3:00 p.m., Friday, November 14, 2008 Event: Mathematics Colloquium Speaker: Laurent Meersseman, PIMS/University of Bourgogne Subject: Foliations by Complex Leaves'' 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 17, 2008 Event: IAM Seminar Series Speaker: Dominik Schötzau, UBC Subject:Exactly Divergence-Free Finite Element Methods for Incompressible Fluid Flow'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: We propose and analyze a new class of exactly divergence-free finite element methods for the numerical approximation of the incompressible Navier-Stokes equations. The methods are based on divergence-conforming Raviart-Thomas finite element spaces for the velocities and on appropriately matched discontinuous finite element spaces for the pressures. The resulting discretization schemes are shown to provide approximate velocity fields that are exactly divergence-free over the computational domain. We further derive optimal a-priori and a-posteriori error estimates. Our findings are illustrated and verified in a series of numerical experiments. Time and Date: 3:10--4:10 p.m., Monday, November 17, 2008 Event: Algebraic Geometry Seminar Speaker: Jim Carrell, UBC Subject:T-equivariant cohomology for projective varieties with a triangular group action: I'' Location: WMAX 110 (PIMS) Time and Date: 4:20--5:20 p.m., Monday, November 17, 2008 Event: Algebraic Geometry Seminar Speaker: Damian Rössler, University of Paris-Sud Subject:A conjecture on the Chern classes of Gauss-Manin bundles'' Location: WMAX 110 Abstract: For any natural number t, we define a certain positive integer \N_t and we conjecture: if H is a Gauss-Manin bundle of a semi-stable fibration of complex projective varieties, then the t-th Chern class of H in Chow theory is a torsion class, which is killed by \N_t. We shall explain the proofs of various consequences of this conjecture. Time and Date: 2:00--3:00 p.m., Tuesday, November 18, 2008 Event: Discrete Maths Seminar Speaker: Andrew Rechnitzer, UBC Subject:Counting Elements of F'' Location: WMAX 110 Abstract: Richard Thompson's group F is a widely studied group which has provided examples of and counter-examples to a variety of conjectures in group theory. It is also an extremely combinatorially appealing object which has a beautiful description in terms of binary trees. In this talk I will give a description of some of the combinatorics of the group and mostly talk about some enumeration questions associated with F. This is work together with Sean Cleary, Murray Elder, Eric Fusy, Buks van Rensburg and Jennifer Taback. Time and Date: 3:30--4:30 p.m., Tuesday, November 18, 2008 Event: DG-MP-PDE Seminar Speaker: Stephane Kirsch, Department of Mathematics, UBC Subject:Obstruction for the existence of prescribed curvature hypersurfaces'' Location: WMAX 110 Abstract: The problem of prescribing curvature of manifolds has been studied quite a lot during the last decades. In this talk I will present a (non complete) overview of existence/non existence results for hypersurfaces for different types of curvature (mean curvature, scalar curvature...) in the euclidean case, and I will present a few new results in the case of closed hypersurfaces of prescribed mean curvature (still in the euclidean case). Time and Date: 12:00--1:00 p.m., Wednesday, November 19, 2008 Event: Complex Fluids Seminar Speaker: Christian Schoof, Dept. of Earth and Ocean Sciences, UBC Subject:Marine ice sheets: tales of thin films, jets, beams and contact lines'' Location: CHBE 204 (2360 East Mall) Abstract: The subject of the talk is the application of asymptotic matching techniques applied to the flow of ice sheets (think Antarctica) that are partially afloat on the surrounding ocean waters. The main big picture' interest lies in the dynamics of the grounded portion of the ice sheet (which is in contact with bedrock), as this is responsible for any contribution the ice sheet makes to sea levels. We expect this grounded part to behave as a standard thin film flow spreading under its own weight, and to be described by a diffusion model. The domain occupied by grounded ice can however evolve as parts of it thin and begin to float, or as the surrounding, floating ice shelves thicken and make contact with bedrock. Describing the evolution of the contact line requires coupling the lubrication flow of the grounded ice with the jet-like flow of the ice shelves. At a coarse level, this coupling involves a boundary layer that describes the transition from a shear stress dominated to a normal stress dominated flow. I will describe how this boundary layer can be cast as a kind of nonlinear eigenvalue problem for a second-order o.d.e system, with the eigenvalue representing flux across the contact line, and I will indicate how a few standard results from dynamical systems theory can be used to show that this flux is determined uniquely by the geometry of the ice sheet bed at the contact line. One a more detailed level, this boundary layer theory however misses some of the details of the transition from grounded to floating ice, which lead to an additional two boundary layers near the contact line, one that show that the floating ice shelves behave as stretched viscous beams near the contact line, and another that supplies the appropriate boundary conditions on the corresponding viscous beam problems. These boundary layers are, however, passive at leading order in the dynamics of the outer problem describing the grounded ice sheet. Time and Date: 3:00-4:00 p.m., Wednesday, November 19, 2008 Event: Probability Seminar Speaker: Ed Perkins, UBC Subject:Voter Model Perturbations and Reaction Diffusion Equations'' Location: WMAX 216 (PIMS) Abstract: We study both high density and low density limit theorems for voter model perturbations including the spatial Lotka-Volterra model introduced by Neuhauser and Pacala. The high density limit produces reaction-diffusion equations while the low density setting leads to superprocesses. In earlier work with Ted Cox, the low density theorems were used to show results on survival (in two and more dimensions) and coexistence (in three and more dimensions). I will report on work with Ted Cox and Rick Durrett where both limit theorems are used to show these results are locally sharp in three and more dimensions and verify a conjecture of Neuhauser and Pacala on the lack of founder control in the competitive regime of the model at least for values near the voter model. Time and Date: 3:00--4:00 p.m., Wednesday, November 19, 2008 Event: Algebra/Topology Seminar Speaker: Laurent Meersseman, PIMS/University of Bourgogne Subject:Moment-angle manifolds and connected sums of sphere products'' Location: WMAX 110 Abstract: Moment-angle complexes coming from simple convex polytopes can be realized as smooth manifolds in different ways. In this talk, I will explain how to realize them as transverse intersection of real quadrics in the complex n-space. One of the main interests of this realization is to make a connection with some results of differential topology. In particular, one immediately obtains from works of D. MacGavran and S. Lopez de Medrano that there exist infinite families of moment-angle manifolds diffeomorphic to connected sums of sphere products. On the other hand, in the case of simple convex polytopes, one can derive very geometric formulas for the cohomology of a moment-angle manifold in terms of subsets of faces of the polytope. From these formulas, it can be proved that their cohomology groups can have arbitrary torsion. Therefore, the families of Mac Gavran and Lopez de Medrano appear to be very special among moment-angle manifolds, and one would like to know if they are the only ones to be diffeomorphic to connected sums of sphere products. The conjecture is that they are not the only ones. Let P be a dual neighborly polytope. From the cohomology formulas, one can prove that the moment-angle manifold associated to P has the cohomology algebra of a connected sum of sphere products. It should be in fact diffeomorphic. This is a joint work with F. Bosio. Time and Date: 12:30--1:30 p.m., Thursday, November 20, 2008 Event: Mathematics Graduate Seminar Speaker: Frank de Zeeuw, Department of Mathematics, UBC Subject:Rational Distances'' Location: MATH 104 Abstract: A rational distance set is a subset of the real plane with all pairwise distances rational numbers. It's not too hard to construct an infinite rational distance set within a line or a circle, but if you do not allow 3 points on a line or 4 on a circle, the current record is a set of 7 points, found a few years ago with a computer. On the other hand, no one has been able to show that a rational distance set, no 3 on a line or 4 on a circle, must be finite, or even that it cannot be dense in the plane. Together with Jozsef Solymosi I showed that the only algebraic curves that contain infinite rational distance sets are lines and circles. I'll explain the main ideas behind this, most of which are very accessible. You can find the article on the arxiv if you search my name. Time and Date: 2:00--3:00 p.m., Thursday, November 20, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Alejandro Adem, UBC Subject:Elements of Finite Group Cohomology I'' Location: MATX 1102 Abstract: In these two lectures we plan to present an introduction to the cohomology of finite groups, including as time permits --basic definitions and properties --restriction, transfers & detection --connections to representation theory --cohomology calculations --examples related to fields Time and Date: 2:00--3:00 p.m., Thursday, November 20, 2008 Event: MITACS/PIMS Mathematical Biology Seminar Speaker: Sohrab Shah, BC Cancer Research Centre and Computer Science, UBC Subject:Model based approaches to array CGH data analysis'' Location: WMAX 216 Abstract: DNA copy number alterations (CNAs) are genetic changes that can produce adverse effects in numerous human diseases, including cancer. CNAs are segments of DNA that have been deleted or amplified and can range in size from one kilobases to whole chromosome arms. Development of array comparative genomic hybridization (aCGH) technology enables CNAs to be measured at sub-megabase resolution using tens of thousands of probes. However, aCGH data are noisy and result in continuous valued measurements of the discrete CNAs. Consequently, the data must be processed through algorithmic and statistical techniques in order to derive meaningful biological insights. We introduce model-based approaches to analysis of aCGH data and develop state-of-the-art solutions to three distinct analytical problems. In the simplest scenario, the task is to infer CNAs from a single aCGH experiment. We apply a hidden Markov model (HMM) to accurately identify CNAs from aCGH data. We show that borrowing statistical strength across chromosomes and explicitly modeling outliers in the data, improves on baseline models. In the second scenario, we wish to identify recurrent CNAs in a set of aCGH data derived from a patient cohort. These are locations in the genome altered in many patients, providing evidence for CNAs that may be playing important molecular roles in the disease. We develop a novel hierarchical HMM profiling method that explicitly models both statistical and biological noise in the data and is capable of producing a representative profile for a set of aCGH experiments. We demonstrate that our method is more accurate than simpler baselines on synthetic data, and show our model produces output that is more interpretable than other methods. Finally, we develop a model based clustering framework to stratify a patient cohort, expected to be composed of a fixed set of molecular subtypes. We introduce a model that jointly infers CNAs, assigns patients to subgroups and infers the profiles that represent each subgroup. We show our model to be more accurate on synthetic data, and show in two patient cohorts how the model discovers putative novel subtypes and clinically relevant subgroups in two types of lymphoma. Time and Date: 3:00--3:50 p.m., Thursday, November 20, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Ruiming Zhang, School of Mathematical Sciences, Guangxi Normal University Subject:On Multiple Sums of Zeros for Some Special Functions'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: In this work we prove an identity for a class of entire functions. Using this identity we give closed form evaluations of certain multiple sums of the zeros for the Bessel function J_u(z), the Airy function A(z), the Riemann zeta function zeta(z), L-series L(s,chi) with real primitive characters, Ramanujan's entire function (a.k.a. q-Airy function) A_q(z), q-Bessel function J_u^{(2)}(z;q). Time and Date: 4:10--5:00 p.m., Thursday, November 20, 2008 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Sander Dahmen, SFU & UBC Subject:Fun with Frey curves'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: Consider an exponential Diophantine equation of the shape F(x,y)=z^n where F denotes a binary form with integer coefficients satisfying certain relations between its coefficients (these relations are for example satisfied by any nondegenerate binary cubic form). By associating a Frey curve with nice invariant properties to F and using standard irreducibility, modularity and level lowering results for Galois representations associated to this Frey curve, we will show how the nonexistence of nontrivial solutions for large enough n to our exponential Diophantine equation can be reduces to the nonexistence of solutions to a much easier Thue-Mahler equation. This is joint work in progress with Mike Bennett. Time and Date: 3:00 p.m., Friday, November 21, 2008 Event: Mathematics Colloquium Speaker: Lun-Yi Tsai Subject: Math and Art: Processes and Representations'' 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 24, 2008 Event: IAM Seminar Series Speaker: Uri Ascher, Department of Computer Science, UBC Subject:Surprising Computations'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: Computer simulations for differential equations (DEs) often require complex numerical methods. It is important and often difficult to devise efficient methods for such purposes and to prove their properties. The resulting computations usually produce expected results, at least qualitatively, which in itself does not diminish the importance of the numerical methods. Occasionally, however, one comes across a (correct) computation that yields surprising results. In the process of writing a textbook on numerical methods for time dependent DEs I have encountered some such, and this talk describes several instances including solving Hamiltonian systems, KdV and NLS, and applying WENO methods for nonlinear conservation laws. What can be qualified as "surprising" is of course a subjective matter, nonetheless the combined effect of this talk hopefully sheds light on using marginally stable methods for solving marginally stable problems. Time and Date: 3:10--4:10 p.m., Monday, November 24, 2008 Event: Algebraic Geometry Seminar Speaker: Jim Carrell, UBC Subject:T-equivariant cohomology for projective varieties with a triangular group action: II'' Location: WMAX 110 (PIMS) Abstract: Given a smooth projective variety X over C with an action B:X of the upper triangular subgroup B of SL(2,C) such that the unipotent radical U of B has a unique fixed point on X, there is a simple geometric description of the T-equivariant cohomology of X, where T is the diagonal torus in B. While such actions would appear to be very special, we will see that there are a number of beautiful examples, including the flag variety of a linear algebraic group. The purpose of these talks is to describe a simple proof of the above result and then use the idea of the proof to describe the B-stable subvarieties Y of X for which the cohomology map H^*(X)\to H^*(Y) is surjective. We will also describe a partial generalization to the case where X^U is one dimensional, but X^T is still finite. Hopefully, this will explain a phenomenon noticed by Behrend and O'Halloran in their Inventiones paper. Time and Date: 12:30--2:00 p.m., Tuesday, November 25, 2008 Event: SCAIM Seminar Speaker: Mohammad Motamed, Department of Mathematics, SFU Subject:Finite difference schemes for second order systems describing black holes'' Location: WMAX 110 Abstract: In the harmonic description of general relativity, the principal part of Einstein~Rs equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem. Time and Date: 12:00--1:00 p.m., Wednesday, November 26, 2008 Event: Complex Fluids Seminar Speaker: Seyed Mohammad Taghavi, Department of Chemical and Biological Engineering, UBC Subject:The viscous regime of buoyancy-dominated slumping displacement'' Location: CHBE 204 (2360 East Mall) Abstract: The viscous limit of miscible displacement of two generalised Newtonian fluids is considered when buoyancy is dominated and there is an imposed flow. The assumed configuration is a close to horizontal plane channel. The lubrication/thin-film approximation is used to simplify the governing equations and leads to obtain a parabolic equation showing the convective-diffusive interface propagation in time. Numerically solving the parabolic equation, the effects of the viscosity ratios, inclinations, and rheological properties are shown on the front height and front velocity, the latter giving a measure of the displacement efficiency. In long time, the front heights and velocities are predictable from the fast solution of associated hyperbolic problem rather than the parabolic one. It is seen that more efficient displacements are generally obtained with a more viscous displacing fluid and modest improvements can also be gained with positive inclination in the direction of the density difference. In addition, considerably shear-thinning displaced fluids are evidently removed better. Generally, yield stress in displacing fluid increases the displacement efficiency and yield stress in displaced fluid decreases it and can even lead to have completely static residual wall layers of displaced fluid. The results of this semi-analytical study are qualitatively in agreement with the outcomes of a few experiments carried out thus far. Time and Date: 3:00-4:00 p.m., Wednesday, November 26, 2008 Event: Probability Seminar Speaker: Asaf Nachmias, Microsoft Research Subject:The Alexander-Orbach Conjecture Holds in High Dimensions'' Location: WMAX 216 (PIMS) Abstract: It is known that the simple random walk on the unique infinite cluster of supercritical percolation on Z^d diffuses in the same way it does on the original lattice. In critical percolation, however, the behavior of the random walk changes drastically. The infinite incipient cluster (IIC) of percolation on Z^d can be thought of as the critical percolation cluster conditioned on being infinite. Alexander and Orbach (1982) conjectured that the spectral dimension of the IIC is 4/3. This means that the probability of an n-step random walk to return to its starting point scales like n^{-2/3} (in particular, the walk is recurrent). In this work we prove this conjecture when d>18; that is, where the lace-expansion estimates hold. Joint work with Gady Kozma. Time and Date: 3:00--4:00 p.m., Wednesday, November 26, 2008 Event: Algebra/Topology Seminar Speaker: Adam Clay, Department of Mathematics, UBC Subject:The structure of the space of left orderings of a group'' Location: WMAX 110 Abstract: A group G is said to be left orderable if its elements admit a strict total ordering invariant under left multiplication. The set of all left orderings of a group then forms a compact topological space, denoted LO(G), and if we suppose that G is countable, LO(G) is also metrizable. Recent works have used compactness of LO(G) to great success, but little is known about the structure of LO(G) in general. I will discuss how to use a natural G-action on LO(G) in order to investigate the structure of LO(G). Specifically, I will characterize isolated points in LO(G) as left orderings of G that have certain special properties. Building upon this result, I will also construct a set of "generic" orderings in the space LO(G), so that in some sense, we can describe "most" left orderings of G. Time and Date: 2:00--3:00 p.m., Thursday, November 27, 2008 Event: Seminar on algebraic groups, Galois cohomology and related topics Speaker: Alejandro Adem, UBC Subject:Elements of Finite Group Cohomology II'' Location: MATX 1102 Abstract: In these two lectures we plan to present an introduction to the cohomology of finite groups, including as time permits --basic definitions and properties --restriction, transfers & detection --connections to representation theory --cohomology calculations --examples related to fields. Time and Date: 3:30--4:30 p.m., Thursday, November 27, 2008 Event: DG-MP-PDE Seminar Speaker: Yu Yuan, University of Washington Subject:Recent results for Special Lagrangian equations'' Location: WMAX 110 Abstract: We survey some recent results on Hessian, gradient estimates, regularity, and global rigidity for special Lagrangian equations with certain convexity. The gradient graph of the solutions are minimal Lagrangian submanifolds in Euclidean space. The special Lagrangian equations in the Pseudo-Euclidean setting are just Monge-Ampere equations, for which one has the corresponding classic results and counterexamples. This is partly joint work with Jingyi Chen and Micah Warren. Time and Date: 12:00 p.m., Friday, November 28, 2008 Event: PIMS/WMAX Postdoctoral Colloquium Speaker: Weiyong He, PIMS Subject:Extremal metrics and the Calabi flow'' Location: WMAX 216 Abstract: In 1980s, Calabi introduced extremal metrics over Kähler manifolds as a generalization of Uniformization theorem on Riemann surfaces. The existence problem of extremal metrics is conjectured to be equivalent to the "stability" of the underlying Kähler structure. It attracts much attention in Kähler geometry. The Calabi flow is a natural gradient flow to approach the existence problem of extremal metrics. We will try to explain some progress concerned with the Calabi flow as well as many interesting open problems. The talk is based on joint work with X. Chen. Attendees may bring their lunches. Time and Date: 3:00--4:00 p.m., Monday, December 1, 2008 Event: IAM Seminar Series Speaker: Guy Baruch, Ph.D. Student, Department of Applied Mathematics, Tel-Aviv University, Israel Subject:Numerical Solution of the Nonlinear Helmholtz Equation'' Location: Room 301, Leonard S. Klinck Bldg. Abstract: The nonlinear Helmholtz equation models the propagation of intense laser beams in Kerr media such as water, silica and air. It is a semilinear elliptic equation which requires non-selfadjoint radiation boundary conditons and which remains unsolved in many configurations. Its commonly-used parabolic approximation, the nonlinear Schrödinger equation (NLS), is known to possess singular solutions. We therefore consider the question that has been open since the 1960s: do nonlinar Helmholtz solutions exist under the conditions for which the NLS becomes singular? In other words – is the singularity removed in the elliptic model? In this work, we develop a numerical method that in some cases produces such solutions, thereby showing that the singularity is indeed removed in the elliptic equation. We also consider the subcritical case, wherein the NLS has stable solitons. For beams whose width is comparable to the optical wavelength, the NLS model becomes invalid, and so the existence of such "nonparaxial solitons" requires the solution of the Helmholtz model. Numerically, we consider the case of grated material that has discontinuities in the direction of propagation. We develop a high-order discretization which is "semi-compact", i.e. compact only in the direction of propagation, which is optimal for this case. Time and Date: 12:30--2:00 p.m., Tuesday, December 2, 2008 Event: SCAIM Seminar Speaker: Bruno Mundim, Physics & Astronomy, UBC Subject:A Numerical Study of Boson Star Binaries'' Location: WMAX 110 (PIMS) Abstract: Extremely dense stars - compact stars - cannot be described accurately by Newtonian gravity. Einstein's theory of general relativity (GR) is the most accurate theory of gravity to date. It is in this context that a numerical study of two compact stars (boson stars) orbiting each other was conducted. After a brief physical motivation of the problem, I will introduce the mathematical formalism necessary to cast the Einstein's equation in a form amenable to numerical treatment. I will then describe how the coupled elliptic-hyperbolic system of PDEs was solved numerically and conclude by showing some movies of the two-star dynamics. Time and Date: 3:30--4:30 p.m., Tuesday, December 2, 2008 Event: DG-MP-PDE Seminar Speaker: Robert Finn, Stanford University Subject:Floating bodies'' Location: WMAX 110 Abstract: The question is examined, as to whether a given rigid body will float or sink in a bath of liquid under the influence of surface tension, in a prescribed gravity field. Time and Date: 2:45--3:15 p.m., Wednesdays Event: PIMS Tea Location: WMAX 1st Flr Lounge Note: PIMS Afternoon Tea will be suspended for the month of December. It will resume in the New Year on Wednesday, January 7, 2009. Time and Date: 2:00--3:00 p.m., Thursday, December 4, 2008 Event: MITACS/PIMS Mathematical Biology Seminar Speaker: Kurt Haas, Department of Cellular and Physiological Sciences, UBC Subject:`Imaging single neuron growth and circuit activity in the awake developing brain: How does activity sculpt structure and function?'' Location: WMAX 216 Abstract: Using techniques to label individual neurons within intact brains and in vivo two-photon rapid time-lapse microscopy we image dynamic growth of neuronal dendritic arbors in awake Xenopus tadpoles. Our result suggest a strong role of neuronal transmission in directing dendrite growth by influencing synapse formation, which in turn, stabilize new dynamic dendritic branches. By loading the entire brain with calcium sensitive dyes, we find that brain neuron responses to sensory stimuli can be increased or decreased by training with sensory input. Combining single neuron morphometric and network activity analysis we hope to understand how neuronal transmission and developmental experience influences brain circuit form and function.