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Past 2007 Seminars

 2007 Seminars Time and Date: 4:00--5:00 p.m., Monday, January 8, 2007 Event: Mathematics Colloquium/IAM Seminar Series Speaker: Doron Levy, Department of Mathematics, Stanford University Subject: Balanced Schemes for the Shallow Water Equations'' Location: MATH 104 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 11:00 a.m. --12:00 p.m., Tuesday, January 9, 2007 Event: UBC SCAIM Seminar Speaker: Doron Levy, Stanford Subject:Modeling the Dynamics of the Immune Response to Chronic Myelogenous Leukemia'' Location: MATX 1102 (Pls note special time and place.) Abstract: Chronic Mylogenous Leukemia (CML) is a blood cancer with a common acquired genetic defect resulting in the overproduction of malformed white blood cells. The cause of CML is an acquired genetic abnormality in hematopoietic stem cells in which a reciprocal translocation between chromosomes 9 and 22 occurs. It is this abnormality that leads to dysfunctional regulation of cell growth and survival, and consequently to cancer. Treatment and control of CML underwent a dramatic change with the introduction of the new drug, Gleevec, which was shown to be an effective treatment available to nearly all CML patient. Nevertheless, by now it is widely agreed that Gleevec does not represent a true cure for CML, with many patients beginning to relapse despite of continued therapy. The only known treatment that can potentially cure CML is a bone-marrow (or stem-cell) transplant. In this talk we will describe our recent works in modeling the interaction between the immune system and cancer cells in CML patients. One model follows this dynamics after a stem-cell transplant. A second model follows the immune-cancer dynamics in patients treated with Gleevec. Related mathematical questions and possible exciting applications of the models will be discussed. This is a joint work with Peter Kim and Peter Lee (Hematology, Stanford Medical School). Time and Date: 12:30--1:30 p.m., Tuesday, January 9, 2007 Event: Mathematics Colloquium Speaker: Dan Knopf, University of Texas at Austin Subject: Local singularities of Ricci flow'' Location: MATH 104 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Wednesday, January 10, 2007 Event: Mathematics Colloquium Speaker: Young-Ju Lee, UCLA Subject: New numerical techniques for some non-Newtonian fluid models and thin film heteroepitaxial growths'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 4:00--5:00 p.m., Wednesday, January 10, 2007 Event: DG-MP-PDE Seminar Speaker: Dan Knopf, University of Texas at Austin Subject:Heatball localizations of monotone functionals on evolving manifolds'' Location: WMAX 110 (PIMS Facility) Abstract: Monotone functionals give important information for the analysis of geometric evolution equations. I will describe a quite general mechanism for localizing such functionals. This construction results in what may be regarded as local mean-value, monotonicity, or Lyapunov formulas. In particular, the construction yields a purely local monotone quantity directly analogous to Perelman's reduced volume for Ricci flow, and another related to Perelman's average energy. This is joint work with Klaus Ecker, Lei Ni, and Peter Topping. Time and Date: 11:00 a.m. --12:00 p.m., Thursday, January 11, 2007 Event: UBC SCAIM Seminar Speaker: Young-Ju Lee, UCLA Subject:Convergence theories of the subspace correction methods for singular and nearly singular system of equations'' Location: MATX 1102 (Pls note special time and place.) Abstract: Many mathematical models lead to singular and/or nearly singular problems. Simple examples include the Laplace equation with the pure Neumann boundary condition, the nearly incompressible linear elasticity equations, variational problems in electromagnetism at certain parameter ranges (in general variational problems on H(div) and/or H(curl)). The main goal of this presentation is to report recent research results on the abstract convergence analysis for both singular and nearly singular system of equations. For singular problems, we will present a sharp convergence rate identity for general subspace correction methods. We then apply the abstract theory in the study of the convergence of the multigrid method for certain singular problems. Our discussion of nearly singular problems will begin with a simple linear system and the difficulties that arise when solving such a system by a classical iterative method. To tackle these difficulties in the simple example, as well as in much more complicated situations, we introduce new abstract assumptions and based upon these assumptions we present a refined convergence analysis of a class of iterative methods via the subspace correction framework. Our new theory clearly shows the crucial role played by the right assumptions in obtaining optimal convergence rate estimates. Throughout this talk, we will present a number of simple examples to clarify the main ideas of various results as well as several motivating examples. Time and Date: 2:00 p.m., Thursday, January 11, 2007 Event: Mathematical Biology Seminar Speaker: Robert Guy, University of Utah and University of California at Davis Subject:A multiphase flow model of calcium induced morphology changes in true slime mold'' Location: WMAX 216 Abstract: The true slime mold Physarum polycephalum is a single cell organism reaching up to meters in size. The cytoplasm shows periodic shuttle streaming through a network of tubular structures attaining velocities up to 1 mm/s. The motion is driven by the periodic contraction of an actin-myosin gel that is regulated by a calcium oscillation. When the organism is small (< 100 microns) no streaming is observed, but as it gets larger regular rhythmic steaming suddenly emerges. We present a mechanochemical multifluid model which is used to explore how the sensitivity to changes in calcium concentration is related to the stability of the sol/gel mixture. Stability of the homogeneous mixture is explored analytically in one-dimension, and computational results are presented for higher dimensions. The model demonstrates that as the organism grows, a calcium-induced spatial instability occurs which may be responsible for the initiation of streaming. The overall goal of this work is to understand the interplay between chemistry and fluid mechanics which is necessary to transmit chemical signals and organize structures over very large distances. In addition to streaming, some other problems related to spatial organization of structure will be discussed. Time and Date: 3:30--4:30 p.m., Thursday, January 11, 2007 Event: DG-MP-PDE Seminar Speaker: Jian Song, John Hopkins University Subject:Bergman metrics and geodesics in the space of Kahler metrics'' Location: WMAX 110 Abstract: The space of positively curved hermitian metrics on a positive holomorphic line bundle over a compact complex manifold is an infinite-dimensional symmetric space. It is shown by Phong and Sturm that geodesics in this space can be uniformly approximated by geodesics in the finite dimensional spaces of Bergman metrics. We prove a stronger C^2-approximation in the case of toric manifolds. This is a joint work with Steve Zelditch. Time and Date: 4:00 p.m., Thursday, January 11, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Mia Hinnerich, Department of Finance, Stockholm School of Economics Subject:Inflation Indexed Swaps and Swaptions'' Location: WMAX 216 Abstract: This article considers the pricing of inflation indexed swaps, inflation indexed swaptions, and options on inflation indexed bonds. To price the inflation indexed swaps, we suggest an extended HJM model. The model allows both the forward rates and the consumer price index to be driven, not only by a standard multidimensional Wiener process but also, by a general marked point process. Our model is an extension of the HJM approach proposed by Jarrow and Yildirim (2003) and later also used by Mercurio (2005) to price inflation indexed swaps. Furthermore we price options on so called TIPS-bonds assuming the model is purely Wiener driven. We then introduce an inflation swap market model to price inflation indexed swaptions. All prices derived have explicit closed form solutions. Furthermore, we formally prove the validity of the so called foreign-currency analogy earlier used by Hughston (1998), Jarrow & Yildirim (2003) and Mercurio (2005). Time and Date: 3:00 p.m., Friday, January 12, 2007 Event: Mathematics Colloquium Speaker: Jian Song, Johns Hopkins University Subject: Canonical Kahler metrics and the Kahler-Ricci flow'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 4:00--5:00 p.m., Monday, January 15, 2007 Event: Mathematics Colloquium/IAM Seminar Series Speaker: Christoph Hauert, Program for Evolutionary Dynamics, Harvard University Subject: Evolutionary Dynamics: Structured Populations and the Problem of Cooperation'' Location: MATH 104 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--1:30 p.m., Tuesday, January 16, 2007 Event: Mathematics Colloquium Speaker: Dan Ciubotaru, MIT Subject: Spherical unitary representations for reductive groups'' Location: MATH 105 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00 p.m., Tuesday, January 16, 2007 Event: Mathematical Biology Seminar Speaker: Christoph Hauert, Harvard University Subject:Cooperation in Social Dilemmas: The Role of Punishment and Volunteering'' Location: WMAX 216 Abstract: The emergence and maintenance of cooperative behavior that is beneficial to others but costly to the individual represents a major conundrum in evolutionary biology. Punishment represents an efficient mechanism to stabilize and maintain cooperation in social dilemmas and is ubiquitous in animal and human societies - ranging from toxin producing microorganisms to law enforcement institutions - but it remains unresolved how initially rare costly punishment can gain a foothold and spread through the population. In nature, animals and humans often select their interaction partners or adjust their behavior in response to them. In the simplest case they simply refuse to participate in risky enterprises. Such voluntary participation in social dilemmas is an efficient mechanism to prevent deadlocks in states of mutual defection, and thus represents a potent promoter of cooperation that nevertheless fails to stabilize it. However, the combined efforts of punishment and volunteering may change the odds in favor of cooperation. Interestingly, even the combined efforts fail in infinite populations, but provide a most efficient mechanism to stabilize cooperation (and punishment) in the stochastic dynamics of finite populations under mutation and selection. Thus the freedom to withdraw leads to prosocial coercion. This implements Hardin's principle: mutual coercion mutually (and voluntarily) agreed upon. Time and Date: 3:00--4:00 p.m., Wednesday, January 17, 2007 Event: Algebra/Topology Seminar Speaker: Adam Clay, Department of Mathematics, UBC Subject:Normal subgroups of the braid groups and the Dehornoy ordering'' Location: WMAX 110 Abstract: The braid groups admit a left-ordering, known as the Dehornoy ordering, which has come up under many guises in recent years. I will show that normal subgroups interact with the Dehornoy ordering in such a way that "nearly all" normal subgroups of the braid groups are densely ordered with respect to this ordering. In particular, some popular normal subgroups--such as the kernels of the Burau representations--can be easily analyzed. This is joint work with Dale Rolfsen. Time and Date: 4:00 p.m., Wednesday, January 17, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Joern Sass, Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Linz, Austria Subject:The numeraire portfolio under transaction costs'' Location: WMAX 110 Note: (unusual day and time) Abstract: We study the existence of a numeraire portfolio for a discrete time financial market with proportional transaction costs. In an incomplete market without frictions, consistent prices for derivative securities can be obtained by taking the expectation of the claim with respect to a certain probability measure under which the discounted asset prices become martingales. The numeraire portfolio allows to replace this change of measure by a change of numeraire. For models with transaction costs, the concept of a martingale measure and thus the concept of a numeraire portfolio have to be modified. Without transaction costs a well known approach is to find the growth optimal portfolio (but the numeraire portfolio might not exist). With some modifications and under reasonable conditions the same approach turns out to work for our model. Time and Date: 3:00--4:00 p.m., Wednesday, January 17, 2007 Event: Representation Theory Seminar Speaker: Dan Ciubotaru, MIT Subject:On the unitarity of the unramified minimal principal series for split p-adic groups'' Location: MATH 204 Abstract: Let \Bbb F denote a p-adic field and let G be the \Bbb F-points of a split reductive algebraic group defined over \Bbb F. By the Borel-Casselman correspondence, the category of representations of G, with vectors fixed under an Iwahori subgroup I (i.e., the representations appearing in the unramified minimal principal series), is equivalent to the category of finite dimensional modules for the Iwahori-Hecke algebra \mathcal H. Barbasch and Moy showed that the determination of the unitary Iwahori-spherical representations can be reduced to the equivalent problem for Iwahori-Hecke algebras, and furthermore to their affine graded version \Bbb H, and modules with \it real infinitesimal character. In this setting, I will report on recent work on the identification of the unitary representations. Time and Date: 12:30--1:30 p.m., Thursday, January 18, 2007 Event: Mathematics Colloquium Speaker: Joern Sass, Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences Linz, Austria Subject: Optimal portfolio policies under transaction costs'' Location: MATH 104 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00 p.m., Thursday, January 18, 2007 Event: Mathematical Biology Seminar Speaker: Claus Rueffler, Zoology, University of Toronto Subject:Work in progress: The evolution of phenotype determination and an attempt to classify simple life-history models'' Location: WMAX 216 Abstract: In this talk I will present two pieces of work in progress. In the first half of the talk I will speak about the evolution of phenotype determining mechanisms. Many heterogeneous environments favour different phenotypes in different places or at different times. Phenotypic diversity can either result from genetic diversity of from a single genotype capable of producing different phenotypes. A single genotype might produce different phenotypes for example in response to an environmental cue (phenotypic plasticity), through a randomization mechanism (bet-hedging), or through a combination of the two. A large part of the existing theoretical literature attempts to give conditions under which one of these specific mechanisms is favoured over a phenotypically monomorphic population. However, in many circumstances different evolutionary responses are favoured simultaneously and the real question becomes which of these different responses might evolve first and possibly pre-empt any selection driving one of the alternative responses. I will address this question by presenting some preliminary results derived from a model designed to study evolution in a temporarily heterogeneous environment. In the second half of the talk I will present a classification of the evolutionary dynamics for a class of simple life-history models. The aim of this classification is to find principles governing the evolutionary dynamics that are valid beyond a single specific model. The family of models considered is characterized by discrete time population dynamics, density-dependent population growth, by the assumption that individuals can occur in two states, and that two evolving traits are coupled by a trade-off. Individual models differ in the choice of traits that are presumed to be evolving and in the way population regulation is incorporated. I classify models according to curvature properties of the fitness landscape and whether the evolutionary dynamics can be analysed by means of an optimization criterion. The first classification allows me to infer whether trait combinations that are characterized by a zero fitness gradient are susceptible to invasion by similar trait combinations. The second classification distinguishes models where evolutionary change is frequency-independent from models that give rise to frequency dependence. I will conclude by summarizing some general patterns emerging from this analysis. Time and Date: 3:00--3:50 p.m., Thursday, January 18, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Hyang-Sook Lee, Ewha Womans University, Seoul, Korea Subject:Tate pairing computation over hyperelliptic curves of genus 3'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: In recent years the Tate pairing and the Weil pairing have been getting a lot of attention for designing various protocols in cryptosystems. It is therefore important to develop an efficient implementation of the pairings for practical applications. In this talk, we introduce some Tate pairing computations over elliptic curves and hyperelliptic curves. In particular, for the Tate pairing computation over hyperelliptic curves, there are developments by Duursma-Lee and Barreto et al. which are focused on degenerate divisors. As divisors are not of degenerate form in general, it is necessary to find algorithms on general divisors for the Tate pairing computation. We also present two efficient methods for computing the Tate pairing over divisor class groups of the hyperelliptic curves y^2 = x^7-x+d of genus 3. First, we provide the pointwise method, which is a generalization of the previous developments by Duursma-Lee and Barreto et al. In the second method, we use the resultant for the Tate pairing computation. According to our theoretical analysis of the complexity, the resultant method is 48.5% faster than the pointwise method in the best case and 15.3% faster in the worst case, and our implementation result shows that the resultant method is much faster than the pointwise method. These two methods are completely general in the sense that they work for general divisors with Mumford representation, and they provide very explicit algorithms. Our results are joint works with Eunjeong Lee and Yoonjin Lee. Time and Date: 4:10--5:00 p.m., Thursday, January 18, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Ronald van Luijk, PIMS, SFU, UBC Subject:Quartic K3 surfaces without nontrivial automorphisms'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: We will deal with a gap in a result of Bjorn Poonen. He found explicit examples of hypersurfaces of degree d³3 and dimension n³1 over any field, such that the group of automorphisms over the algebraic closure is trivial, except for the pairs (n,d)=(1,3) or (2,4). Examples of the former pair, cubic curves, do not exist. We deal with the remaining case, quartic surfaces. For any field k of characteristic at most 19 we exhibit an explicit smooth quartic surface in projective threespace over k with trivial automorphism group over the algebraic closure of k. We also show how this can be extended to higher characteristics. Over the rationals we also construct an example on which the set of rational points is Zariski dense. Time and Date: 1:00 p.m., Friday, January 19, 2007 Event: Mathematics Colloquium Speaker: Arturo Pianzola, Department of Mathematical and Statistical Sciences, University of Alberta Subject: The language of forms (A journey from the Mobius strip to affine Kac-Moody and superconformal algebras)'' Location: WMAX 110 Note: Refreshments will be served at 12:45 p.m. (PIMS Lounge). Time and Date: 3:00 p.m., Friday, January 19, 2007 Event: Mathematics Colloquium Speaker: Claus Rueffler, Zoology, University of Toronto Subject: The evolutionary ecology of resource specialization'' 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 22, 2007 Event: IAM Seminar Series Speaker: Michael Ward, UBC Subject:The Dynamics of Pulses for Reaction-Diffusion Systems'' Location: Room 301, LSK Bldg. Abstract: The behavior of transition layers in mathematical models of materials science, notably the Cahn-Hilliard equation, was well-studied in the 1990s. For these systems, where a variational structure exists, it is well-known that transition layers undergo a slow dynamical coarsening process whereby layers are annihilated pairwise, until the minimal energy equilibrium state is reached. In contrast, for many reaction-diffusion systems with no variational structure, numerical computations have revealed that localized pulses or spikes can exhibit intricate dynamical behavior and can also be subject to instability mechanisms that do not occur in variational systems. These diverse dynamical behaviors and instabilities of pulse-type solutions are illustrated and then analyzed for different parameter regimes of the one-dimensional Gray-Scott model. In one parameter regime of this model, it is shown that a Nonlocal Eigenvalue Problem determines the stability of the spike pattern, and can lead to either an oscillatory instability of the pulse amplitudes or the annihilation of pulses. In another parameter regime of the Gray-Scott model, the center of the pulse can undergo a large-scale oscillatory time-dependent motion in a bounded domain. A novel Stefan-type problem with a moving source is shown to determine the dynamics of the pulse center. In yet another parameter regime, a localized pulse can undergo a dynamic self-replication. Finally, some remarks are made regarding the universality of these behaviors for other reaction-diffusion systems, and corresponding behavior in two spatial dimensions is highlighted. This is joint work with Wan Chen (UBC). Time and Date: 1:00--2:00 p.m., Tuesday, January 23, 2007 Event: Probability Seminar Speaker: Chris Hoffman, Department of Mathematics, University of Washington, Seattle Subject:Phase transitions for topological properties of random two dimensional simplicial complexes'' Location: MATX 1102 Abstract: The Erdos-Renyi random graph G(n,p) is the probability measure on all graphs on the vertex set [n]={1,2,...n}, with each edge inserted independently with probability p. Usually p is defined to be a function of n, and one asks whether a graph in G(n,p) is likely to have some (monotone) property as n goes to infinity. In their seminal 1959 paper, Erdos and Renyi showed that if p << log(n)/n then G(n,p) is almost always disconnected, but if p >> log(n)/n, then it is almost always connected. We view this as a topological statement and seek two-dimensional analogues of the Erdos-Renyi Theorem. We construct a measure on two-dimensional simplicial complexes and look at two questions about phase transitions for topological properties. For which values of p is the random complex almost always simply connected, and for which values of p does the random complex almost always have trivial homology? This is based on joint work with Matt Kahle and Eric Babson. Time and Date: 2:30--3:30 p.m., Tuesday, January 23, 2007 Event: Representation Theory Seminar Speaker: Joel Kamnitzer, UC Berkeley Subject:Mirkovic-Vilonen cycles on the affine Grassmannian'' Location: WMAX 110 (PIMS Facility) Abstract: The geometric Satake correspondence relates representation theory to the geometry of the affine Grassmannian. In particular, certain subvarieties of the affine Grassmanian, called Mirkovic-Vilonen cycles, give bases for representations of complex semisimple groups. Moreover, their moment map images (the MV polytopes) can be used to understand the combinatorics of these representations. In this talk, we will explain these results as well as give new results concerning an explicit description of these cycles and polytopes. These new results provide a combinatorial link between MV cycles and Lusztig’s canonical basis. Time and Date: 3:30--4:30 p.m., Tuesday, January 23, 2007 Event: DG-MP-PDE Seminar Speaker: Gadi Fibich, Tel Aviv Subject:New singular solutions of the Nonlinear Schrodinger equation (NLS)'' Location: WMAX 110 Abstract: The study of singular solutions of the NLS goes back to the 1960s, with applications in nonlinear optics and, more recently, in BEC. Until recently, the only known singular solutions had a self-similar "peak-type" profile that approaches a delta function near the singularity. In this talk I will present new families of singular solutions of the NLS that collapse with a self-similar ring profile, and whose blowup rate is different from the one of the "old" singular solutions. I will also show, both theoretically and experimentally, that these new blowup profiles are attractors for large super-Gaussian initial conditions. Time and Date: 2:00 p.m., Wednesday, January 24, 2007 Event: Mathematical Biology Seminar Speaker: Kristan Schneider, University of Vienna Subject:Long-term evolution of polygenic traits under frequency-dependent intraspecific competition'' Location: WMAX 216 Abstract: We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive selection induced by intraspecific competition and frequency-independent stabilizing selection. Moreover, the trait is restricted to a finite range by constraints on the particular loci. Our investigations are based on explicit analytical on the short-term dynamics under the assumption of linkage equilibrium. We show that the population always reaches a long-term equilibrium (LTE), i.e., an equilibrium that is resistant against perturbations of mutations of sufficiently small effect. In general, several LTEs can coexist. They can be calculated explicitly, and we provide necessary and sufficient conditions for their existence. In the case that more than one LTE exists, we exemplify numerically that the evolutionary outcome depends crucially on the initial genetic architecture, on the joint distribution of mutational effects across loci, and on the particular realization of the mutation process. Therefore, long-term evolution cannot be predicted from the ecology alone. We further show that a partial order exists for the LTEs. The set of LTEs has a largest' element, an LTE, which is reached during long-term evolution if the effects of the occurring mutant alleles are sufficiently large. Time and Date: 3:00--4:00 p.m., Wednesday, January 24, 2007 Event: Mathematics Colloquium Speaker: Joel Kamnitzer, UC Berkeley Subject: A geometric representation theory approach to Khovanov's knot homology'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 12:30--1:30 p.m., Thursday, January 25, 2007 Event: Mathematics Colloquium Speaker: Kristan Schneider, University of Vienna Subject: A Multilocus-Multiallele Analysis of Frequency-Dependent Selection induced by Intraspecific Competition'' Location: MATH 105 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Time and Date: 3:00--4:00 p.m., Thursday, January 25, 2007 Event: Representation Theory Seminar Speaker: Lior Silberman, Harvard University Subject:The geometric approach to fixed-point properties: recursive recognition of property (T) and random groups'' Location: WMAX 110 Abstract: A discrete group has "Property (T)" if every isometric (affine) action of the group on Hilbert space has a global fixed point. This is a spectral-gap property and was originally defined by Kazhdan to study lattices in Lie groups. Recently Gromov formulated a probabilistic model for constructing (T) groups of very differnet character, starting with graphs with large spectral gaps ("expanders"). I shall describe the metric geometry approach to fixed point properties, and give two applications: showing that the 'wild' groups constructed by Gromov have a much stronger fixed- point property, and an algorithm which enumerates the finite presentations with property (T). Time and Date: 4:00 p.m., Thursday, January 25, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Tan Wang, Sauder School of Business, UBC Subject:Robust Stochastic Discount Factors'' Location: WMAX 216 Abstract: When market is incomplete a new non-redundant derivative security cannot be priced by no arbitrage arguments alone. Moreover there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new derivative security. This paper develops an approach to the selection of a stochastic discount factor for pricing a new derivative security. The approach is based on the idea that the price of a derivative security should not vary too much when the payoff of the primitive security is slightly perturbed, i.e., the price of the derivative should be robust to model misspecification. The paper develops two metrics of robustness. The first is based on robustness in expectation. The second is based on robustness in probability and draws on tools from the theory of large deviations. We show that in a stochastic volatility model, the two metrics yield analytically tractable bounds for the derivative price as the underlying stochastic volatility model is perturbed. The bounds can be readily used for numerical examination of the sensitivity of the price of the derivative to model misspecification. Time and Date: 3:00 p.m., Friday, January 26, 2007 Event: Mathematics Colloquium Speaker: Lior Silberman, Harvard University Subject: Arithmetic quantum chaos on higher-rank locally symmetric spaces'' 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 29, 2007 Event: IAM Seminar Series Speaker: Carl Olivier-Gooch, Department of Mechanical Engineering, UBC Subject:High-Fidelity Methods in Computational Fluid Dynamics'' Location: Room 301, LSK Bldg. Abstract: The rise in complexity of numerical simulations for problems in science and engineering has been driven historically both by advances in computer technology and in simulation methodology. This talk will describe my research group's focus on developing techniques to enable highly-accurate solutions of problems with complex physics and geometry at reasonable computational cost. I will discuss the approach we take to produce high-order accurate spatial discretizations using unstructured meshes and to get efficient steady-state convergence for these schemes. Also, I will discuss the meshing issues that must be addressed to take full advantage of the solver technology. Time and Date: 3:00--4:30 p.m., Monday, January 29, 2007 Event: Algebraic Geometry Seminar Speaker: D.K. Shin, Konkuk University Subject:Computation of plurigenera of a canonical threefold'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Abstract: For a canonical threefold, there are few known results about plurigenera. We know that a sufficient multiple of canonical divisor generates a nontrivial linear system and that there is a universal multiple. In this talk, we are going to introduce an algorithm for computing plurigenera. Furthermore, when the algebraic euler characteristic is small, especially 1 or 2, we are going to compute plurigenera. Time and Date: 1:00--2:00 p.m., Tuesday, January 30, 2007 Event: Graduate Student Seminar Speaker: Mclean Edwards, Mathematics, UBC Subject:Sum-preserving rearrangements of series'' Location: MATH 225 Abstract: To take a rearrangement of a series is to sum the terms in that series with a permutation in the ordering of the natural numbers. When dealing with series, it would be useful to know which rearrangements are sum preserving. For more than a quarter of a century we have known the necessary and sufficient conditions for permutations to be sum preserving, and I will present various characterizations of these results. I will also demonstrate the result that the class of sum-preserving permutations contain a subclass of rearrangements that, while ensuring all convergent series remain convergent, allow some divergent series to converge under the new ordering. This talk will be accessible to everyone and has the potential to benefit many areas of research. I will be providing a small handout summarizing the results of the first part of the talk, and will be recruiting research collaborators to help answer questions raised by the second part of this seminar. Time and Date: 3:00--4:00 p.m., Wednesday, January 31, 2007 Event: Algebra/Topology Seminar Speaker: Matjaz Omladic, University of Ljubljana, Slovenia Subject:Nilpotent commutators and reducibility of semigroups'' Location: WMAX 110 Abstract: Let f be a noncommutative polynomial in two variables. Let \mathcal{S} be a multiplicative semigroup of linear operators on a finite-dimensional vector space and T a fixed linear operator such that f(T,S)=0 for all S in \mathcal{S}. What can we say about the invariant subspace structure of \mathcal{S}? We study special cases of this and other related conditions. Time and Date: 3:00--3:50 p.m., Thursday, February 1, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Adrian Belshaw, SFU Subject:Strong normality and modular normality'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: The notion of normality was intended to capture random behaviour in the digits of numbers, but some clearly patterned numbers pass the normality test; we propose a stronger test of normality that is passed by almost all numbers but failed by Champernowne's number. We also propose a modular definition of normality to generalize the original definition and make a wild conjecture. Time and Date: 4:00--5:30 p.m., Thursday, February 1, 2007 Event: Complex Fluids Seminar Speaker: James J. Feng, Department of Chemical and Biological Engineering and the Department of Mathematics, UBC Subject:An informal survey of the contact line problem'' Location: MATH 202 Abstract: The contact line problem has a well-known singularity where the continuum no-slip boundary condition breaks down. There have been various schemes for circumventing this difficulty. I will briefly survey these in terms of the mathematical formulation and physical justifications. In particular, I will discuss the different length scales involved, and how different models can be integrated to bridge the gaps between these scales. The phase field model appears promising as a framework in which physics on microscopic scales can be incorporated more or less rationally into a continuum description. Time and Date: 4:10--5:00 p.m., Thursday, February 1, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Ronald van Luijk, PIMS, SFU, UBC Subject:Quartic K3 surfaces without nontrivial automorphisms'' Location: UBC Campus, WMAX 110 (PIMS) Abstract: We will deal with a gap in a result of Bjorn Poonen. He found explicit examples of hypersurfaces of degree d³3 and dimension n³1 over any field, such that the group of automorphisms over the algebraic closure is trivial, except for the pairs (n,d)=(1,3) or (2,4). Examples of the former pair, cubic curves, do not exist. We deal with the remaining case, quartic surfaces. For any field k of characteristic at most 19 we exhibit an explicit smooth quartic surface in projective threespace over k with trivial automorphism group over the algebraic closure of k. We also show how this can be extended to higher characteristics. Over the rationals we also construct an example on which the set of rational points is Zariski dense. Time and Date: 5:00 p.m., Thursday, February 1, 2007 Event: Contemporary Immunology: How the Physical Sciences and Mathematics are Shaping Immunology: Speaker Seminar Speaker: David Mowat, Deputy Chief Public Health Officer of Canada Subject:Public Health: from Evidence to Practice'' Location: Green College Coach House Description: How does an understanding of how evidence is used in making decisions about programs and policies to protect the health of the pubic help us to make better decisions? Time and Date: 3:00--4:00 p.m., Monday, February 5, 2007 Event: IAM Seminar Series Speaker: Steven Ruuth, Department of Mathematics, SFU Subject:A Simple Technique for Solving Partial Differential Equations on Surfaces'' Location: Room 301, LSK Bldg. Abstract: Many applications require the solution of time-dependent partial differential equations (PDEs) on surfaces or more general manifolds. Methods for treating such problems include surface parameterization, methods on triangulated surfaces and embedding techniques. In particular, embedding techniques using level set representations have received recent attention due to their simplicity. However, level set based methods have several limitations. These include the inability to naturally treat open surfaces or objects of codimension two or higher. Level set methods also typically lead to a degradation in the order of accuracy when solved on a banded grid. This talk describes an approach based on the closest point representation of the surface which eliminates these and other limitations. A noteworthy feature of the method is that it is remarkably simple, requiring only minimal changes to the corresponding three-dimensional codes to treat the evolution of PDEs on surfaces. Time and Date: 3:00--4:30 p.m., Monday, February 5, 2007 Event: Algebraic Geometry Seminar Postponed until Feb. 12, 2007. Speaker: Patrick Brosnan, UBC Subject:Essential dimension and algebraic stacks'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Note: The talk will be preceded by an organizational meeting. Abstract: I will discuss recent work with Z. Reichstein and A. Vistoli on the subject of essential dimension. Time and Date: 3:30--4:30 p.m., Tuesday, February 6, 2007 Event: DG-MP-PDE Seminar Speaker: Nassif Ghoussoub, UBC Subject:Selfdual variational principles for Schrodinger and Navier-Stokes equations'' Location: WMAX 110 Time and Date: 3:00--4:00 p.m., Wednesday, February 7, 2007 Event: Algebra/Topology Seminar Speaker: Kee Y Lam, UBC Subject:Proof of Yuzvinsky's conjecture in the case of square matrices'' Location: WMAX 110 Abstract: Yuzvinsky's conjecture, posed in 1981, is concerned with a certain matrix coloring problem which arose from the classical studies of sums of squares. In this talk I will present a proof of the conjecture in the case of square matrices. The ideas of the proof are inspired by algebra and topology, despite the purely combinatorial nature of the conjecture itself. Time and Date: 3:10--4:00 p.m., Wednesday, February 7, 2007 Event: Probability Seminar Speaker: Ivar Ekeland, UBC Subject:The term structure of interest rates'' Location: WMAX 216 Abstract: The interest rate r(t,t+x) between time t and time t+x is a smooth function of x, say \rho_t(x). We consider \rho_t as a stochastic process on (0,\infty) into a suitable Hilbert space of curves, and we seek to define it as the solution of an appropriate equation, relying on accepted financial modelling. Unfortunately, this equation is not a SDE, for the right-hand term contains an unbounded operator on the Hilbert space, namely the derivative d/dx. We show in what sense this equation has a solution, we apply the result to optimal portfolio management, and if time permits we will touch upon the existence of finite-dimensional realizations. Time and Date: 3:30--5:00 p.m., Thursday, February 8, 2007 Event: Working Seminar on Character Varieties of 3-Manifold Groups Speaker: Gabriel Indurskis, Department of Mathematics, UBC Subject:Culler-Shalen (semi-)norms'' Location: WMAX 110 Abstract: Let M be a 3-manifold with boundary consisting of one torus. I will show how Culler and Shalen defined a norm on the (real) Dehn-surgery space R^2=H_1(\partial M; R) associated to the canonical component of the character variety of M. I will then show how this was generalized by Boyer and Zhang to a semi-norm for other components in the character variety. I will then discuss properties of this (semi-)norm, in particular its relationship to the so-called A-polynomial. I also will discuss some important results regarding exceptional fillings of hyperbolic manifolds which were proven using this machinery. Time and Date: 4:00 p.m., Thursday, February 8, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Michael Kupper, E.T.H. Zurich Subject:Composition of Time-Consistent Dynamic Monetary Risk Measures in Discrete Time'' Location: WMAX 216 Abstract: In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions.We first study risk measures for random variables modeling financial positions at a fixed future time. Then we consider the more general case of risk measures that depend on stochastic processes describing the evolution of financial positions. In both cases the new representations allow for a simple composition of one-step risk measures in the dual. We discuss several explicit examples and provide connections to the recently introduced class of dynamic variational preferences. It is joint work with Patrick Cheridito (Princeton University). Time and Date: 3:00--4:00 p.m., Monday, February 12, 2007 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: James R. Rice, Department of Earth and Planetary Sciences, Division of Engineering and Applied Sciences, Harvard University Subject:Episodic Slow Slipping of Seafloor under Cascadia: What Physical Processes cause Aseismic Deformation Transients?'' Location: Room 301, LSK Bldg. Abstract: In several shallow-dipping subduction zones, including Cascadia, the seafloor undergoes episodes of more rapid than usual creep-slippage under the overlying margin, but at rates vastly slower than usual earthquake slip. In some locations, also including Cascadia, non-volcanic seismic tremors occur during the slip episodes. Graduate student Yajing Liu and I have been trying to understand what physical processes underlie these phenomena. We have shown that transients, with features somewhat like the observations, are a natural outcome of modern "rate and state" formulations of fault zone friction, in a regime for which the ambient fluid pore pressure within the fault zone is very high and close to the compressive normal stress clamping the fault walls together. Evidence for such pressure conditions is provided by independent mechanical and petrological constraints. Time and Date: 3:00--4:30 p.m., Monday, February 12, 2007 Event: Algebraic Geometry Seminar (postponed from Feb. 5th) Speaker: Patrick Brosnan, UBC Subject:Essential dimension and algebraic stacks'' Location: WMAX 110 (West Mall Annex, PIMS Facility) Note: The talk will be preceded by an organizational meeting. Abstract: I will discuss recent work with Z. Reichstein and A. Vistoli on the subject of essential dimension. Time and Date: 3:30--4:30 p.m., Tuesday, February 13, 2007 Event: DG-MP-PDE Seminar Speaker: Razvan Fetecau, SFU Subject:Leray-type regularizations of the Burgers and the isentropic Euler equations'' Location: WMAX 110 Abstract: We start from the Burgers equation vt + vvx = 0 and investigate a smoothing mechanism that replaces the convective velocity v in the nonlinear term by a smoother velocity field u. This type of regularization was first proposed in 1934 by Leray, who applied it in the context of the incompressible Navier-Stokes equations. We show strong analytical and numerical indication that the Leray smoothing procedure yields a valid regularization of the Burgers equation. We also study the stability of the front traveling waves. The front stability results show that the regularized equation mirrors the physics of rarefaction and shock waves in the Burgers equation. Finally, we apply the Leray regularization to the isentropic Euler equations and use the weakly nonlinear geometrical optics (WNGO) asymptotic theory to analyze the resulting system. As it turns out, the Leray procedure regularizes the Euler equations only in special cases. We further investigate these cases using Riemann invariants techniques. Time and Date: 3:00--4:00 p.m., Wednesday, February 14, 2007 Event: Algebra/Topology Seminar Speaker: Nathalie Wahl, University of Copenhagen Subject:Homological Stability, Part I'' Location: WMAX 110 Abstract: Homological stability theorems have been proved for many families of groups like symmetric groups, linear groups, mapping class groups of surfaces and of 3-manifolds. I will review some examples and explain how such theorems are proved. As a more concrete example, I will give a proof of the stability of the homology of the wreath product of any group with the symmetric groups. Time and Date: 3:10--4:00 p.m., Wednesday, February 14, 2007 Event: Probability Seminar Speaker: Gord Slade, UBC Subject:The lace expansion and the enumeration of self-avoiding walks'' Location: WMAX 216 Abstract: The lace expansion is an elegant combinatorial construction that provides a recursion relation for the number of self-avoiding walks. We first give an introduction to the lace expansion, and then explain how it has been used recently (in joint work with Nathan Clisby and Richard Liang) to enumerate self-avoiding walks on the hypercubic lattice up to n=30 steps in dimension 3, and up to n=24 steps in all dimensions above 3. Major improvements to the 1/d expansion for the connective constant have also been obtained. In addition, an algorithmic improvement called the two-step method will be described. Time and Date: 4:00 p.m., Thursday, February 15, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Traian Pirvu, Department of Mathematics, UBC Subject:On Robust Utility Maximization'' Location: WMAX 216 Abstract: We study the problem of optimal investment in incomplete markets, robust with respect to stopping times. We work on a Brownian motion framework and the stopping times are adapted to the Brownian filtration. Robustness can only be achieved for logartihmic utility, otherwise a cashflow should be added to the investor's wealth. The cashflow can be decomposed into the sum of an increasing and a decreasing process. The last one can be viewed as consumption. The first one is an insurance premium the agent has to pay. Finally these results can be applied to obtain a portfolio decomposition formula. This is joint work with Professor Ulrich G. Haussmann. Time and Date: 4:00 p.m., Thursday, February 15, 2007 Event: Fluid Mechanics Seminar Speaker: Gregory Lawrence, Department of Civil Engineering, UBC Subject:Holmboe's Instability'' Location: MATH 202 Abstract: Holmboe (1962) investigated the stability of a sharp interface between two inviscid, nondiffusive, unbounded fluids of slightly different density. He assumed a linear variation of velocity across a shear layer of finite thickness centered about the density interface. This configuration supports two modes of instability. If the bulk Richardson number is sufficiently low, the primary instability is not significantly different from the Kelvin-Helmholtz instability. Higher Richardson number flows are subject to Holmboes instability, consisting of two trains of interfacial waves of equal strength travelling at the same speed, but in opposite directions with respect to the mean flow. This presentation will give, from a personal perspective, an overview of studies prompted by Holmboes work. Interest in Holmboes instability has been relatively slow to develop. There are a number of reasons for this, including the fact that the original paper was published in a somewhat obscure journal. Early laboratory experiments that might have been expected to yield Holmboe instabilities produced disturbances that were distinctly one-sided. Eventually, this one-sidedness was explained in terms of a vertical displacement of the velocity profile with respect to the density interface in laboratory experiments. In due course laboratory experiments without this asymmetry were performed that exhibited interfacial waves travelling in both directions. The waves were observed to cusp with wisps of fluid being drawn from these cusps. The fact that corresponding field observations in geophysical flows have been elusive, coupled with the expectation that these instabilities would not be a significant source of mixing, has limited enthusiasm for the study of Holmboe instabilities. However, interest in Holmboe instabilities has been revived in recent years by the direct numerical simulations (DNS) of Smyth and Winters (2003). These simulations showed that the Holmboe instability may, in some circumstances, generate more mixing than the Kelvin-Helmholtz instability. This work has recently been extended to flows with profile asymmetry resulting in even more mixing. While tantalizing, the practical relevance of these simulations remains an open question as the simulations have all been carried out at relatively low Reynolds numbers. Nevertheless, the mechanisms by which mixing is achieved are of interest in their own right. Time and Date: 3:00--4:00 p.m., Friday, February 16, 2007 Event: Algebra/Topology Seminar Speaker: Nathalie Wahl, University of Copenhagen Subject:Homological Stability, Part II'' Location: WMAX 110 Abstract: Homological stability theorems have been proved for many families of groups like symmetric groups, linear groups, mapping class groups of surfaces and of 3-manifolds. I will review some examples and explain how such theorems are proved. As a more concrete example, I will give a proof of the stability of the homology of the wreath product of any group with the symmetric groups. Time and Date: 4:00 p.m., Monday, February 19, 2007 Event: PIMS 10th Anniversary Speaker Series 2007 Speaker: Jerry Sacks, National Institute of Statistical Sciences and Duke University Subject:The Reality of Computer Models: Statistics and Virtual Science'' Location: WMAX 110 (PIMS West Mall Annex Facility) Abstract: Computer models are imperfect representations of real phenomena. An austere view is that validating a model cannot be done, the "primary value of models is heuristic: models are representations, useful for guiding further study but not susceptible to proof." This view may have substantial basis in purely scientific roles, as distinct from a model's use in policy and engineering contexts. But the real validation issue, we contend, is not whether a model is absolutely correct or only a useful guide. Rather, it is to assess the degree to which it is an effective surrogate for reality: does the model provide predictions accurate enough for intended use? Incisive argument on the validity of models, seen as assessment of their utility, has previously been hampered by the lack of a structure in which quantitative evaluation of a model's performance can be addressed. The lack has given wide license to challenge computer model predictions (just what is the uncertainty in temperature predictions connected with increases in CO2?). A structure for validation should: * Permit clear cut statements on what and how performances are to be addressed and assessed; * Account for uncertainties stemming from a multiplicity of sources including field measurements and, especially, model inadequacies; and * Recognize the confounding of calibration/tuning with model inadequacy – tuning can mask flaws in the model; flaws in the model may lead to incorrect values for calibration parameters. We will describe such a structure (and applications). It is built on methods and concepts for the statistical design and analysis of virtual experiments, drawing on elements of Gaussian stochastic processes and Bayesian analysis. Time and Date: 3:00--4:00 p.m., Wednesday, February 21, 2007 Event: Algebra/Topology Seminar Speaker: Max Karoubi, University of Paris - 7 Subject:Twisted K-theory (old and new), Part I'' Location: WMAX 110 Abstract: 1st lecture : The Brauer group of a space and of a finite group. How are they related to K-theory ? 2nd lecture : Twisted K-theory in terms of Banach algebras and Fredholm operators in an Hilbert space. Some computations. Twisted K-theory has its origins in the author's PhD thesis [K1] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper of P. Donovan and the author : http://www.numdam.org/item?id=PMIHES_1970__38__5_0 about 37 years ago. The objective of the lectures is to revisit the subject in the light of new developments inspired by Mathematical Physics. See for instance J. Rosenberg http://anziamj.austms.org.au/JAMSA/V47/Part3/Rosenberg.html and M.F. Atiyah-G. Segal paper in the ArXiv math/0407054 The unifiyng theme is the notion of K-theory of graded Banach algebras, already present in [K1], from which most of the theorems in twisted K-theory are derived. A clear distinction is made between ? graded ? and ? ungraded ? twisted K-theory, although they are linked via a new Thom isomorphism. Some explicit computations are also given in the twisted equivariant case, related to previous known results. (see http://www.math.jussieu.fr/~karoubi/ for more details) Time and Date: 4:00 p.m., Thursday, February 22, 2007 Event: Fluid Mechanics Seminar Speaker: Anja Slim, Department of Mathematics, UBC Subject:Gravity currents in an ambient flow'' Location: MATH 202 Abstract: Gravity currents occur whenever fluid of one density flows, predominantly horizontally, into fluid of a different density. In natural and man-made situations they are frequently generated in the presence of a flowing ambient. For example, both volcanic ash clouds and toxic gas releases are affected by atmospheric winds, while river plumes and pollutant releases in the sea are affected by marine currents. We theoretically study the canonical problem of a homogeneous, high Reynolds number gravity current generated by a constant source in a uniform ambient flow. We employ a shallow-water formulation and present both numerical and asymptotic solutions for how the current evolves and its dimensions, particularly its maximum upstream extent. We also briefly describe unusual features of gravity currents generated by a slowly sedimenting particle load. Time and Date: 3:00--4:00 p.m., Friday, February 23, 2007 Event: Algebra/Topology Seminar Speaker: Max Karoubi, University of Paris - 7 Subject:Twisted K-theory (old and new), Part II'' Location: WMAX 110 Abstract: 1st lecture : The Brauer group of a space and of a finite group. How are they related to K-theory ? 2nd lecture : Twisted K-theory in terms of Banach algebras and Fredholm operators in an Hilbert space. Some computations. Time and Date: 3:00--4:00 p.m., Monday, February 26, 2007 Event: IAM Seminar Series Speaker: Emily Stone, Department of Mathematical Sciences, University of Montana Subject:Analysis of Stomatal Dynamics'' Location: Room 301, LSK Bldg. Abstract: In this talk I will discuss data analysis techniques for the two-dimensional patterns seen in systems that display emergent distributed computation, namely patches of synchronized stomata on the surface of a respiring leaf. Image segmentation of the video data to identify patches was performed, followed by a hybrid method that incorporates principal component analysis and archetypal analysis. Once represented in terms of archetypes, the data can be analyzed directly or used to build lower-order model reconstructions. In the context of the leaf data, it is a method to interpret dynamic patterns as states that encode information and to allow the analysis of the time-dependent transitions between these states. Time and Date: 3:00--4:30 p.m., Monday, February 26, 2007 Event: Algebraic Geometry Seminar Speaker: Gregory Pearlstein, Michigan State University Subject:TBA'' Location: WMAX 110 (PIMS Facility) Time and Date: 12:30 p.m., Tuesday, February 27, 2007 Event: UBC SCAIM Seminar Speaker: Emily Stone, Department of Mathematical Sciences, University of Montana Subject:Detecting Spillover: A dynamical systems modeling approach to glutamatergic synaptic signaling'' Location: WMAX 216 Abstract: The connectivity of neurons in the hippocampus depends in part on whether neurotransmitter from one release site can leak out and activate receptors in another synapse or extrasynaptic patch. The existence of such spillover" is under debate in the neuroscience community, since direct measurements of neurotranmitter in such detail cannot, as of yet, be made. Experimental evidence of spillover is thus indirect, and should be sifted through as many different filters as possible. In this talk I present the contributions of dynamical systems modeling to this effort. Time and Date: 1:00--2:00 p.m., Tuesday, February 27, 2007 Event: Graduate Student Seminar Speaker: Sunil Chhita, UBC Subject:The Arctic Circle Phenomenon'' Location: MATH 225 Abstract: The Arctic Circle phenomenon is the amazing result that polar regions are formed when randomly tiling an Aztec diamond with dominos. We shall first introduce the concept of domino tilings, then provide connections to the total asymmetric exclusion process in discrete time and to Young diagrams. Time and Date: 3:30--4:30 p.m., Tuesday, February 27, 2007 Event: Discrete Mathematics Seminar Speaker: Soojin Cho, Ajou University, Korea Subject:Littlewood-Richardson coefficients: Reduction formulae and a conjecture by King, Tollu and Toumazet'' Location: WMAX 216 Abstract: Littlewood-Richardson coefficients are structural constants of the cohomology ring of Grassmannians and the ring of Schur functions, and they are counted by the number of skew tableaux with certain properties. In this talk, we introduce well known reductive formulae for Littlewood-Richardson coefficients and a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients). First, we give combinatorial proofs for reduction formulae. Then, we show that reduction formulae are special cases of a conjecture by King, Tollu and Toumazet on the factorization of Littlewood-Richardson polynomials (coefficients). Finally, we give a combinatorial proof of KTT's conjecture for some special cases, which can be realized as generalized reduction formulae. This is a joint work with E. Jung and D. Moon. Time and Date: 3:00--4:00 p.m., Wednesday, February 28, 2007 Event: Algebra/Topology Seminar Speaker: Luzius Grunenfelder, UBC Subject:On braided and ordinary Hopf algebras'' Location: WMAX 110 Abstract: Braided Hopf algebras occur naturally in the structure theory of ordinary Hopf algebras. I will show how they arise in this context and how they can be used to construct (and possibly to classify) ordinary finite dimensional Hopf algebras. Time and Date: 3:10--4:00 p.m., Wednesday, February 28, 2007 Event: Probability Seminar Speaker: Nathanael Berestycki, UBC Subject:On Card Shuffling'' Location: WMAX 216 Abstract: I will talk about some famous results of Bayer and Diaconis (1992) which permit a rigorous answer to the following question: given a deck of n cards, how many times should it be shuffled so that the deck is in approximately random order? The goal is to prove the existence of a cutoff phenomenon: if the deck is shuffled less than (3/2)log(n) times it is "far" from being random but after that it is "very close" to being random. Aside from practical interest (in casinos and magic tricks) and from having made the front page of the New York Times, this leads to some really beautiful mathematical developments. The level of the talk will be as basic as possible. Time and Date: 3:00--3:50 p.m., Thursday, March 1, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Vishaal Kapoor, UBC Subject:Almost-primes represented by quadratic polynomials'' Location: UBC Campus, PIMS WMAX 110 Abstract: Dirichlet's theorem on primes in arithmetic progressions characterizes those linear polynomials which take on prime values infinitely often. However, this is where the current state of knowledge ends. For the case of polynomials with higher degrees, heuristic arguments lead us to believe that for an irreducible polynomial with integer coefficients, if the leading coefficient is positive and the polynomial has no fixed prime divisor, then the polynomial represents primes infinitely often. I will discuss the case for quadratic polynomials with an emphasis on the work of Iwaniec. Time and Date: 4:00 p.m., Thursday, March 1, 2007 Cancelled Event: Complex Fluids Seminar Speaker: Onno Bokhove, Department of Applied Mathematics, University of Twente, Enschede, The Netherlands Subject:Supercritical shallow granular and slurry flows through a contraction'' Location: MATH 202 Abstract: Supercritical granular flow through a linear contraction on a smooth inclined plane is investigated by means of experiments, theoretical analysis and numerical simulations. Our work was motivated by a volcanic event in the German Eifel in which tephra flows blocked the Rhine river. The experiments have been performed with three size classes of spherical glass beads, and poppy seeds (non-spherical). Flow states and flow regimes have been categorized in the phase space spanned by the supercritical Froude number and the minimum width of the contraction. A theoretical explanation is given for the formation of steady reservoirs in the contraction observed in experiments using glass beads and water. For this purpose, the classical, one-dimensional shallow-water theory is extended to represent frictional and porosity effects. The occurrence of the experimentally observed flow states and regimes can be understood by introducing integrals of acceleration. The flow state with a steady reservoir arises because friction forces in the reservoir are much smaller than in other parts of the flow. Three-dimensional discrete particle simulations quantitatively agree with the measured granular flow data, and the crucial part of the theoretical frictional analysis is clearly confirmed. The simulations of the flow further reveal that porosity and frictional effects interact in a complicated way. In addition, the numerical database is employed to investigate the rheology in a priori tests for several constitutive models of frictional effects. Finally, work is in progress on fluid-particle slurry flows; preliminary experimental results will be shown. Time and Date: 4:10--5:00 p.m., Thursday, March 1, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Greg Martin, UBC Subject:Goldton-Yildirim-Pintz and small gaps between primes'' Location: UBC Campus, PIMS WMAX 110 Abstract: I'll give an expository talk, following the recent article of Soundararajan, on the theorem of Goldston, Yildirim, and Pintz that there are infinitely many primes p such that the next prime q satisfies q – p = o(log p). Time and Date: 3:00--4:00 p.m., Friday, March 2, 2007 Event: Mathematics Colloquium Speaker: Csaba D. Toth, MIT Subject: Triangles of unit and distinct areas'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:30 p.m., Monday, March 5, 2007 Event: PIMS 10th Anniversary Lecture Speaker: George Papanicolaou, Stanford University Subject:Imaging in random media'' Location: WMAX 110 (PIMS Facility) Note: This video conference lecture will originate from the IRMACS Theatre at SFU. Come for refreshments at 2:00 p.m. Abstract: I will present an overview of some recently developed methods for imaging with array and distributed sensors when the environment between the objects to be imaged and the sensors is complex and only partially known to the imager. This brings in modeling and analysis in random media, and the need for statistical algorithms that increase the computational complexity of imaging, which is done by backpropagating local correlations rather than traces (interferometry). I will illustrate the theory with applications from non-destructive testing and from other areas. Time and Date: 4:00--5:00 p.m., Monday, March 5, 2007 Event: The Ivan and Betty Niven Distinguished Lectures (Lecture #1/Math Colloquium) Speaker: Fernando Rodriguez-Villegas, University of Texas at Austin Subject: Combinatorics as geometry'' Location: MATX 1100 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Tuesday, March 6, 2007 Event: The Ivan and Betty Niven Distinguished Lecture #2 (Student Lecture) Speaker: Fernando Rodriguez-Villegas, University of Texas at Austin Subject:Puzzles and groups'' Location: MATH Bldg., Room 203 Note: Refreshments will be served after the lecture at 4:30 p.m. (MATX 1115, Math Lounge). Abstract: In this talk I will discuss several puzzles (15-puzzle, lights-out, Rubik's cube, Blet, etc.) and how they are related to group theory. We will see how group theory can give important insights into the structure of the puzzles and, in some cases, provides a complete solution. Time and Date: 3:30--4:30 p.m., Tuesday, March 6, 2007 Event: DG-MP-PDE Seminar Speaker: Ivar Ekeland, UBC Subject:Non-convex non-coercive variational problems arising from the economics of asymmetric information'' Location: WMAX 110 Time and Date: 3:00--4:00 p.m., Wednesday, March 7, 2007 Event: Algebra/Topology Seminar Speaker: Hamid Usefi, Department of Mathematics, UBC Subject:Identifications in Modular Group Algebras'' Location: WMAX 110 Abstract: Let G be a finite p-group and F a field of characteristic p>0. In this talk I shall explain how Lie theoretic methods can be used to identify certain subgroups of G inside the augmentation ideal of the group algebra FG. Time and Date: 3:10--4:00 p.m., Wednesday, March 7, 2007 Event: Probability Seminar Speaker: Richard Bass, University of Connecticut Subject:Symmetric Markov chains on Z^d with unbounded range'' Location: WMAX 216 Abstract: We consider symmetric Markov chains on \Z^d where we allow arbitrarily large jumps. Under a uniform second moment condition on the conductances, we look at estimates on the transition probabilities, Harnack inequalities, and CLTs. This is joint work with Takashi Kumagai. Time and Date: 4:00--5:00 p.m., Wednesday, March 7, 2007 Event: IAM Seminar Series Speaker: Yoichiro Mori, Department of Mathematics, UBC Subject:Convergence Proof for a Stokes Flow Immersed Boundary Method'' Location: Room 301, LSK Bldg. Abstract: The immersed boundary method is a computational framework for problems involving the interaction of a fluid and immersed elastic structures. It makes use of a regular Cartesian fluid grid and a Lagrangian curvilinear mesh to represent the elastic structure. The main algorithmic step is to find the solution of the fluid equations with a singular external force field. The singular force field, supported on a manifold of codimension 1 (the immersed boundary), is regularized using discrete delta functions so that the underlying fluid grid can "feel" its presence. This regularized singular force field is then used as the right-hand side of the discretized fluid equations to solve for the fluid velocity. Such regularizations are used not only in the context of the immersed boundary method but also in level set method and front-tracking method. In this talk, I will outline a proof of convergence of a stationary immersed boundary problem for two-dimensional periodic Stokes flow. The key to the proof is an estimate on the difference between the discrete and continuous Green's function. We obtain both pointwise and global L^\infty error estimates to prove that the solution converges up to the immersed boundary. We demonstrate computational examples to show that the error estimates capture the overall features of the convergence rates. Time and Date: 3:30--5:00 p.m., Thursday, March 8, 2007 Event: Working Seminar on Character Varieties of 3-Manifold Groups Speaker: David Boyd, Department of Mathematics, UBC Subject:A-polynomials'' Location: WMAX 110 Abstract: The A-polynomial A(x,y) is a 2-variable polynomial invariant of an orientable 3-manifold. This introductory talk will present various different definitions of A(x,y) from the point of view of the SL(2,C)-character variety and the deformation variety of a hyperbolic 3-manifold. We describe some of the basic properties of A(x,y) and the information that A(x,y) gives about the manifold. Time and Date: 4:00 p.m., Thursday, March 8, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Michael Savidant, BC Hydro Subject:Risk management for a hydro-based generator -- How to deal with correlated variability in the underlying commodity position'' Location: WMAX 216 Note: Coffee, tea and cookies will be served at 3:45 in the PIMS lounge. Please bring your own mug to allow PIMS to be more environmentally friendly. Abstract: This talk will cover some of the practical applications of risk analysis and hedging programs for a hydro-based energy generator such as BC Hydro. Risk management for BCH provides a unique challenge due to the significant variability in available energy and prices, and the ability to defer purchases between years. We will look at a simplified version of BC Hydro’s system optimization model and methods to determine the risk profile of purchase costs for a hydro system. We will then discuss methods for developing an optimal hedge portfolio in order to minimize long-term cost risk, and how these differ from more common hedge portfolios. Time and Date: 4:00 p.m., Thursday, March 8, 2007 Event: Complex Fluids Seminar Speaker: Steve Cochard, Ecole Polytechnique Federale de Lausanne, Switzerland Subject:Tracking the free surface of time-dependent flows: Image processing for the dam-break problem'' Location: MATH 202 Abstract: The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the last few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge's free-surface variations with time, we have developed a new imaging system, consisting in a digital camera coupled with a synchronized micro-mirror projector. The object surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 0.1 mm over a surface of 1.8 x 1.1 m2. Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to date in practical applications. Time and Date: 3:00--4:00 p.m., Friday, March 9, 2007 Event: Mathematics Colloquium Speaker: Ander Holroyd, UBC Subject: Random Sorting Networks'' 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 12, 2007 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Emmanuel Candes, Department of Applied Mathematics, California Institute of Technology Subject:Compressive Sampling'' Location: Room 301, LSK Bldg. Abstract: One of the central tenets of signal processing is the Shannon/ Nyquist sampling theory: the number of samples needed to reconstruct a signal without error is dictated by its bandwidth-the length of the shortest interval which contains the support of the spectrum of the signal under study. Very recently, an alternative sampling or sensing theory has emerged which goes against this conventional wisdom. This theory allows the faithful recovery of signals and images from what appear to be highly incomplete sets of data, i.e. from far fewer data bits than traditional methods use. Underlying this metholdology is a concrete protocol for sensing and compressing data simultaneously. This talk will present the key mathematical ideas underlying this new sampling or sensing theory, and will survey some of the most important results. We will argue that this is a robust mathematical theory; not only is it possible to recover signals accurately from just an incomplete set of measurements, but it is also possible to do so when the measurements are unreliable and corrupted by noise. We will see that the reconstruction algorithms are very concrete, stable (in the sense that they degrade smoothly as the noise level increases) and practical; in fact, they only involve solving very simple convex optimization programs. An interesting aspect of this theory is that it has bearings on some fields in the applied sciences and engineering such as statistics, information theory, coding theory, theoretical computer science, and others as well. If time allows, we will try to explain these connections via a few selected examples. Time and Date: 3:00--4:30 p.m., Monday, March 12, 2007 Event: Algebraic Geometry Seminar Speaker: Dmitriy Boyarchenko, University of Chicago Subject:Characters of unipotent groups over finite fields" (Joint work with Vladimir Drinfeld) Location: WMAX 110 (PIMS Facility) Abstract: Let G be a connected unipotent group over a finite field F_q. For each natural number n, we have the unique extension F_{q^n} of F_q of degree n, and we can form the finite group G(F_{q^n}) of points of G defined over F_{q^n}. An interesting problem, motivated by Lusztig's theory of character sheaves, is to study irreducible characters of these finite groups (over an algebraically closed field of characteristic 0) and relate them to the geometry of G. If the nilpotence class of G is less than p (the characteristic of the field F_q), there exists an explicit description of irreducible characters of G(F_{q^n}), provided by Kirillov's orbit method. It allows one to introduce the notion of an L-packet of irreducible representations of G(F_{q^n}). This notion is morally analogous to the notion of an L-packet in Lusztig's theory, even though Lusztig's definition cannot be applied to unipotent groups. If the nilpotence class of G is at least p, no analogue of the orbit method is known to us. Nevertheless, we have succeeded in giving a geometric definition of L-packets of irreducible characters of G(F_{q^n}) for every connected unipotent group G over F_q. My talk will be devoted to giving a precise statement of our result, explaining some motivation behind it, and sketching a few of the essential ideas used in its proof. Time and Date: 4:00--5:00 p.m., Monday, March 12, 2007 Event: Probability Seminar (Postponed) Speaker: Ander Holroyd, UBC Subject:Poisson Matching'' Location: WMAX 216 Abstract: Red points and blue points occur as independent Poisson processes in R^d, and we consider schemes to perfectly match red points to blue points in a translation-invariant way. For any matching scheme in dimensions 1 and 2, the distance X from a typical red point to its blue partner has infinite d/2-th moment, while in dimensions >=3 there exist schemes where X has exponential tails. For the variant problem of matching points of a single colour to each other, there exist schemes where X has exponential tails, but if we insist that the matching is a deterministic factor of the points then in dimension 1, X must have infinite mean. The Gale-Shapley stable marriage is a natural greedy matching scheme. It is close to optimal (in terms of X) for two-colour matching in dimension 1, but far from optimal for dimensions >=3 and for one-colour matching. Joint work with Robin Pemantle, Yuval Peres and Oded Schramm. Time and Date: 5:00 p.m., Monday, March 12, 2007 Event: Contemporay Immunology, How the Physical Sciences and Mathematics are Shaping Immunology Lecture Series Speaker: Greg Hammond, Director of Public Health, Manitoba Health Branch Subject:New Vaccine Programs or Not? Lessons for Shaping Public Policy through Science and Partnership'' Location: Green College, Coach House Abstract: I will explore the background for the recent introduction of four new childhood vaccine programs across Canada and some challenges facing all countries in the introduction of new vaccine programs in the future. Time and Date: 12:30--1:30 p.m., Tuesday, March 13, 2007 Event: Mathematics Colloquium Speaker: Michael Minion, University of North Carolina Subject: Spectral Deferred Corrections for PDEs: A Framework for Multiscale Temporal Integration'' Location: MATH 100 Note: Refreshments will be served at 12:15 p.m. (Math Lounge, MATX 1115). Time and Date: 3:30--4:30 p.m., Tuesday, March 13, 2007 Event: DG-MP-PDE Seminar Speaker: Xiaobo Liu, Notre Dame Subject:Mean Curvature Flows for Isoparametric Submanifolds'' Location: WMAX 110 Abstract: Isoparametric submanifolds in Euclidean spaces and spheres are submanifolds with constant pincipal curvatures. We will show that the mean curvature flows of such submanifolds behaves very well. They always converge in finite time to smooth submanifolds of lower dimension. This is a joint work with Chuu-Lian Terng. Time and Date: 9:30--10:30 a.m., Wednesday, March 14, 2007 Event: Applied Mathematics Seminar Speaker: Michael Minion, University of North Carolina Subject:Auxiliary Variables and Projection Methods for 0-Mach Number Gas Dynamics'' Location: WMAX 216 Abstract: Auxiliary variable methods for the incompressible Navier-Stokes equations approximate the evolution of the velocity through a dynamic variable which does not satisfy a divergence constraint but from which the correct incompressible velocity can be computed by a projection. This approach is a departure from traditional projection methods wherein the intermediate variable is considered only as a byproduct of a fractional step scheme. I will discuss the connections between auxiliary variables, impulse variables, and projection methods; discuss how auxiliary variables resolve the question of applying boundary conditions in projection methods; and discuss recent work on constructing fourth-order methods for the equations of 0-Mach number gas dynamics based on auxiliary variables. Time and Date: 3:00--4:00 p.m., Wednesday, March 14, 2007 Event: Algebra/Topology Seminar Speaker: Jose Cantarero-Lopez, Department of Mathematics, UBC Subject:Equivariant twisted K-theory'' Location: WMAX 110 Time and Date: 2:00 p.m., Thursday, March 15, 2007 Event: Mathematical Biology Seminar Speaker: Michael Gilchrist, University of Tennessee at Knoxville Subject:Predicting Protein Production Rates from Codon Usage Patterns: A Nested Model Approach'' Location: WMAX 216 Abstract: Genes are often biased in their use of particular codons. The degree of bias displayed changes as a function of expression level and intra-genic position. Numerous indices measuring such bias have been developed. While the expression level of a gene and such indicies are often correlated, the huristic nature of these metrics precludes a deeper understanding between expression and bias. Here I employ mechanistic models of cellular and population processes to develop a framework for evaluating codon usage bias in an explicitly evolutionary framework. Time and Date: 3:00--3:50 p.m., Thursday, March 15, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Amy Goldlist, Department of Mathematics, UBC Subject:Prime Divisors of Certain Quartic Linear Recurrences'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: Recurrence sequences appear in many areas of mathematics and are studied by many. A recurrence sequence of order n is defined by a polynomial of degree n, and n initial values. Given a sequence, there are several important questions which one can ask about the sequence: 1. Which primes divide at least one number in the sequence? What is their (relative) density in the set of all primes?"; and 2. Which primes divide several consecutive numbers in the sequence? What is their density in the set of all primes?''. This last question is the one I will address. Though density is at heart an analytic problem, we will explore ways of rephrasing density questions in an algebraic way, using the Chebotarev Density Theorem. Time and Date: 3:00 p.m., Thursday, March 15, 2007 Event: DG-MP-PDE Seminar Speaker: Pascal Chossat, CIRM Subject:Intermittent behaviour in hydrodynamical systems with spherical symmetry: theory and an experiment'' Location: WMAX 216 Abstract: It has been known since 20 years that spherical symmetry can generate intermittent-like flow near onset of convection for a fluid subjected to a central temperature gradient and gravity field. This has been shown by applying the techniques of center manifold reduction and equivariant bifurcation theory to the classical hydrodynamical model (Navier-Stokes and heat equations in the Boussinesq approximation). An experiment to be mounted in the ISS could verify this theoretical prediction. However in this experiment, the gravity field is replaced by an electrophretic field, which turns out to considerably change the expected bifurcation diagram. I explain the reasons for this and I present the latest results on this issue. Time and Date: 4:00 p.m., Thursday, March 15, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Peter Bank, Department of Mathematics, Columbia University in the city of New York Subject:Pricing and Hedging in Illiquid Financial Markets'' Location: WMAX 216 Abstract: Ever since the seminal work of Black, Scholes, and Merton, typical models studied in Mathematical Finance specify price dynamics exogenously via some more or less explicit semimartingale dynamics. This is in contrast to the basic economic paradigm that prices ought to be determined by demand and supply. We propose a new model which bridges the gap (or at least tries to) between these two approaches by studying the dynamics of utility indifference prices. For exponential utility, the resulting nonlinear wealth dynamics allow for explicit solutions to the classical problems of pricing, hedging, and utility maximization in complete and incomplete financial markets. We shall also show how these results extend tho general utilities. This talk is based on joint work with Dmitry Kramkov and Jeffrey Said. Time and Date: 4:00 p.m., Thursday, March 15, 2007 Event: Complex Fluids Seminar Speaker: Josef Dufek, University of California, Berkeley Subject:Linking Deposits to Dynamics in Explosive Volcanic Eruptions: Advances and Open Questions in Geophysical Multiphase Flow'' Location: MATH 202 Time and Date: 4:10--5:00 p.m., Thursday, March 15, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Peter Borwein, SFU Subject:The Liouville function and friends'' Location: SFU Campus, Room ASB 10900 (IRMACS) Time and Date: 3:00--4:00 p.m., Friday, March 16, 2007 Event: Mathematics Colloquium Speaker: Ron Douglas, Texas A&M University Subject: Operator Theory and Complex 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, March 26, 2007 Event: IAM Seminar Series Speaker: Ozgur Yilmaz, Department of Mathematics, University of British Columbia Subject:Mathematical problems related to analog-to-digital conversion'' Location: Room 301, LSK Bldg. Abstract: Digital computers and their efficiency on processing data is one of the main driving forces behind much of our modern technology. On the other hand, in many occasions, the data sets we would like to store and process, e.g., images, audio, and video, are analog by their nature. This places a high demand on providing accurate conversion between the analog and digital worlds. However, the technology used in the analog-to-digital conversion, by necessity, involves analog devices which have physical limitations that, at first sight, conflict with accuracy demands. To cope with these problems, special signal processing techniques have been developed leading to alternative signal and number representations that are quite different from the standard decimal or binary representations. I will give an overview of these techniques, and present some new results on how to introduce and exploit redundancy for obtaining more robust representations of signals using analog hardware. Time and Date: 4:00--5:00 p.m., Monday, March 26, 2007 Event: PIMS 10th Anniversary Speaker Series Speaker: Nancy Reid, University of Toronto Subject:The interface between Bayesian and frequentist statistics'' Location:WMAX 110 Abstract: Statistical theory is often categorized as either "Bayesian" or "frequentist", and statisticians often self-identify in the same categories. During the development of theoretical statistics as a separate field in the twentieth century this categorisation led to a great deal of discussion, some of which was surprisingly bitter and antagonistic. With the development of several key results in the asymptotic theory of inference based on the likelihood function, it is becoming clear that the mathematical differences between Bayesian and frequentist methods are rather less important than the philosophical ones. Some of this work is based on efforts to construct priors which minimize the difference between the two approaches and some is based on an ongoing effort to develop so-called 'reference', or 'objective' or 'default' priors. Perhaps not surprisingly, even the correct terminology to be used in this setting has been the subject of debate! I will give an overview of some of the asymptotic theory behind the development of approaches to constructing priors that minimize the differences between Bayesian and frequentist inference, with special attention to 'strong matching' priors that have been developed recently in joint work with Don Fraser and colleagues. The construction of these priors provides some insight into the exact points of departure between Bayesian and frequentist methods, at least from the mathematical point of view. The philosophical debate may well continue for some time. Time and Date: 12:30--2:00 p.m., Tuesday, March 27, 2007 Event: UBC SCAIM Seminar Speaker: Yogi Ahmad Erlangga, Technische Universitat, Berlin, Germany Subject: A robust iterative method for the heterogeneous Helmholtz equation'' Location: ICICS/CS 238 Abstract: In this talk I will focus on an iterative method used to solve 2D and 3D Helmholtz problems efficiently in sequential or parallel machines. The method is based on Krylov subspace iterative methods, preconditioned by an operator specially designed for the Helmholtz equation called the shifted Laplacian operator. The effectiveness of this preconditioner can be deduced from simple analysis on the 1D Helmholtz equation, which results can be easily generalized to higher dimensions. Recent analysis from more algebraic point of view shows that the conclusion also holds for general discretizations, including different type of boundary conditions and heterogeneities in the media: i.e., the spectrum in terms of conjugate gradient iterations applied to the normal equations the preconditioned system is always bounded above by one. Furthermore, only the small eigenvalues very close to zero may rise problems to convergence, which is mainly due to the increase of wavenumbers. Numerical experiments show that the convergence of a suitable Krylov subspace method, with special shift in the preconditioner, is linearly dependent of the wavenumber with only small proportionality constant. This convergence is well behaved and consistent. Furthermore, the convergence is independent of the gridsize. In order to have a fully iterative method, the shifted Laplacian preconditioner is handled by one multigrid cycle. This cycle leads to a rough approximation to the inverse of the shifted Laplacian, but is sufficient for Krylov subspace convergence acceleration. Numerical examples related to forward modelling in the seismic inversion will be given for some hard problems: 2D Marmousi and 3D Saltdome model of the North sea. Time and Date: 3:30--4:30 p.m., Tuesday, March 27, 2007 Event: DG-MP-PDE Seminar Speaker: Alain Pajor, Universite de Marne-la-Valle Subject: Reconstruction and subgaussian operator'' Location: WMAX 110 Abstract: Candes, Romberg and Tao recently studied problems of approximate and exact reconstruction of sparse signals from incomplete random measurements and related them to the eigenvalue behavior of submatrices of matrices of random measurements. In particular they introduced the notion they called the "uniform uncertainty principle" (UUP) and studied it for Gaussian, Bernoulli and Fourier ensembles. We shall introduce a different--geometric--approach to approximate and exact reconstruction problem which yields to a more general setting for all subgaussian random measurements. Time and Date: 12:30--2:00 p.m., Wednesday, March 28, 2007 Event: Representation Theory Seminar Speaker: Laura Scull, Department of Mathematics, University of British Collumbia Subject: Group cohomology and grade school arithmetic'' Location: MATH 203 Abstract: Time and Date: 3:10--4:00 p.m., Wednesday, March 28, 2007 Event: Probability Seminar Speaker: Adam Timar, Department of Mathematics, University of British Columbia Subject: Matchings of exponential tail on coin flips in Z{\accent 94 d}'' Location: WMAX 216 Abstract: We construct a translation-invariant matching between vertices of different labels of Bernoulli(1/2) percolation on Z^d, in such a way that the probability that a vertex is at distance > r from its pair decays as an exponential function of the d-2'nd power of r. Our method implies earlier results about matching n uniformly distributed red points with n uniformly distributed blue points in the unit square with minimal average distance. Other consequences to invariant matchings in R^d and optimal matchings in the unit cube are also presented. Time and Date: 4:00--5:00 p.m., Thursday, March 29, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Uli Haussmann, University of British Columbia Subject: Portfolio optimization in a hidden Markov model for stock returns with jumps '' Location: WMAX 216 Abstract: In a market consisting of a money market and one stock with price process dS(t)=S(t)[a(t) dt + b dW(t) + g dM(t)] where W is a Wiener process and M is a compensated Poisson process, an agent invests his initial wealth in a portfolio to maximize utility of wealth at terminal time T. The portfolio strategy may only depend on the observed stock price S(t). The constants b and g may be inferred from this, but not the unknown drift a(t). It is assumed to be a Markov process with known states and rate matrix.We reduce the problem to a martingale representation problem for Levy processes. This is joint work with Dr. Joern Sass. Time and Date: 4:00 p.m., Thursday, March 29, 2007 Event: Complex Fluids Seminar Speaker: Siddharth Khullar, Department of Chemical and Biological Engineering, UBC Subject: Dynamics of defects around a micro-bubble rising in a nematic liquid crystal'' Location: MATH 202 Abstract: Liquid crystals are a phase of matter critical both in many recent scientific developments in biology, chemistry, and physics and in significant applications in the display industry. With fluids they share the ability to flow, however, they also exhibit anisotropies in their dielectric, magnetic, and optical properties reminiscent of crystals. They have been studied as one of the experimentally accessible systems showing a rich variety of topological defects. The elastic distortions of the host liquid crystal due to the surface anchoring of particles or droplets immersed in it bring about various interesting properties unique to liquid crystal colloidal dispersions, thus playing a determining role for the behavior of colloidal dispersions in a nematic environment. Recently there have been some theoretical predictions indicating that such type of defects occurring around a particle in a nematic liquid crystal can be convected downstream by hydrodynamic flow. Our study provides a direct evidence of such an occurrence whilst also yielding some unique observations of transition among defects. In particular, we use the property of optical anisotropy of liquid crystals using polarized light microscopy to enhance the observation of dynamic behaviour of these defects. In addition we also do birefringence measurements with a quantitative imaging system to analyze and verify the molecular order in the region of interest. Time and Date: 3:00--3:50 and 4:10--5:00 p.m., Thursday, March 29, 2007 Event: SFU/UBC Number Theory Seminar Speaker: 3:00 p.m. - Nils Bruin, Simon Fraser University. 4:10 p.m. - Stefan Erickson, Colorado College Subject: 3:00 p.m. - Fake 2-descent on the Jacobian of a genus-3'' curve. 4:10 p.m. - TBA Location: UBC Campus, Room WMAX 110 (PIMS) for both talks Fake 2-descent on the Jacobian of a genus-3 curve'' Abstract: For many questions in explicit arithmetic geometry of curves, one needs detailed information on the rational points of the Jacobian of the curve. A first step is to bound the free rank of the finitely generated group that they form. For hyperelliptic curves [curves admitting a model of the form y2 = f(x)], we have fairly good methods for producing bounds, and curves of genus 2 are always hyperelliptic. Curves of genus 3 (for instance smooth plane quartics) are generally not hyperelliptic. A straightforward generalization of the standard methods to these curves would lead to infeasible computational tasks involving number fields up to degree 756. We propose a modification, which requires number fields up to degree 28 and is sometimes just about feasible. Time and Date: 3:00--4:00 p.m., Friday, March 30, 2007 Event: Mathematics Colloquium Speaker: Todd Kemp, MIT Subject: Dimension in global analysis and free probability'' 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, April 2, 2007 Event: IAM Seminar Series Speaker: Richard Craster, Imperial College London, UK Subject:Fingering of a Surfactant Droplet on a Thin Liquid Film'' Location: Room 301, LSK Bldg. Abstract: Spreading processes involving surfactants are of importance to numerous industrial, biomedical and daily life settings; these include coating flow technology, micro-fluidics, surfactant replacement therapy for neonates, film drainage in emulsions and foams and drying of semi-conductor wafers in microelectronics. Fluid flow in many of these applications is primarily driven by surface tension gradients caused by surfactants (surface active agents) that act to locally reduce the surface tension and are mobile. The gradients arise due to non-uniformities in the surfactant interfacial concentration. These gradients, in turn, give rise to so-called Marangoni stresses that drive rapid surfactant spreading in the direction of the uncontaminated (surfactant-free) liquid. A long standing question has been the physical origin of the striking fingering mechanism that is observed when a surfactant-laden drop is placed atop a pre-existing, uncontaminated, thin film. Both the fluid within the droplet and that of the thin film are identical, so this is not viscous fingering in the classical sense, but even so it is clearly driven by a mobility gradient; i.e., the droplet with its much lower surface tension and much greater height is, in some sense, more mobile than the thin, high surface tension, film that surrounds it. This talk will present the theory that explains the mechanism behind the fingering phenomenon together with detailed computations that are then compared qualitatively with experimental trends; the theory is capable of reproducing the observed trends. Time and Date: 3:00 p.m., Monday, April 2, 2007 Event: PIMS 10th Anniversary Speaker Series Speaker: Michael L. Stein, Chicago Subject:Statistical Models for Global Processes'' Location: MATX 1100 Abstract: This talk explores some of the issues that arise in statistical modeling of atmospheric phenomena on a global scale, using total column ozone as measured by the satellite-based Total Ozone Mapping Spectrometer (TOMS) as a case study. A basic issue in all statistical models for natural phenomena is finding statistical regularities that enable one to take meaningful averages. Since the statistical characteristics of total column ozone strongly depend on latitude, we consider the use of axial symmetry (invariance of statistical properties to rotations about the Earth's axis) as a possible exploitable regularity. Methods for summarizing, modeling, estimating and visualizing spatial dependence for axially symmetric processes are addressed. A computationally convenient approach to modeling using truncated expansions of spherical polynomials is shown to capture much of the larger-scale latitudinal variation in spatial dependence. However, the approach performs disastrously in terms of describing the local behavior of the process, leaving a need for the development of statistical models that provide good descriptions of the data and computational methodologies that allow one to fit these models with reasonable degrees of statistical efficiency. Lessons learned from this only partially successful modeling effort, including suggestions for new data products based on TOMS, are described. Time and Date: 4:30 p.m., Monday, April 2, 2007 Event: PIMS 10th Anniversary Speaker Series Speaker: Peter Lax, Courant Institute Subject:Asymptotic behavior at infinity of solutions of elliptic equations'' Location: MATX 1100 Abstract: The prototype problem is the behavior at infinity of all solutions of a linear elliptic equation that have finite L1 norm in a half cylinder 0 < y, x in D,D a smoothly bounded domain. We assume that the coefficients of the elliptic operator, as well as the boundary conditions in D, are independent of y. Such a space of solutions can be abstracted as a linear space K of functions f(y), whose values lie in a Banach space B, are translation invariant, |f(y)| integrable, and which are interior compact, an abstract version of ellipticity. We show that the asymptotic behavior as y tends to infinity of such functions is given as a sum of exponential functions contained in K. Time and Date: 12:30--1:30 p.m., Tuesday, April 3, 2007 Event: Mathematics Colloquium Speaker: Albert Chau, U. Waterloo and MSRI Subject: The Ricci flow and applications to complex geometry'' Location: MATH 104 Note: Refreshments will be served at 12:15 p.m. (MATX 1115, Math Lounge). Time and Date: 3:30--4:30 p.m., Tuesday, April 3, 2007 Event: DG-MP-PDE Seminar Speaker: Albert Chau, U. Waterloo and MSRI Subject:Yau's uniformization conjecture and the Kahler Ricci flow'' Location: WMAX 110 (PIMS Facility) Abstract: Yau's uniformization conjecture states: a positively coruved complete non-compact Kahler manifold is biholomorphic to complex Euclidean space. In this talk I will report on recent progress on Yau's conjecture using the Kahler Ricci flow. Time and Date: 3:30--4:30 p.m., Tuesday, April 3, 2007 Event: Discrete Mathematics Seminar Speaker: Cedric Chauve, SFU Subject:Conservation of the combinatorial structure in genome'' Location: WMAX 216 Abstract: We investigate the problem of computing an evolution scenario based on genome rearrangements between two genomes modelized by synteny blocks, or in mathematical terms, sorting signed permutations by reversals. We consider the case of scenarios that do not break groups of synteny blocks that are common to the two considered genomes. We show that this problem is deeply linked with tools developed inb the theory of modular decomposition of graphs. Work in collaboration with Severine Berard (INRA, France), Anne Bergeron (LaCIM, UQAM) and Christophe Paul (CNRS, France). Time and Date: 3:00 p.m., Wednesday, April 4, 2007 Event: Algebra-Topology Seminar Speaker: Ekaterina Yurasovskaya, Department of Mathematics, UBC Subject:String links and classification of links up to link-homotopy'' Location: WMAX 110 Abstract: I shall discuss classification of links up to link-homotopy as solved in 1990 by Nathan Habbager and Xiao-Song Lin. The main tool in classification was a group of link-homotopy classes of string links - H(k). Since then H(k) itself became an object of interest in low-dimensional topology. If time permits, I shall discuss H(k) as an example of orderable groups appearing in topology. Time and Date: 3:10--4:00 p.m., Wednesday, April 4, 2007 Event: Probability Seminar Speaker: Ed Perkins, UBC Subject:Two Dimensional Lotka-Volterra Models and Superprocesses'' Location: WMAX 216 Abstract: Neuhauser and Pacala (99) introduced a particle system to model the dynamics of two competing types on an integer lattice. We study the model near the parameter values for which there is a cross-over from preference of one's own type to preference of the other type. The rescaled system converges to a super-Brownian motion with non-trivial branching and growth rates. As a corollary, local information about parameter values for which rare types can survive and both types can co-exist is obtained. These results had been obtained earlier for dimensions greater than 2. We extend many of these results to two dimensions where the mathematics is more delicate, and perhaps the biology more interesting. This is joint work with Ted Cox (Syracuse U.). Time and Date: 2:00 p.m., Thursday, April 5, 2007 Event: Mathematical Biology Seminar Speaker: Junling Ma, University of Victoria Subject:Evolutionary Branching'' Location: WMAX 216 Abstract: Evolutionary branching is sympatric speciation driven by competition between dominant species and their mutants. The traditional approach to study evolutionary branching is to use pairwise-invasibility plot (PIP). However, PIP is only suitable for the branching of a single species with a single trait. With multiple co-evolving traits or species, this method breaks down because the evolution/branching in one trait changes the PIP of other traits. In this talk, I introduce a dynamical method to study the branching of multiple co-evolving traits and species, and give the branching conditions. Time and Date: 3:30--4:30 p.m., Thursday, April 5, 2007 Event: DG-MP-PDE Seminar Speaker: Amir Moradifam, UBC Subject:Improved Hardy inequalities'' Location: MATH 102 Time and Date: 3:30--5:00 p.m., Thursday, April 5, 2007 Event: Working Seminar on Character Varieties of 3-Manifold Groups Speaker: David Boyd, UBC Subject:A-polynomials II'' Location: WMAX 110 Abstract: I'll continue the discussion of A-polynomials begun in the seminar on March 8th showing how the A-polynomial of a hyperbolic 3-manifold can be defined and computed from a triangulation of the manifold into ideal tetrahedra. I'll also discuss the relationship with volume (of the manifold and of representations of the fundamental group). Some illustrative examples will be given. Time and Date: 4:00 p.m., Thursday, April 5, 2007 Event: Fluid Mechanics Seminar Speaker: Zhong-Sheng Simon Liu, NRC Institute for Fuel Cell Innovation, Vancouver Subject:Fluid Mechanics Problems in PEM Fuel Cells'' Location: MATH 202 Abstract: Fluid mechanics problems are encountered in many fields of fuel cell technology, such as water transport through meso- & macro-scale porous catalyst layers and macro-scale gas diffusion layers, water transport through polymer membranes, water evaporation and condensation, water morphology inside porous catalyst layers and gas diffusion layers, two-phase flow through flow channels, and water freeze/thaw cycles. All of these fluid mechanics problems are of importance in the fuel cell technology, and they are always encountered in conjunction with other disciplines such as electrochemistry, physics, and materials. Moreover, they occur often in nano-scale or micro-scale. Besides, they generally involve other branches of engineering and require experimental methods for their understanding and solution, i.e., fluid mechanics problems in fuel cell technology are interdisciplinary in nature. In this presentation, the basic concept of a PEM fuel cell and its current R&D status are first outlined. Then the fluid mechanics problems in catalyst layers and gas diffusion layers are addressed. They include the morphology of liquid water inside catalyst layers and how it affects effective electro-chemical-active surface areas. The mechanism of water transport through catalyst layers is also examined. Thereafter, the effect of surface contact angles upon liquid water morphology and transport is analyzed. In the gas diffusion layers, the VOF model for simulating liquid water flow patterns such as channeling and fingering is described and the effect of pore size distribution and contact angles upon the pattern of liquid water flow is illustrated. The experimental studies of water droplet behaviors are discussed, and at the end of the presentation the research needs are listed. Time and Date: 12:30--2:00 p.m., Tuesday, April 10, 2007 Event: UBC SCAIM Seminar Speaker: Paul Tseng, University of Washington Subject:Gauss-Seidel for Constrained Nonsmooth Optimization and Applications'' Location: ICICS/CS 238, UBC Abstract: A classical method for unconstrained smooth convex optimization is the Gauss-Seidel method. This method iteratively minimizes the objective function with respect to a small subset of coordinates, while the other coordinates are held fixed at their current value. We discuss extensions of this method to constrained nonsmooth (possibly nonconvex) optimization, and applications to Basis Pursuit, Group Lasso, and Support Vector Machine training. The extensions involve iteratively approximating the smooth part of the objective function by a strongly convex quadratic function. (This work is joint with Sylvain Sardy and Sangwoon Yun.) Time and Date: 3:00 p.m., Wednesday, April 11, 2007 Event: Algebra Topology Seminar Speaker: Izak Grguric, Department of Mathematics, UBC Subject:Constructions in Equivariant Bordism'' Location: WMAX 110 (PIMS Facility) Abstract: Let G be a finite group acting on a manifold M. How can we determine if M is the boundary of some other manifold with a G-action? In the classical setting (G={e}), one can translate this problem into the language of stable homotopy and show that the vanishing of certain characteristic numbers is necessary and sufficient. However, when G is nontrivial, this approach is almost never possible. I will discuss an equivariant construction, discovered by R. Stong, which allows one to come up with a set of characteristic numbers that completely determine G-bordism type when G is a 2-nilpotent group (a group whose set of elements of odd order forms a subgroup). Time and Date: 3:10--4:00 p.m., Wednesday, April 11, 2007 Event: Probability Seminar Speaker: Rick Kenyon, UBC Subject:Branched polymers'' Location: WMAX 216 Abstract: This is joint work with Peter Winkler. A branched polymer is a connected set of unit balls with non-overlapping interiors. In 2002, David Brydges and John Imbrie computed the volume of the space of branched polymers with n balls, in 2 and 3 dimensions. We give a combinatorial proof of their results, and use it to get a finer description of the space of polymers. In particular we show that the diameter of a 3D branched polymer on n disks is of order n^(1/2), and give some exact simulations. Time and Date: 4:15 p.m., Wednesday, April 11, 2007 (follows Rick Kenyon's Probability Seminar) Event: Probability Seminar Speaker: Ander Holroyd, UBC Subject:"Poisson Matching" Location: WMAX 216 Abstract: Red points and blue points occur as independent Poisson processes in R^d, and we consider schemes to perfectly match red points to blue points in a translation-invariant way. For any matching scheme in dimensions 1 and 2, the distance X from a typical red point to its blue partner has infinite d/2-th moment, while in dimensions >=3 there exist schemes where X has exponential tails. For the variant problem of matching points of a single colour to each other, there exist schemes where X has exponential tails, but if we insist that the matching is a deterministic factor of the points then in dimension 1, X must have infinite mean. The Gale-Shapley stable marriage is a natural greedy matching scheme. It is close to optimal (in terms of X) for two-colour matching in dimension 1, but far from optimal for dimensions >=3 and for one-colour matching. Joint work with Robin Pemantle, Yuval Peres and Oded Schramm. Time and Date: 2:00--3:00 p.m., Thursday, April 12, 2007 Event: UBC SCAIM Seminar Speaker: Eldad Haber, Emory University Subject:Adaptive mesh refinement methods for elastic image registration'' Location: ICICS/CS 238 (Computer Science Bldg, 2366 Main Mall, UBC) Abstract: In this talk we present an adaptive multilevel refinement method for non-parametric image registration. We use the elastic potential as a regularizer and demonstrate that it can be effectively and accurately discretized on octree grids. We use the L-BFGS method for optimization which requires the solution of a linear system involved the Hessian of the regularizer. We develop a refinement criteria based on the accurate evaluation of the variational form. Numerical experiments demonstrate that an order reduction in problem size and computational time is obtained by using our method. Time and Date: 9:00--5:15 p.m., Friday, April 13, 2007 Event: IAM Seminar Retreat Organizers: Dan Coombs, Michael Ward, Marek Labecki, IAM Website: http://www.iam.ubc.ca/newsevents/Retreat2007/ .html Location: Minnekhada Lodge, Minnekhada Regional Park Time and Date: 4:00--5:00 p.m., Monday, April 16, 2007 Event: PIMS 10th Anniversary Speaker Series Speaker: Gunnar Carlsson, Stanford Subject:Algebraic Topology and Geometric Pattern Recognition'' Location: WMAX 110 (PIMS Facility) Abstract: With the "blizzard" of data being generated by scientists in all disciplines, the development of tools for analyzing it has become a very high priority task. In particular, methods for quick qualitative analysis are of particular value. In this talk, I will describe one such method, based on the mathematical formalism called homology theory. I will discuss the mathematical background, how it is modified to be able to deal with situations where there is noise and where one has incomplete information, and finally illustrate with some examples. Time and Date: 3:30--4:30 p.m., Tuesday, April 17, 2007 Event: DG-MP-PDE Seminar Speaker: Cyril Imbert, Paris Dauphine Subject:Homogenization results for dislocation dynamics'' Location: WMAX 110 Time and Date: 3:00 p.m., Wednesday, April 18, 2007 Event: Algebra Topology Seminar Speaker: John Guaschi, University P. Sabatier, Toulouse, France Subject:Braid groups of the projective plane and the splitting problem'' Location: WMAX 110 Time and Date: 3:10--4:00 p.m., Wednesday, April 18, 2007 Event: Probability Seminar Speaker: Gord Slade, UBC Subject:Random walk on the incipient infinite cluster for oriented percolation'' Location: WMAX 216 Abstract: We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation in d spatial dimensions and one time dimension. For dɲ, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is 4/3, and thereby prove a version of the Alexander-Orbach conjecture in this setting. This is joint work with Martin Barlow, Antal Jarai and Takashi Kumagai. Time and Date: 3:30--4:30 p.m., Tuesday, April 24, 2007 Event: DG-MP-PDE Seminar Speaker: Benoit Perthame, ENS Paris Subject:Mathematical analysis of models for chemotaxis: parabolic, hyperbolic, kinetic'' Location: WMAX 110 (PIMS Facility) Time and Date: 4:00--5:00 p.m., Wednesday, April 25, 2007 Event: PIMS 10th Anniversary Speaker Series Speaker: Tai-Ping Liu, Stanford Subject:Prandtl Conjecture and von Neumann Paradox for Shock Reflections'' Location: WMAX 110 Abstract: We plan to discuss the two fundamental problems, the Prandtl Conjecture and von Neumann Paradox, in the theory of supersonic flows with shock waves. These problems were raised in the first half of the 20th century and clearly formulated in the classical treaty of Courant-Friedrichs. There have been spetacular progresses made on one-dimensional shock wave theory during the second half od 20th century. For the past several years, serious efforts are made in the study of multi-dimensional shock wave theory, centered mostly around aforementioned two problems. These problems involve nonliear partial differential equations of mixed types and free boundaries. We plan to discuss the recent progresses and open research directions on these problems. Time and Date: 2:00 p.m., Thursday, April 26, 2007 Event: Mathematical Biology Seminar Speaker: Joshua Weitz, Georgia Tech Subject:Evolutionary and Population Dynamics of Bacteria and Phage'' Location: WMAX 216 Abstract: Bacterial viruses, aka bacteriophage or phage, are ubiquitous in nature, yet many central aspects of host-phage biology have not been integrated into mathematical models. In this talk I present a series of theoretical efforts to understand the diversity, population dynamics and life history of phage. First, I discuss an evolutionary ecology model of host-phage diversification using the framework of adaptive dynamics and show how the principle of competition exclusion is modified in the context of coevolutionary arms races. Second, current models of host-phage population dynamics neglect to include the reduction of lytic effectiveness as hosts approach stationary phase. Incorporating reduced lysis into dynamics leads to a prediction of alternative stable states, which are discussed in the context of simple experiments. Finally, I explore ongoing experimental and theoretical efforts to understand how phage may optimally exploit their hosts by utilizing a variety of life history strategies. Time and Date: 3:00--4:00 p.m., Monday, April 30, 2007 Event: Algebraic Geometry Seminar Speaker: Hendryk Pfeiffer, Department of Mathematics, UBC Subject:Modular tensor categories from semisimple algebras'' Location: WMAX 110 (PIMS Facility) Abstract: Modular tensor categories are finitely semisimple Abelian categories with some additional structure that allows us to obtain combinatorial invariants of oriented framed tangles. Reshetikhin and Turaev invented them in order to construct their 3-manifold invariant. Algebraically, these categories can be constructed as follows: There exist very special finite-dimensional and non-semisimple Hopf algebras. Restrict the category H-Mod of such a Hopf algebra H to its full subcategory of tilting modules. The modular tensor category then appears as a quotient of the category of tilting modules. I find this recipe too complicated. Question: Is every modular tensor category equivalent to A-Mod for some finite-dimensional semismple algebra A? I show how to fix Tannaka-Krein reconstruction in order to give an affirmative answer to this question. As the term 'modular' suggests, there are plenty of similarities with representation theory in positive characteristic p. Using quantum groups, however, one obains equivalent categories by merely working in characteristic zero and one can even treat the case in which p' is not prime. Time and Date: 3:00 p.m., Wednesday, May 2, 2007 Event: Algebra Topology Seminar Speaker: Bernardo Uribe, Universidad de los Andes Subject:Orbifold String Topology I'' Location: WMAX 110 Abstract: In these two lectures I will survey my recent work with Lupercio and Xicotencatl on the properties of the homology of the free loop space of an orbifold. In the first lecture I will review the work of Chas and Sullivan on string topology and I will describe how this theory could be generalized to the space of free loops on an orbifold. I will also review the Hochschild version of string topology due to Cohen and Jones and how this construction could also be generalized to the orbifold case. At the end of the lecture I will show some simple examples to get a flavor of the theory. In the second lecture I will show how the orbifold string topology on the symmetric product gives rise to a ring structure on the cohomology of the inertia orbifold; this we have coined the virtual cohomology. Then I will explain the relation between the virtual cohomology and the Chen-Ruan cohomology. To finish I will show how to calculate in general the virtual cohomology, and I will give some examples. Time and Date: 3:10--4:00 p.m., Wednesday, May 2, 2007 Event: Probability Seminar Speaker: Russ Lyons, Indiana University Subject:Spanning Trees, Random Graphs, and Random Walks'' Location: WMAX 216 Abstract: In the usual Erdõs-Rényi model of random graphs, each pair of n vertices is connected by an edge independently with probability c/n for some constant c. When c > 1, it has a unique giant" component. How quickly does the number of spanning trees of the giant component grow with n compared to the growth in the number of its vertices? Is it monotonic in c? We answer this in joint work with Ron Peled and Oded Schramm. Time and Date: 3:00 p.m., Friday, May 4, 2007 Event: Algebra Topology Seminar Speaker: Bernardo Uribe, Universidad de los Andes Subject:Orbifold String Topology II'' Location: WMAX 110 Time and Date: 3:00--4:00 p.m., Monday, May 7, 2007 Event: Special Algebraic Geometry Seminar Speaker: Shuji Saito, University of Tokyo Subject:Chow group of 0-cycles on surface over p-adic fields with infinite torsion subgroup'' Location: WMAX 216 (note special location in PIMS facility) Abstract: In this talk I would like to demonstrate how Hodge theory can play a crucial role in an arithmetic question. The issue is to construct an example of a projective smooth surface X over a p-adic field K such that for any prime l different from p, the l-primary torsion subgroup of CH_\subscript 0(X), the Chow group of 0-cycles on X, is infinite. A key step in the proof is disproving a variant of the Block-Kato conjecture which characterizes the image of an l-adic regulator map from a higher Chow group to a continuous étale cohomology of X by using p-adic Hodge theory. By aid of theory of mixed Hodge modules, we reduce the problem to showing the exactness of de Rham complex associated to a certain variation of Hodge structure, which follows from Nori's connectivity theorem. Time and Date: 4:00--5:00 p.m., Monday, May 7, 2007 Event: Special PIMS Math Finance Seminar Speaker: Darrell Duffie, Stanford University Subject:Frailty Correlated Default'' Location:WMAX 110 Note: (Coffee and refreshments will be served half an hour before the talk.) Abstract: We analyze portfolio credit risk in light of dynamic "frailty”, in the form of incompletely observed covariates. Common dependence by firms on unobservable time-varying default covariates is estimated to cause large changes in conditional mean default rates above and beyond those predicted by observable factors, and large increases in the fatness of the tails of the distributions of portfolio default losses for U.S. corporates during 1980-2004. Time and Date: 2:00--3:00 p.m., Wednesday, May 9, 2007 Event: Mathematics Colloquium hosted by PIMS-UBC Speaker: Bob Jerrard, University of Toronto Subject: Gamma-Convergence and Saddle Points'' Location: WMAX 110 Time and Date: 4:00--5:00 p.m., Wednesday, May 9, 2007 Event: Mathematics Colloquium hosted by PIMS-UBC Speaker: Chris Jones, University of North Carolina/SAMSI Subject: Boundary Value Problems for Elliptic PDEs and the Morse Index Theorem in Multi-Dimensions'' Location: WMAX 110 Time and Date: 2:00 p.m., Monday, May 14, 2007 Event: DG-MP-PDE Seminar Speaker: Matania Ben-Artzi, Hebrew U. Subject:Viscous Hamilton-Jacobi equations, (Minicourse: Lecture 1)'' Location: WMAX 110 (PIMS Facility) Abstract: The VHJ equations are Hamilton-Jacobi equations with additional diffusion/viscosity (or the heat equation with additional nonlinear term depending on the gradient of the unknown function). These equations appear in a variety of applications, from financial mathematics to crystal growth models. In addition, they can be viewed as "regularized" versions of the Hamilton-Jacobi equation, analogous to the relation between the "viscous" and "inviscid" Burgers equations. Topics covered in these lectures will include: 1) Introduction and motivation. 2) Comparison principles for nonlinear equations. 3) Global (in time) well-posedness in continuous function spaces. 4) Bernstein-type estimates and zero viscosity limits. 5) Local and global well-posedness in Lebesgue spaces. 6) Self-similar solutions (travelling waves). 7) Large-time behavior. Time and Date: 3:30 p.m., Tuesday, May 15, 2007 Event: DG-MP-PDE Seminar Speaker: Guy Katriel, Hebrew U. Subject:Differences of semigroups, eigenvalue bounds, and their application to Schroedinger operators'' Location: WMAX 110 Time and Date: 3:10--4:00 p.m., Wednesday, May 16, 2007 Event: Probability Seminar Speaker: Alex Roitershtein, UBC Subject:Oscillating random walk on Z driven by its occupation time at zero'' Location: WMAX 216 Abstract: I will consider a nearest-neighbor random walk X_n on integers with the drift at time n (conditional on the past expectation of X_{n+1}-X_n) equals to -sign(X_n)f^{-1}(\eta_n), where \eta_n is the number of visits to zero by time n and f(n) is a regularly varying function with index a \geq 0. If a > 1, we show that the functional central limit theorem with standard normalization \sqrt{n} holds for X_n. In addition, we prove that the law of the random walk is equivalent in this case to the distribution of the simple random walk. If a is in [0,1), we show that the law of X_n/b_n converges to a non-degenerate (non-gaussian) limit distribution. Here b_n is an explicit regularly varying function of index a/(1+a). This is a joint work with Iddo Ben-Ari (UC Irvine) and Mathieu Merle (UBC). Time and Date: 4:00--5:00 p.m., Thursday, May 17, 2007 Event: Math Finance Seminar Speaker: Freddy Delbaen, ETH Zurich Subject:Monetary utilities and BDEs'' Location: WMAX 216 Notes: If you are interested in having lunch with Prof. Freddy Delbaen on May 17th, please contact Prof. Ivar Ekeland. Time and Date: 3:00 p.m., Friday, May 18, 2007 Event: SCAIM UBC Seminar Speaker: Hans De Sterck, Department of Applied Mathematics, University of Waterloo Subject:Markov Chains and Web Ranking: a Multilevel Adaptive Aggregation Method'' Location: WMAX 216 (PIMS Facility) Abstract: Google's PageRank method for ranking web pages models how a random surfer' follows links between web pages in a random fashion. The stationary probability vector of the resulting Markov chain provides a ranking of all the pages in the network. Calculating this stationary probability vector is a very large problem: Google now indexes more than 25 billion internet web pages. We present a multilevel adaptive aggregation method for the linear algebra problem of calculating the stationary probability vector of a Markov chain. The method described is a variant of adaptive algebraic multigrid methods for sparse linear systems, and is also related to existing aggregation methods for Markov chains. We apply our multilevel method to a set of stochastic matrices that provide models for web page ranking. These numerical tests serve to illustrate for which types of stochastic matrices our multilevel adaptive method may provide significant speedup compared to standard iterative methods. The tests also provide some insight into why the PageRank model is a successful model for determining a ranking of web pages. Time and Date: 3:10--4:00 p.m., Wednesday, May 23, 2007 Event: Probability Seminar Speaker: Jesse Goodman, Department of Mathematics, UBC Subject:Invasion percolation on regular trees'' Location: WMAX 216 (PIMS Facility) Abstract: Invasion percolation is a dynamic process closely linked to critical percolation, but without an external parameter. In joint work with Omer Angel, Frank den Hollander and Gord Slade we showed that the cluster of invaded points consists of a backbone together with sub-critical trees hanging off the backbone, with parameters that increase towards criticality. By this analysis we derive scaling estimates for the r-point functions and related quantities, and show that the scaling behaviour differs from the incipient infinite cluster. In ongoing joint work with Mathieu Merle, we also analyze the continuum limit of the random trees obtained in invasion percolation. Time and Date: 3:00--4:00 p.m., Friday, May 25, 2007 Event: SCAIM UBC Seminar Speaker: Daniel B. Szyld, Department of Mathematics, Temple University Subject:Inexact Krylov Subspace Methods for PDEs and Control Problems'' Location: WMAX 216 Abstract: In many circumstances, a known good preconditioner is not easily computable. Instead, an approximation to it is available. This is the case, for example, when the preconditioner has an inverse associated with it, such as in Schur complements (e.g., in saddle point problems), or in the reduced Hessian in some control problems. The application of the preconditioner implies then an iterative solution of a linear system. In these cases, the question is how accurately to solve the (inner) iteration. In our work on Inexact Krylov methods, we have shown that the inner iterations can be solved progressively less accurately, as the underlying Krylov method (e.g., GMRES or Conjugate Gradients) converges to the overall solution. Computable inner stopping criteria have been developed to guarantee convergence of the overall method. We will discuss these criteria, and illustrate its application to several problems. Currently, we are applying these ideas to parabolic control problems, where the reduced Hessian has two different inverses; and thus two inner iteration criteria are needed. Time and Date: 9:00 a.m.-p.m., Monday-Wednesday, June 18-20, 2007 Event: PIMS CRG Workshop in Mathematical Modeling and Computation in Biology Note: Details can be found at http://www.pims.math.ca/science/2007/07srb/. Organized by Rachel Kuske (UBC Applied Math), Yue Xian Li (UBC Math Biology) and Lawrence Ward (UBC Psychology). Subject:Synchronous Rhythms in the Brain'' Location: Peter Wall Institute, UBC Time and Date: 3:10 p.m., Monday, June 18, 2007 Event: Probability Seminar Speaker: Iddo Ben-Ari, UC Irvine Subject:Large deviations for partition functions of directed polymers and other models in an IID field'' Location: MATX 1118 (NOTE UNUSUAL TIME AND PLACE.) Abstract: Consider the partition function of a directed polymer in an IID field. It is well-known that under some mild assumption on the field, the free energy of the polymer is equal to some deterministic constant for almost every realization of the field and that the upper tail of the large deviations has an exponential tail. In this talk I'll discuss the lower tail of the large deviations (LTLD). In a recent work, Cranston, Gautier and Mountford, have obtained estimates on the LTLD for the one-dimensional Gaussian case as well as for fields which are "almost" positive, in some appropriate sense. I'll present a new, robust, method for obtaining estimates on the the LTLD. As a consequence, the LTLD exhibits three regimes, determined by the tail of the negative part of the field. The method can be applied to other oriented and non-oriented models, such as first-passage percolation. A preprint is available on www.math.uci.edu/~ibenari Time and Date: 1:00 p.m., Wednesday, June 20, 2007 Event: SCAIM Seminar (Pizza and pop will be provided.) Speaker: Paul Tupper, McGill University Subject:A Model for Mesoscale Simulation and its Numerical Difficulties'' Location: WMAX 216 (PIMS Facility), 1933 West Mall Abstract: One of the problems with computer simulation of materials is that most interesting behaviour occurs on long time scales while atomic motion occurs on very small time scales. I will discuss recent work on a class of models which overcomes this difficulty by coarse-graining the system in time. The resulting equations describe a slowing evolving microscopic density. These systems show promise for modelling a range of physical situations, but at present there are not satisfactory algorithms for integrating them in time. The difficulty is finding an efficient way to take an implicit time step. I will survey the problem and explain some possible approaches to it. Time and Date: 3:00--4:00 p.m., Thursday, June 28, 2007 Event: DG-MP-PDE Seminar Speaker: Allan Greenleaf, Department of Mathematics, University of Rochester Subject:Cloaking Devices and Electromagnetic Wormholes: The Mathematics of Invisibility'' Location: WMAX 110 (PIMS Facility), 1933 West Mall Abstract: The last year has seen much theoretical, numerical and experimental work on invisibility, or "cloaking". Mathematically, this involves looking at solutions of the conductivity, Helmholtz or Maxwell's equations with certain degenerate coefficient coming from singular changes of variables. I will describe an "ideologically correct" way of thinking about this general phenomenon, and then describe recent work on electromagnetic wormholes, which are (mostly) invisible tunnels allowing waves to pass from one region to another. This is joint work with Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann. Time and Date: 2:00 p.m., Thursday, July 5, 2007 Event: Math Biology Seminar Speaker: Stewart Chang, University of Michigan Subject:Multi-scale modeling of antigen presentation with applications to tuberculosis'' Location: WMAX 216 (PIMS Facility), 1933 West Mall Abstract: Antigen presentation is the process by which cells of the immune system display peptides from pathogens on their surface after binding the peptides to major histocompatibility complex (MHC) molecules. T helper cells recognize peptides from pathogens in this context then secrete cytokines that activate other cells, initiating an immune response. Antigen presentation is therefore a requisite for immunity to several pathogens including Mycobacterium tuberculosis (Mtb). To approach questions related to antigen presentation and disease, I represented antigen presentation at different scales using a series of mathematical and statistical models. At the molecular scale, I asked whether heterogeneity in peptide length affects binding to MHC class II, the class of MHC responsible for binding peptides from bacteria such as Mtb. By developing statistical models of peptide-MHC binding, I found that length has a nonlinear effect on binding affinity and that this information could improve the accuracy of binding prediction. At the cellular scale, I asked why Mtb possesses multiple mechanisms to inhibit antigen presentation on the cell surface. My mathematical model shows that these mechanisms may be acting on different timescales and therefore complementary rather than merely redundant. Finally, at the multi-cellular level, I asked how polymorphisms in multiple genes related to antigen presentation might affect T cell response and susceptibility to infectious diseases such as tuberculosis. Using a multi-scale model representing both the antigen-presenting cell and T cell, I found that polymorphisms in two different genes may exert the same influence on the output, potentially canceling out their effects. Future work with these models may include evaluation of candidate peptide-based vaccines to ensure high-affinity binding, T cell response, and broad efficacy in diverse populations. Time and Date: 3:00 p.m., Tuesday, July 10, 2007 Event: UBC SCAIM Seminar Speaker: Mark Peletier, TU Eindhoven Subject:Localization and Imperfection-sensitivity in Cylinder Buckling'' Location: WMAX 216 (PIMS Facility), 1933 West Mall, UBC Abstract: The buckling of thin shells is a classical problem in engineering. Within this class the axially-loaded cylinders is the worst-case scenario: here the buckling is very unstable, and as a result the behaviour is highly imperfection-sensitive and nearly impossible to predict. We investigate a solution of the equations that is central to this phenomenon, known as a mountain-pass solution. It is unstable, has the form of a localized dimple, and separates the basins of attraction of the unbuckled and the buckled states. We postulate an energy-comparison rule that leads to a lower bound on the buckling load, and investigate its properties. Time and Date: 10:00--11:00 a.m., Thursday, July 12, 2007 Event: Complex Fluids Seminar Speaker: Tomoaki Kunugi, Kyoto University Subject:Multiscale modelling for gas-liquid interface'' Location:MATX 1102 Abstract: At a gas-liquid interface, there are many physics and unknown phenomena related to thermodynamics, electromagnetics, hydrodynamics, and heat and mass transfer. Therefore, a modeling of gas-liquid interface is one of key issues of the numerical research on multiphase flow. Currently, the Continuum Surface Force model (CSF) proposed by Brackbill (1990) is popular to model a gas-liquid interface in computational fluid dynamics. However, the CSF model cannot explain the physics of the gas-liquid interface because this model is derived by a mechanical energy balance at the interface. In this presentation, assuming that the interface is a thin fluid-membrane and has a finite thickness, we introduce a new gas-liquid interfacial model based on thermodynamics (Phase Field theory) via mathematical approach. In particular, we derive the equation of free energy based on a lattice gas model (i.e., Ising model) including the effect of the electric double layer caused by a contamination on the interaction between the bubble interfaces. Moreover, we introduce the importance of contamination at the interface from the perspective of our experiment: microbubbly flow. In general, it is believed that the microbubbles hardly coalesce with each other unlike bubbles of millimeter size. However, we found lots of microbubble coalescence in the microbubbly flow. Until today, the microbubble coalescence has not been reported via the experimental observations. In this presentation, we report new findings regarding the microbubble coalescence by using a high speed camera, and try to elucidate the mechanism of the microbubble coalescence. Through our experiment and interfacial modeling, we have been trying to understand the mechanism with respect to bubble coalescence including the contamination effect and the heat/mass transport processes. Time and Date: 3:00--4:30 p.m., Monday, August 27, 2007 Event: Special Algebraic Geometry Seminar Speaker: Martin Guest, Tokyo Metropolitan University Subject:Differential equations aspects of quantum cohomology'' Location: MATH 104 Time and Date: 3:00--4:30 p.m., Friday, September 7, 2007 Event: Joint PIMS Distinguished Lecture/Mathematics Colloquium Speaker: Damien Roessler, Institut de Mathematiques de Jussieu Subject:The fixed formula and Nori's approach to the Riemann-Roch theorem'' Location: MATX 1100 Note: This was originally announced as a Thursday, September 6th (3-4:30 p.m.) PIMS Distinguished Lecture. Date moved to joint event. Abstract: We shall explain the content of the Lefschetz fixed point formula in the coherent setting and we shall explain its connection, established by M. Nori, with the Riemann-Roch theorem. Detailed computations in the case of curves will be given. Time and Date: 3:00--4:00 p.m., Monday, September 10, 2007 Event: IAM Seminar Series Speaker: Anthony Peirce, Mathematics, UBC Subject: An Implicit Level Set Algorithm for modeling Hydraulically Driven Fractures'' Location: Room 301, LSK Bldg. Abstract: There has been considerable analytic and experimental effort devoted to characterizing the different physical regimes of propagation for hydraulic fractures. The near-tip asymptotic form of the fracture width w exhibits a different power law behavior depending on the dominant physical process governing the propagation of the fracture. In general, this behavior is even more complex and occurs on multiple length scales. Indeed, as one moves away from the tip, w assumes different functional forms depending on the dominant physical process active locally. A hitherto open computational problem has been to develop robust numerical algorithms that will be able to simulate planar fractures in three dimensional elastic media that are able to capture these multiple length scales and regimes of propagation with reasonable computational resources. One of the major challenges in this process has been to find a robust algorithm that will locate the unknown boundary of the fracture. In this talk we describe a novel algorithm that is based on an implicit level set method to locate the free boundary. The algorithm exploits the applicable local tip asymptote to locate the unknown fracture front. The algorithm does not rely on the calculation of the normal front velocity from the pressure gradient field, which is typically singular at the tip. In fact, the implicit algorithm is able to provide accurate estimates of the normal velocity of the front by solving an appropriate nonlinear equation within each element of a small set of elements close to the fracture front. The fact that this implicit algorithm does not require the velocity field as an input function is also novel in the level set context. We provide numerous examples that demonstrate the robustness, efficiency, and accuracy of the algorithm for fractures that propagate in a variety of regimes: toughness dominated, viscosity dominated, and leak-off dominated. Time and Date: 3:00--4:30 p.m., Monday, September 10, 2007 Event: Algebraic Geometry Seminar Speaker: Steve Mitchell, University of Washington Subject:Schubert varieties in affine Grassmannians'' Location: WMAX 110 (PIMS Facility) Abstract: In every Lie type there is an infinite-dimensional projective variety called the affine Grassmannian, homotopy-equivalent to the loop space of the appropriate compact Lie group and very much analogous to an ordinary Grassmannian. It is a union of finite-dimensional "affine Schubert varieties", and one can ask: Which affine Schubert varieties are smooth? Which are palindromic (i.e. satisfy Poincare duality additively)? I will describe recent joint work with Sara Billey, in which we give complete answers to these questions in all Lie types. Time and Date: 2:15--3:15 p.m. (pls note unusual time), Tuesday, September 11, 2007 Event: UBC SCAIM Seminar Speaker: Uri Ascher, Computer Science, UBC Subject:On Inverse Problems, Regularization, Level Sets, Conjugate Gradients and Sparse Solutions'' Location: WMAX 216 Abstract: In this informal talk I will attempt to draw some connections among the various items appearing in the title. Emphasis will be placed on the role of regularization and on efficient solution techniques for tough reconstruction problems. Time and Date: 3:00--4:30 p.m., Tuesday, September 11, 2007 Event: PIMS Distinguished Lectures Speaker: Damian Roessler, Institut de Mathematiques de Jussieu Subject:The Adams-Riemann-Roch theorem and applications'' Location: WMAX 110 Abstract: We shall formulate the Adams-Riemann-Roch theorem, which is a refinement of the Grothendieck-Riemann-Roch theorem taking into account torsion. We shall apply the theorem to the de Rham complex. This will lead to a conjecture on the torsion of the Chern classes of Gauss-Manin bundles. Time and Date: 3:00--4:00 p.m., Wednesday, September 12, 2007 Event: Probability Seminar Speaker: Benjamin Graham, Mathematics, UBC Subject:A balls and boxes Markov chain'' Location: WMAX 216 Abstract: Consider N boxes, each with R balls in. Each step, pick two boxes uniformly at random. If the first box is not empty, move a ball from the first box to the second. The empirical distribution tends to the geometric law with mean R. We look at the time to convergence. Time and Date: 3:30--4:30 p.m., Wednesday, September 12, 2007 Event: Algebra/Topology Seminar Speaker: Enrique Torres-Giese, Mathematics, UBC Subject:Spaces of Homomorphisms and Group Cohomology'' Location: WMAX 110 Abstract: In this talk I will discuss the construction of a family of simplicial spaces built of spaces of homomorphisms. This family yields a filtration of the classifying space of a group and it is parametrized by group theoretical data. Time and Date: 3:00--4:30 p.m., Thursday, September 13, 2007 Event: PIMS Distinguished Lectures Speaker: Damian Roessler, Institut de Mathematiques de Jussieu Subject:Deligne's functorial Riemann-Roch formula'' Location: WMAX 110 Abstract: We shall formulate a refinement, due to Deligne, of the Riemann-Roch theorem for fibrations of curves. This theorem provides canonical isomorphisms between certain determinant bundles. We shall show how this theorem leads to a new construction of the modular units. Time and Date: 3:00--4:00 p.m., Thursday, September 13, 2007 Event: DG-MP-PDE Seminar Speaker: Olivier Druet, ENS Lyon and PIMS Subject:Critical elliptic PDE systems: stability and compactness issues'' Location: WMAX 216 Abstract: I will discuss elliptic systems which are built on the model of the Yamabe equation. I will be mainly interested in compactness and stability issues for these systems. The aim of this work was to recover some properties coming from conformal invariance of the equations (like in the scalar equation case) and to discover some phenomena due to the interactions between the lines in the system. This is a joint work in progress with Emmanuel Hebey. Time and Date: 4:00 p.m., Thursday, September 13, 2007 Event: Complex Fluids Seminar Speaker: Seyed Majid Hosseini, Department of Chemical and Biological Engineering, UBC Subject:Industrial flow simulation with SPH method'' Location: MATH 225 Abstract: We present novel applications for an incompressible Smoothed Particle Hydrodynamics (SPH) method by proposing a new algorithm and utilizing some new treatments. The governing equations for fluid phase are Navier-Stokes equations along with the continuity equation which are described in a Lagrangian framework. In elastic solid simulations Navier-Stokes equations is replaced by momentum equation for each solid particle. The proposed SPH method uses a Poisson pressure equation to satisfy the incompressibility constraints. The solution algorithm is an explicit predictor-corrector scheme which employs an adaptive smoothing length based on density variations. In our current works SPH method is used for applications such as: non-Newtonian fluid flow problems, unsteady free-surface flows (both Newtonian and viscoelastic fluids are considered). In the case of viscoelastic fluids, both Maxwell and Oldroyd-B models are investigated, fluid-structure interaction (FSI) problems particularly, in cases when FSI is combined with solid-rigid contacts, elastic-perfectly plastic solid deformation, high-velocity impact and membrane-like materials. The results obtained by the proposed SPH algorithm are in close agreement with available experimental or numerical data. Time and Date: 3:00 p.m., Friday, September 14, 2007 Event: Mathematics Colloquium Speaker: Domingo Luna, Universite Grenoble 1 Subject: Wonderful varieties'' 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 17, 2007 Event: IAM Seminar Series Speaker: Hong Qian, Department of Applied Mathematics, University of Washington Subject: The Chemical Master Equation: Theories, Computations, and Applications'' Location: Room 301, LSK Bldg. Abstract: Chemical master equation, i.e., a birth-death process with continuous time, has become the mathematical foundation of chemical reaction kinetics in both small and large systems. It has wide applications to biochemical models in cellular biology. In this talk, I shall discuss the unifying theory that encompasses both stochastic models and deterministic nonlinear chemical oscillations. The essential difference between open and closed systems in terms of the "chemical detailed balance" will be discussed. The dynamic consequences of open-systems will be presented. Time and Date: 3:00--4:30 p.m., Monday, September 17, 2007 Event: Algebraic Geometry Seminar Speaker: Jim Bryan, UBC Subject:Donaldson-Thomas and Gromov-Witten theory of orbifolds and their resolutions'' Location:WMAX 110 (PIMS Facility) Abstract: A general principle in physics asserts that string theory on a Calabi-Yau orbifold should be equivalent to string theory on any Calabi-Yau resolution of the orbifold. A mathematical realization of this principle is the idea that Donaldson-Thomas theory or Gromov-Witten theory of the orbifold should be equivalent to the corresponding theory on the resolution. We will discuss these ideas in general and for some specific examples. Time and Date: 12:30--2:00 p.m., Tuesday, September 18, 2007 Event: Joint UBC SCAIM and Mathematical Biology Seminar Speaker: Hong Qian, University of Washington Subject:A Nonequilibrium Steady-State Theory of Phosphorylation-Dephosphorylation Switch in Cellular Signaling'' Location:WMAX 216 Abstract: We present a mathematical theory for a biochemical switch system, which can be either the phosphorylation-dephosphorylation cycle (PdPC) reactions catalyzed by a kinase and a phosphatase, or GTPase cycles catalyzed by a guanine exchange factor (GEF) and a GTPase activating protein (GAP). The theory is based on the recently developed open-system nonequilibrium thermodynamics, the chemical master equation, and the traditional enzyme kinetics. We show how ultrasensitivity, as a new form of cooperativity, arisies in an open system, and the role of cellular energy in the functioning of switches. We also investigate PdPC/GTPase systems with feedbacks and how it leads to various nonlinear bifurcations. Time and Date: 3:30--4:30 p.m., Tuesday, September 18, 2007 Event: Discrete Mathematics Seminar Speaker: Farzin Barekat, Mathematics, UBC Subject:Exact Bounds for Forbidden Configurations'' Location:WMAX 216 Abstract: We explore some exact bounds for Forbidden Configurations', which have a design theory flavour. Let q be given. Consider an m-rowed (0,1)-matrix A, which has no repeated columns. Assume there is no qx2 submatrix of A which is a row and column permutation of 11..11 11..11 00..00 Given that m is large with respect to q, we establish the correct upper bound on the number of columns that A can have, improving quite a bit on a pigeonhole bound. An existence theorem of Dehon (1983) for simple triple design is important in establishing that the bound is exact. We also establish exact bounds for the following cases: 11..11 00..00 11..11 11..11 00..00 00..00 Time and Date: 3:00--4:00 p.m., Wednesday, September 19, 2007 Event: Probability Seminar Speaker: Marco Ferrante, Mathematics, UBC Subject:Linear Stochastic Differential-Algebraic Equations'' Location:WMAX 216 Abstract: A Differential-Algeraic Equation is, essentially, an Ordinary Differential Equation F(x,\dot x)=0 that cannot be solved for the derivative \dot x . In a recent joint paper with A. Alabert of UAB, Barcelona, we studied the linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalized process. In the talk I will present the results of this paper, providing a sufficient condition for the existence of the density of the law of the solution. Time and Date: 3:00--4:00 p.m., Wednesday, September 19, 2007 Pls note unusual day/time/location. Event: DG-MP-PDE Seminar Speaker: Leo Tzou, Stanford Subject:Inverse Problems with Multiple Coefficients'' Location:MATH 204 Time and Date: 3:30--4:30 p.m., Wednesday, September 19, 2007 Event: Algebra/Topology Seminar Speaker: Thomas Mattman, CSU Chico and UBC Subject:Boundary Slope Diameter and Crossing Number of 2-Bridge Knots'' Location:WMAX 110 Abstract: In joint work with Maybrun and Robinson, we prove that for 2-bridge knots, the diameter of the set of boundary slopes is twice the crossing number. We also show that 2-bridge knots with four or fewer boundary slopes have a boundary slope of genus two or less. After some topological preliminaries, the argument quickly becomes combinatorial and is based on comparing various continued fraction representations of the same fraction. Time and Date: 2:00 p.m., Thursday, September 20, 2007 Event: Mathematical Biology Seminar Speaker: Adriana Dawes, University of Washington, Friday Harbor Labs Subject:Stable segregation of PAR proteins in the early C elegans embryo relies on a bistable switch mechanism'' Location:WMAX 216 Abstract: PAR proteins, collectively termed the anterior and posterior PAR proteins, establish distinct intracellular spatial domains in the one cell C elegans embryo, polarizing the cell. This polarization is persistent, lasting approximately 10-20 minutes until first cleavage. It has been established experimentally that the anterior and posterior PAR proteins interact through mutual phosphorylation, and recent genetic studies indicate that the anterior PAR proteins are capable of oligomerizing. Using mathematical modelling, I show that known interactions between the PAR proteins give rise to a bistable switch that may account for the stable segregation of the PAR proteins. The presence of a bistable switch in the C elegans embryo is verified experimentally by depleting the anterior PARs using RNA interference, providing a direct test of the mathematical model. Time and Date: 4:00 p.m., Thursday, September 20, 2007 Event: Complex Fluids Seminar Speaker: Yoichiro Mori, Mathematics, UBC Subject:The Immersed Boundary Method'' Location:MATH 225 Abstract: The immersed boundary method is a numerical method/framework that allows one to perform fluid-structure interaction calculations. It has been widely used in biofluid dynamics simulations. It is characterized by the use of an Eulerian grid for the fluid and a Lagrangian grid for the elastic strucure. The communication between the two grids is achieved through the use of regularized Dirac delta functions. In this talk, I will explain the method in some detail and present some recent algorithmic developments if time permits. Time and Date: 3:00 p.m., Friday, September 21, 2007 Event: Mathematics Colloquium Speaker: Christiane Frougny, Universite Paris 8 Subject: Number representation and symbolic dynamics'' 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 24, 2007 Event: IAM-PIMS-MITACS Distinguished Colloquium Series Speaker: Howard Elman, Computer Science Department, University of Maryland at College Park Subject: Fast Iterative Solution of Models of Incompressible Flow'' Location: Room 301, LSK Bldg. Abstract: We discuss new efficient algorithms for computing the numerical solution of the incompressible Navier-Stokes equations. We show that preconditioning algorithms that take advantage of the structure of the linearized equations can be combined with Krylov subspace methods to produce algorithms that are optimal with respect to discretization mesh size, largely insensitive to Reynolds numbers, and easily adapted to handle both steady and evolutionary problems. We also show the relation between these approaches and traditional methods derived from operator splittings, and we demonstrate the performance of the new methods in some practical settings. Time and Date: 3:00--4:30 p.m., Monday, September 24, 2007 Event: Algebraic Geometry Seminar Speaker: Zack Treisman, University of Washington Subject:Rationally generated arcs'' Location:WMAX 110 (PIMS Facility) Abstract: An m-arc (or m-jet, to some) on a variety X can be thought of as an equivalence class of curves lying on X. Such an arc is rationally generated if there is a rational curve in that equivalence class. Using rationally generated arcs, some questions about rational curves can be studied. In particular, rationally generated arcs can be applied to the study of uniruled or "almost rational" varieties. Time and Date: 4:00--5:30 p.m., Monday, September 24, 2007 Event: Mathematics Colloquium Speaker: Felix Otto, Universitat Bonn Subject: Turbulent heat transport: upper bounds by a priori estimates'' Location:MATH 105 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, September 25, 2007 Event: UBC SCAIM Seminar Speaker: Abigail Wacher, Finavera Renewables Inc. Subject:From Finite Elements to String Gradient Weighted Moving Finite Elements'' Location: WMAX 216 Note: Pizza and pop will be provided. Abstract: Since 2001 my work has focused on adaptive mesh methods and in particular a Moving Finite Element Method (MFE) for solving systems of Partial Differential Equations (PDEs). I developed and implemented a moving mesh method called String Gradient Weighted Moving Finite Elements (SGWMFE) and have applied it successfully to several model problems in one and two dimensions. In this talk I will describe the theoretical derivation of the method beginning with a standard Finite Element approach for solving one PDE in one dimension and explaining how to proceed from there to obtain the MFE, GWMFE and SGWMFE methods for systems of PDEs. Time and Date: 3:30--4:30 p.m., Tuesday, September 25, 2007 Event: DG-MP-PDE Seminar Speaker: Julien Vovelle, CNRS and ENS Cachan Subject:On renormalized solutions of parabolic equations'' Location:WMAX 110 Time and Date: 3:00--4:00 p.m., Wednesday, September 26, 2007 Event: Special Mathematics Colloquium Speaker: Abigail Wacher, Finavera Renewables Inc. Subject: Weighted Moving Finite Elements applied to systems of Partial Differential Equations'' Location: MATH 104 Time and Date: 4:00--5:00 p.m., Wednesday, September 26, 2007 Event: Probability Seminar Note: change of hour Speaker: Martin Barlow, UBC Subject:Recent progress in the random conductance model'' Location:WMAX 216 Abstract: Consider the standard Euclidean lattice, and put random i.i.d. 'conductances' V(e) on each bond. We allow the possibility that V(e) is zero. Let Y be a continuous time Markov chain which jumps along the edge e with probability proportional to V(e). We assume that the probability that V(e) is positive is greater than p_c, the critical probability for bond percolation on the Euclidean lattice. Thus there exists (a.s.) a unique infinite connected subgraph on which Y can run. A special case of the above is when V(e) is either 0 or 1, and so Y is a random walk on a supercritical percolation cluster. Various kinds of 'trapping' can arise if V(e) can take either small positive values, or large values. In this talk I will discuss invariance principles for Y, and Gaussian bounds for its transition densities. Time and Date: 3:30--4:30 p.m., Wednesday, September 26, 2007 Event: Algebra/Topology Seminar Speaker: Thomas Mattman, CSU Chico and UBC Subject:Bounds on the Crosscap Numbers of Torus Knots'' Location:WMAX 110 Abstract: In joint work with Sizemore, we build on Teragaito's calculation of the crosscap number c(K) of a torus knot K to give bounds in terms of the genus g(K) and crossing number n(K): c(K) \leq \lfloor (g(K) + 9)/6 \rfloor and c(K) \leq \lfloor (n(K)+16)/12 \rfloor . The (6n-2, 3) torus knots show that these bounds are sharp. Time and Date: 2:00--3:00 p.m., Thursday, September 27, 2007 Event: Mathematical Biology Seminar Speaker: Pauline van den Driessche, University of Victoria Subject:Modeling the Spread of West Nile Virus'' Location:WMAX 216 Abstract: West Nile virus was detected in New York State in 1999, and has spread rapidly across the continent causing bird, horse and human mortality. The aim of this lecture is to model this spread. Biological assumptions are summarized and lead to the development of a reaction-diffusion model for the spatial spread of West Nile virus with cross infection between birds and mosquitoes. For a simplified model, the existence of traveling waves is proved and the spatial spread of infection is calculated. Related models for West Nile virus spread are briefly discussed. Time and Date: 3:00--3:50 p.m., Thursday, September 27, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Greg Martin, UBC Subject:\lambda (\lambda (n)): A case study in analytic number theory'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: A 2005 result of Carl Pomerance and myself identifies the normal order (that is, the asymptotic size for 100% of integers) of the twice-iterated Carmichael lambda-function ?(?(n)), a function that arises when considering an exponential pseudorandom number generator xk+1 = xk^C (mod n). Often I suppress most of the technical details of the multi-stage proof in talks on this topic; however, today I will use the result as an excuse to point out the techniques involved, techniques that might be labeled “Erdos mathematics” — elementary yet involved and (in his case) inspired calculations. Time and Date: 4:00--5:30 p.m., Thursday, September 27, 2007 Event: Complex Fluids Seminar Speaker: Anja Slim, Mathematics, UBC Subject:Shear Buckling'' Location:MATH 225 Abstract: Elastic buckling is a ubiquitous phenomenon from engineering to biology and geology. Using the Foppl--von Karman equations, we explore the onset of linear instability and the subsequent weakly and fully nonlinear development of patterns for shear-induced buckling. We find that the theory compares reasonably well with experiments in which a sheet of Neoprene is clamped and sheared along its edges. Time and Date: 4:10--5:00 p.m., Thursday, September 27, 2007 Event: SFU/UBC Number Theory Seminar Speaker: Michael Bennett, UBC Subject:Powers in progression, Chebotarev, and Hilbert class polynomials'' Location: UBC Campus, Room WMAX 110 (PIMS) Abstract: I will sketch some rather odd connections between ternary Diophantine equations, the Chebotarev Density Theorem and heights of Hilbert class polynomials evaluated at rational arguments. Time and Date: 3:00--4:30 p.m., Friday, September 28, 2007 Event: Mathematics Colloquium Speaker: Laura Scull, UBC Subject: Spaces with symmetry: orbifolds and equivariant homotopy'' 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 1, 2007 Event: IAM Seminar Series Speaker: Eric Cytrynbaum, UBC Subject:Global Bifurcations and the Appearance of a One-Dimensional Spiral Wave in Excitable Media'' Location: Room 301, LSK Bldg. Abstract: It is well known that excitable media can sustain a “fast” stable traveling pulse of excitation. In models for which analysis is tractable, the corresponding solution is known to appear through a saddle-node bifurcation accompanied by a “slow” unstable traveling pulse. Furthermore, the homogeneous rest state is also a stable solution. It is generally assumed that the boundary between the basins of attractions of the rest state and fast pulse consists of the stable manifold of the slow pulse. In this talk, I will present numerical evidence that this is the case near the saddle-node bifurcation, but that further away from the saddle-node, a global bifurcation involving the heteroclinic connection between slow and fast pulses occurs. We conjecture and provide numerical evidence that, through this bifurcation, a previously unreported unstable periodic solution, sometimes known as a one-dimensional spiral, appears. Time and Date: 3:00--4:30 p.m., Monday, October 1, 2007 Event: Algebraic Geometry Seminar Speaker: Roya Beheshti-Zavareh, Washington University Subject:Singularities of generic projections'' Location: WMAX 110 (PIMS Facility) Abstract: I will talk about generic projections of smooth varieties, a conjecture on the regularity of the fibers of generic projections, and some results in the direction of the conjecture. This is joint work with David Eisenbud. Time and Date: 4:00--5:00 p.m., Monday, October 1, 2007 Event: Special Mathematics Colloquium Speaker: Mahta Khosravi, Johns Hopkins University Subject: Spectral Asymptotics on Compact Manifolds and Related Problems in Analytic Number Theory'' Location: MATH 105 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 12:30--2:00 p.m., Tuesday, October 2, 2007 Event: UBC SCAIM Seminar Speaker: Kirill Pichon Gostaf, Laboratoire Jacques-Louis Lions, University Paris VI Subject:Finite Element Analysis of CAD Large Assemblies'' Location: WMAX 216 Abstract: In today's product development and engineering process, usage of computer aided design (CAD) platform is obvious. It allows crating of quite realistic models, precisely describing not only the geometry of the developed prototype, but also its physical properties. These models, usually referred as parts, are brought together (assembled) into assemblies, like it occurs in real world. The final digital prototype consists sometimes of thousands of parts and sub-assemblies so, its finite element based optimization is limited by computing architectures that cannot hold and process large models in a timely way. It is therefore desirable to use multiprocessor parallel computers to solve the large mathematical systems. We propose to apply domain decomposition methodology (DDM) to run numerical simulation of CAD large assemblies. Instead of exporting a complex assembly as a single component, and later dividing it in numerous, randomly created sub-domains, we propose to use assembly topology, which was previously created by designer while modeling process period. Thus, each part represents an independent sub-domain, and could be analyzed simultaneously with other parts, by sharing only the contact information. In order to enforce the matching of the local solutions, interface conditions and projection operators have to be written on the boundary between sub-domains. These terms and conditions are imposed iteratively. The convergence rate is very sensitive to these interface conditions. The classical Schwarz algorithm without overlap, as well as FETI-based methods are presented. A brief presentation of the finite element open-source FreeFem3D software could be initiated. Time and Date: 2:00--3:00 p.m., Tuesday, October 2, 2007 Event: DG-MP-PDE Seminar Speaker: Mahta Khosravi, Johns Hopkins University Subject:New Moment Results for Weyl's Law on Heisenberg Manifolds and the Dirichlet Divisor Problem'' Location: WMAX 110 Abstract: Let R(t) be the remainder term of Weyl's law for (2n+1)-dimensional Heisenberg manifolds (the first, natural, noncommutative generalization of tori). Petridis and Toth have conjectured that R(t)=O_\delta(t^{n-1/4+\delta}). We first review pointwise and moment results we have obtained that provide evidence for the Petridis-Toth conjecture in three dimensions and a proof for it in higher dimensions. Next, I will discuss my proof of a new third moment result for R(t) on Heisenberg manifolds. The methods used to attack this problem can also be applied to analogous problems from analytic number theory and I will discuss my proof of a new fifth moment result for the error term \Delta(t) in the Dirichlet Divisor problem. Time and Date: 3:00--4:00 p.m., Tuesday, October 2, 2007 Event: DG-MP-PDE Seminar Speaker: Meiyue Jiang, Peking University Subject:2-Dimensional L_p-Minkowski problem'' Location: WMAX 110 Abstract: Let S^{n-1}\subset R^n be the unit sphere. The L_p-Minkowski problem proposed by Lukwak is a natural generalization of the classical Minkowski problem. Analytically, it is equivalent to find positive solutions of the equation det(\nabla_{ij}u+e_{ij}u)=g(x)u^{p-1}, x\in S^{n-1}, (1) where g is a function on S^{n-1}, p\in \bf R, e_{ij} is the standard Riemannian metric. In this talk we will present some existence results for the case n=2, that is, 2\pi and positive solutions of the equation \"u+u=g(x)u^{p-1}, x\in S^1 (2) based on variational method. Some generalizations of equation (2) will also be discussed. Time and Date: 3:30--4:30 p.m., Tuesday, October 2, 2007 Event: Algebra/Topology Seminar Speaker: Veronique Godin, Harvard University Subject:Higher string operations'' Location: MATH 105 Abstract: Chas and Sullivan have defined an intersection-type product on the free loop space of a manifold. I'll explain a recent construction which extends this string product to include operations parameterized by the homology of certain moduli space of Riemann surfaces. I'll then discuss conjectured extensions and their consequences. Time and Date: 3:30--4:30 p.m., Tuesday, October 2, 2007 Event: Discrete Mathematics Seminar Speaker: Richard Anstee, UBC Subject:Exact Bounds for Forbidden Configurations II'' Location: WMAX 216 Abstract: This is a continuation of the previous talk. Time and Date: 3:00--4:00 p.m., Wednesday, October 3, 2007 Event: Special Mathematics Colloquium Speaker: Veronique Godin, Harvard University Subject: Intersection in the Loop Space'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Afternoon Tea). Time and Date: 4:00--5:00 p.m., Wednesday, October 3, 2007 Event: Probability Seminar Note: change of hour from 3:00 p.m. to 4:00 p.m. Speaker: Ed Perkins, UBC Subject:Catalytic Branching Networks'' Location:WMAX 216 Abstract: We establish weak uniqueness for a system of degenerate SDE's representing a catalytic branching network. In two dimensions the result is needed for the two-type renormalization program of Dawson, Greven, den Hollander, Sun and Swart. This is joint work with Rich Bass. Time and Date: 4:30--5:30 p.m., Wednesday, October 3, 2007 Event: Algebra/Topology Seminar (Please note the unusual time.) Speaker: Jose Manuel Gomez, University of Michigan Subject:Higher Twistings in K-theory'' Location: WMAX 110 Abstract: It is known that for a compact space X, twistings of K-theory over X are classified by [X,BK_\otimes]. Here K_\otimes\simeq\bbb Z/2\times K(\bbb Z,2)\times BSU_\otimes is the space of units of K with H-space structure induced by the tensor product of vector bundles. The twistings corresponding to the factor [X,BBSU_\otimes] are called higher twistings. In the talk I will give a definition for the most general twistings of K-theory. This has been worked out rigorously in the literature only for the lower twistings and only sketched for the general situation. I will also discuss the equivariant setting limited to the case over a point. I will show that if G is a compact Lie group, then there are no higher twistings for completed twisted G-equivariant K-theory over a point. In contrast, one can see that this is not the case for topological groups in general. Time and Date: 2:30--3:30 p.m., Thursday, October 4, 2007 Event: DG-MP-PDE Seminar Speaker: Louis Nirenberg, Courant Institute Subject:Degree theory and some inequalities'' Location: WMAX 110 Abstract: We discuss degree theory for some maps which are not necessarily continuous, and give estimates for the degree in terms of various norms. Time and Date: 4:00 p.m., Thursday, October 4, 2007 Event: PIMS-MITACS Math Finance Seminar Please note: Erik Taflin of Ceremade will give his seminar next week (Oct. 11th). Speakers were interchanged to accommodate schedules. Speaker: Tomas Björk, Stockholm School of Economics Subject:Optimal investment under partial information'' Location: WMAX 216 Abstract: We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions on the the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory. Time and Date: 3:00--4:30 p.m., Friday, October 5, 2007 Event: Mathematics Colloquium Speaker: Tomas Björk, Stockholm School of Economics Subject: On the geometry of interest rate models'' 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 9, 2007 Event: UBC SCAIM Seminar Speaker: Mi-Ray Ohm, Dongseo University, Korea Subject:Error Estimates of Discontinuous Galerkin Methods for Elliptic Problems'' Location:WMAX 216 Abstract: We introduce the discontinuous Galerkin methods for elliptic problems, which are closely related to the penalty methods, to establish the optimal error estimates in the energy and L^2 norms of the discontinuous Galerkin methods, and to verify the optimality result in the L^2 norm of the discontinuous Galerkin methods numerically. Time and Date: 2:30--3:30 p.m., Tuesday, October 9, 2007 Event: DG-MP-PDE Seminar Speaker: Benjamin Texier, Paris 7 Subject:Galloping instability of detonation waves'' Location:WMAX 110 Abstract: We show that transition to longitudinal instability of strong detonations solutions of reactive compressible Navier-Stokes equations is generically associated with Hopf bifurcation to time-periodic "galloping" solutions, in agreement with physical and numerical observations. Time and Date: 3:30--4:30 p.m., Tuesday, October 9, 2007 Event: Discrete Mathematics Seminar Speaker: John Steinberger, Department of Mathematics, UBC Subject:A new proof of the four-color theorem'' Location:WMAX 216 Abstract: We present a new proof of the four-color theorem along the lines of the two existing proofs, namely the Appel-Haken proof [1976] and the Robertson et al. proof [1994]. As people will know, the idea behind these proofs is to exhibit an "unavoidable set" of "reducible configurations". A "reducible configuration" is a configuration of countries which cannot appear in a smallest counterexample, and a set of configurations is "unavoidable" if every map must have at least one of the configurations. A less known fact is that configurations come in two flavors: so called "D-reducible" and "C-reducible" configurations. D-reducible configurations are simpler but more rare than C-reducible configurations. It has been conjectured since the early '70s that there exists an unavoidable set consisting only of D-reducible configurations. Our proof exhibits such a set. As of this abstract the set has 4492 elements. Time and Date: 3:00--4:00 p.m., Wednesday, October 10, 2007 Event: Probability Seminar Speaker: Martin Barlow, UBC Subject:Recent progress in the random conductance model II'' Location:WMAX 216 Abstract: Consider the standard Euclidean lattice, and put random i.i.d. 'conductances' V(e) on each bond. We allow the possibility that V(e) is zero. Let Y be a continuous time Markov chain which jumps along the edge e with probability proportional to V(e). We assume that the probability that V(e) is positive is greater than p_c, the critical probability for bond percolation on the Euclidean lattice. Thus there exists (a.s.) a unique infinite connected subgraph on which Y can run. A special case of the above is when V(e) is either 0 or 1, and so Y is a random walk on a supercritical percolation cluster. Various kinds of 'trapping' can arise if V(e) can take either small positive values, or large values. In this talk I will discuss invariance principles for Y, and Gaussian bounds for its transition densities. Time and Date: 3:30--4:30 p.m., Wednesday, October 10, 2007 Event: Algebra/Topology Seminar Speaker: Liam Watson, UQAM Subject:Two-fold branched covers, mutation and Khovanov homology'' Location:WMAX 110 Abstract: This talk will discuss some aspects of Khovanov homology relating to the problem of mutation invariance. Our focus is a particular class of distinct knots with identical Khovanov homology. While the question of whether knot mutation preserves Khovanov homology remains open, we construct an infinite family of knots admitting a mutation that is undetected by Khovanov homology. Time and Date: 2:00--3:00 p.m., Thursday, October 11, 2007 Event: Mathematical Biology Seminar Speaker: Rodrigo Restrepo, UBC Subject:RNA and prebiotic evolution'' Location:WMAX 216 Abstract: By considering many regularities in the occurrences of purines and pyrimidines in 6241 gene sequences for the tRNAs of the prokaryotes in the Bayreuth Database, this study uncovers a strand (collection) of long RNA segments that fit a large fraction of those tRNAs. This strand suggests a plausible data-based scenario for prebiotic evolution that may explain the relatively uniform size of the tRNAs, the fact that the messenger is RNA, not DNA, with a reason for its introns, suggesting a plausible conjecture about some steps in the origin of the genetic code. Time and Date: 2:30--3:30 p.m., Thursday, October 11, 2007 Event: DG-MP-PDE Seminar Speaker: Weiyong He, Department of Mathematics, UBC Subject:The Calabi flow on Kahler surfaces'' Location:WMAX 110 Abstract: We discuss the formation of singularities along the Calabi flow, in particular on K\"ahler surfaces with the assumption of the uniformly bounded Sobolev constant. On some classes of certain K\"ahler surface, the Sobolev constant can be achieved a priori. And also in some certain case, we can show that the singularity can't form along the flow with small initial energy and get convergence of the Calabi flow. Also a new existence result regarding the constant scalar curvature metric is proved. Time and Date: 4:00--5:00 p.m., Thursday, October 11, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Erik Taflin, Ceremade Subject:Mutual fund theorems'' (joint work with M. Sirbu and W. Schachermayer) Location:WMAX 216 Abstract: The Mutual Fund Theorem (MFT) is considered in a general semimartingale financial market with a finite time horizon T. It is established that: 1) If for given utility functions (i.e. investors) the MFT holds true in all Brownian financial markets S then all investors uses the same utility function U (modulo affine transformations), where U must be a logarithmic or power utility function. This generalizes a result of Cas and Stiglitz for discrete time markets. 2) Let N be the wealth process of the num\'eraire portfolio (i.e. the optimal portfolio for the log utility). If the market is such that all path independent options on N with maturity T are replicable by trading in N only, but using all information available in the market, then MFT holds for "all" utility functions. Moreover supposing that all path independent options on N with maturity T are replicable in the market S, also the converse of this statement is true. This generalizes Merton's classical result on MFT in Black-Scholes markets. Time and Date: 3:00--4:30 p.m., Friday, October 12, 2007 Event: Mathematics Colloquium Speaker: James Feng, UBC Subject: Defect dynamics near bubbles and drops rising in a liquid crystal: observations and computations'' Location:MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:00--3:00 p.m., Monday, October 15, 2007 Event: DG-MP-PDE Seminar (note unusual day and time) Speaker: Jean-Pierre Rosay, University of Wisconsin-Madison Subject:Holomorphy, J-holomorphy (almost complex structures), and differential inequalities'' Location: WMAX 110 (PIMS Facility) Time and Date: 3:00--4:00 p.m., Monday, October 15, 2007 Event: IAM Seminar Series Speaker: Michael L. Overton, Computer Science Dept. and Dept. of Mathematics, Courant Institute of Mathematical Sciences Subject:Nonsmooth, Nonconvex Optimization'' Location: Room 301, LSK Bldg. Abstract: There are many algorithms for minimization when the objective function is differentiable or convex, but few options when it is neither. We describe two simple algorithmic approaches for minimization of nonsmooth, nonconvex objectives: BFGS (a new look at an old method) and Gradient Sampling (a method that, although computationally intensive, has a nice convergence theory, which we will describe). Both methods require the user to provide a routine that computes the function value and, if it exists, the gradient at a given point, the idea being that the function is virtually never evaluated at a point where it is not differentiable, even though it is typically not differentiable at local optimizers. These methods are combined in a new publicly available code, HANSO (Hybrid Algorithm for NonSmooth Optimization). Applications abound in engineering, particularly control. Of particular interest to me are those involving eigenvalues and singular values of nonsymmetric matrices. Sometimes even easily stated problems in a few variables are hard. Another publicly available code HIFOO (H-Infinity Fixed-Order Optimization) is intended for use by practising control engineers and has solved some open theoretical and practical problems in control. Time and Date: 3:00--4:30 p.m., Monday, October 15, 2007 Event: Algebraic Geometry Seminar Speaker: Renzo Cavalieri, University of Michigan Subject:G-Hodge Integrals, Gerby Localization and the GW Theory of C^3/Z_3'' Location: WMAX 110 Abstract: In this talk we discuss a successful approach to the computation of orbifold Gromov-Witten invariants, focusing in particular on the orbifold C^3/Z_3, which has recently been source of interest to both physicists and mathematicians. Such invariants are interpreted in terms of G-Hodge integrals, and relations among G-Hodge integrals are obtained via Atiyah-Bott localization. In order to find sufficiently many relations to reconstruct all invariants, we turn our attention to moduli spaces of maps to gerbes over P^1. This is joint work with C. Cadman. Time and Date: 4:00--5:30 p.m., Monday, October 15, 2007 Event: Mathematics Colloquium Speaker: Jean-Pierre Rosay, University of Wisconsin-Madison Subject: Holomorphic bundles on the unit disc'' Location: MATH 105 Note: Refreshments will be served at 3:45 p.m. (MATX 1115, Math Lounge). Time and Date: 2:30--3:30 p.m., Tuesday, October 16, 2007 Event: DG-MP-PDE Seminar Speaker: Leo Rosales, Department of Mathematics, UBC and PIMS Subject:Minimal Immersions with Prescribed Boundaries'' Location:WMAX 110 Abstract: Recently L. Simon and N. Wickramasekera introduced a PDE method for producing examples of stable branched minimal immersions in \mathbb{R}^{3}. This method produces q-valued functions u over the punctured unit disk in \mathbb{R}^{2} so that either u cannot be extended continuously across the origin, or G the graph of u is a C^{1,\alpha} stable branched immersed minimal surface. The present work gives a more complete description of these q-valued graphs G in case a discontinuity does occur, and as a result, we produce more examples of C^{1,\alpha} stable branched immersed minimal surfaces, with a certain evenness symmetry. Time and Date: 3:00--4:30 p.m., Wednesday, October 17, 2007 Event: Algebraic Geometry Seminar, Note special date and location. Speaker: Vladimir Chernousov, University of Alberta Subject:Torsors on the affine line and on the punctured line'' Location:MATH 105 Abstract: Joint work with P. Gille and A. Pianzola. In the talk we present a simpler proof of Raghunathan-Ramanathan theorem on torsors over an affine line. We also show how our approach can be applied to describe torsors over a punctured line. Time and Date: 3:00--4:00 p.m., Wednesday, October 17, 2007 Event: Probability Seminar Speaker: Arnaud Doucet, Computer Science Statistics, UBC Subject:Sequential Monte Carlo Samplers'' Location:WMAX 216 Abstract: We will present a methodology to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time using Sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo interact in a principled way, to perform global optimization and sequential Bayesian estimation and to compute ratios of normalizing constants. We will illustrate these algorithms for various integration tasks arising in the context of Bayesian inference and we will discuss several convergence results. (This is a joint work with Pierre Del Moral, Department of Mathematics, Universite Nice-Sophia Antipolis, France and Ajay Jasra, Department of Mathematics, Imperial College London, UK) Time and Date: 3:30--4:30 p.m., Wednesday, October 17, 2007 Event: Algebra/Topology Seminar Speaker: Jaume Aguade, University Autonoma de Barcelona and UBC Subject:The arboreal approach to pairs of involutions'' Location: WMAX 110 Abstract: Representations of the infinite dihedral group in GL_2(p-adics) where classified in a recent joint paper with Broto and Saumell, using some "strange" invariants which appeared while computing the cohomology of the classifying spaces of the rank two Kac-Moody groups. In this talk we see how using J.-P. Serre's machinery of trees we can give geometric interpretations of these invariants and give a new proof, simplify and clarify the classification theorem. Time and Date: 2:00--3:00 p.m., Thursday, October 18, 2007 Event: Mathematical Biology Seminar Speaker: Maria-Rita D'Orsogna, California State University at Northridge Subject:Patterns, stability and collapse for two-dimensional biological swarms'' Location: WMAX 216 Abstract: One of the most fascinating biological phenomena is the self-organization of individual members of a species moving in unison with one another, forming elegant and coherent aggregation patterns. Schools of fish, flocks of birds and swarms of insects arise in response to external stimuli or by direct interaction, and are able to fulfill tasks much more efficiently than single agents. How do these patterns arise? What are their properties? How are individual characteristics linked to collective behaviors? In this talk we model a swarm as a non-linear system of self propelled agents that interact via pairwise attractive and repulsive potentials. We are able to predict distinct aggregation morphologies, such as flocks and vortices, and by utilizing statistical mechanics tools, to relate the interaction potential to the collapsing or dispersing behavior of aggregates as the number of constituents increases. We also discuss passage to the continuum and possible applications of this work to the development of artificial swarming teams. Time and Date: 3:00--3:50 p.m., Thursday, October 18, 2007 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Tony Shaska, Oakland University Subject:Genus two curves which admit a degree 5 map to an elliptic curve'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: We study genus 2 curves C that admit a cover C \rightarrow E to a genus 1 curve E of prime degree n. These curves C form an irreducible 2-dimensional subvariety L_n of the moduli space M_2 of genus 2 curves. Here we study the case n=5. This extends earlier work for degree 2 and 3, aimed at illuminating the theory for general n. We compute a normal form for the curves in the locus L_5 and its three distinguished subloci. Further, we compute the equation of the elliptic subcover in all cases, give a birational parametrization of the subloci of L_5 as subvarieties of M_2 and classify all curves in these loci which have extra automorphisms. Time and Date: 4:10--5:00 p.m., Thursday, October 18, 2007 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Mat Rogers, Department of Mathematics, UBC Subject:An extension of a p-adic algorithm due to Boyd, and consequences'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: I will talk about a computational problem that I recently encountered. Suppose that p is an odd prime and y is rational, then define J_p(y) = {n : \Sigma_{1\leq j\leq n} y^j/j \equiv 0 (mod p)} . I have shown that it is possible to obtain results such as |J_{13}(9)| = 18763, |J_{47}(8)| = 27024, and |J_7(2)| = 0. I will mention ways to apply my method to sums involving Fibonacci numbers, connections to classical problems, and a possible connection with mirror maps. Time and Date: 3:00--4:30 p.m., Friday, October 19, 2007 Event: Mathematics Colloquium Speaker: Nike Vatsal, UBC Subject: Special values of L-functions modulo p'' 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 22, 2007 Event: IAM Seminar Series Speaker: Yue-Xian Li, UBC Subject: Noise and Synchrony in Neuronal Networks'' Location:Room 301, LSK Bldg. Abstract: A rich variety of rhythms in human brain have been observed through the electroencephalogram (EEG), ranging from low frequency (1-4 Hz) delta rhythms in deep dreamless sleep to high frequency (>14 Hz) beta rhythms in alert states. Rhythms picked up by electrodes on the surface of the scalp are synchronized oscillations of many neurons. A deterministic theory of coupled oscillators has been developed over the past decades in which individual neurons are treated as spontaneous oscillators. A novel mechanism for generating synchronized rhythms, called coherence resonance (CR), was discovered recently. It refers to coherent oscillations triggered by noise in a system that is quiescent in the absence of noise. In this talk, I will review several distinct examples of noise-induced synchrony and oscillations, including the spike-reset-recover (SRR) model recently proposed by myself and coworkers. In most known examples of CR, the oscillation frequency increases as the noise level increases. In our SRR model, however, the frequency is determined by the intrinsic properties of the neuron but not by the noise level. The significance of this model in understanding the origin of brain rhythms will be discussed together with some other intriguing effects of noise. Some preliminary results toward developing a stochastic phase theory of coupled oscillators will also be discussed. Collaborators in the work presented here are S. Reinker, R. Kuske and N. Yu. Time and Date: 3:00--4:30 p.m., Monday, October 22, 2007 Event: Algebraic Geometry Seminar Speaker: Paul Horja, Department of Mathematics, UBC and PIMS Subject:Triangulated categories and toric varieties'' Location:WMAX 110 (PIMS Facility) 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: 12:30--2:00 p.m., Tuesday, October 23, 2007 Event: UBC SCAIM Seminar Speaker: Yoichiro Mori, Department of Mathematics, UBC Subject:Convergence Proof of a Stokes Flow Immersed Boundary Method'' Location:WMAX 216 Abstract: The immersed boundary method is a popular method for computations in fluid-structure interaction problems. It is charactrized 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: 2:30--3:30 p.m., Tuesday, October 23, 2007 Event: DG-MP-PDE Seminar Speaker: Stephane Kirsch, Department of Mathematics, UBC and PIMS Subject:Convergence of an elliptic Allen-Cahn equation to a prescribed mean curvature problem'' Location:WMAX 110 Abstract: We study the following Allen-Cahn functional for u \in H1\cap L4: E_\varepsilon(u) = \int_{T^N} \varepsilon \frac{|\nabla u|^2}{2} + \frac{W(u)}{\varepsilon} - \mathcal{H}u, where T^N is a N-dimensional flat torus, W a double-well potential vanishing for 0 and 1, and \mathcal{H} a positive and Lipschitz function. We will discuss the existence and properties of mountain-pass critical points for this functional, and their behaviour for the asymptotic \varepsilon \to 0. Time and Date: 3:00--4:00 p.m., Wednesday, October 24, 2007 Event: Probability Seminar Speaker: Lung-Chi Chen, Department of Mathematics, UBC and PIMS Subject:Critical behavior and the limit distribution for long-range oriented percolation'' Location:WMAX 216 Abstract: We consider oriented percolation on \Zd\times\Zp whose bond-occupation probability is pD(\,\cdot\,), where p is the percolation parameter and D is a probability distribution on \Zd. Suppose that D(x) decays as |x|^{-d-\alpha} for some \alpha>0. We show that the two-point function obeys an infrared bound which implies that various critical exponents take on their respective mean-field values above the upper-critical dimension \dc=2(\alpha\wedge2). We also show that the Fourier transform of the normalized two-point function at time n, with a proper spatial scaling, has a convergent subsequence to e^{-c|k|^{\alpha\wedge2}} for some c>0. Time and Date: 2:00--3:00 p.m., Thursday, October 25, 2007 Event: Mathematical Biology Seminar Speaker: Fred Brauer, UBC Subject:Epidemic models with heterogeneous mixing'' Location:WMAX 216 Abstract: The classical compartmental epidemic models are too simple, because they assume homogeneous mixing of all members of the population. The modern network models are too complicated because they asume too much kknowledge of the population and are too difficult to analyze. We seek something in between, starting with a population consisting of two groups with different activity levels, assuming proportionate mixing between the groups, calculating the basic reproduction number and using the final size relation to determine what the size of the epidemic would be if there were no disease deaths. We show that if the disease death rate is small, this is a good approximation. We compare numerical simulations for one - group and two - group models to examine whether the extension to more groups is worthwhile. We show how to extend to models with treatment and other compartments, more general mixing (in which case there is a final size relation even though the reproduction number can not be calculated explicitly), and more groups. Time and Date: 3:00--3:50 p.m., Thursday, October 25, 2007 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: Youness Lamzouri, Universite de Montreal Subject:The two-dimensional distribution of values of \zeta (1+it)'' Location:UBC Campus, Room WMAX 110 (PIMS) Abstract: In 1928, Littlewood proved that |\zeta (1+it)| < (2e^Y+o(1)) log log t assuming the Riemann Hypothesis, and conjectured that max_{t=T} |\zeta (1+it)| ~ e^Y log log T. Recently, Granville and Soundararajan computed the distribution function of |\zeta (1+it)|, giving strong evidence for Littlewood's Conjecture. In this talk, we present several results on the joint distribution function of arg \zeta (1+it) and |\zeta (1+it)|. One consequence of our work is that almost all values \zeta (1+it) with large norm (close to the conjectured maximum) are concentrated near the positive real axis. Indeed, we prove that the larger the arguments, the more it becomes rare to find values with large norm. Also for t\in [T,2T] and t < (e^Y+o(1)) log log T, we show that arg \zeta (1+it) with |\zeta (1+it)| \approx t is normally distributed with mean zero and variance depending on t. Finally we prove similar results in the case of L(1,\chi ), where \chi varies over non-principal characters modulo a large prime q. Time and Date: 4:00--5:30 p.m., Thursday, October 25, 2007 Event: Complex Fluids Seminar Speaker: Chunfeng Zhou, Department of Chemical and Biological Engineering, UBC Subject:Dynamic Simulation of Droplet Interaction and Self-Assembly in a Nematic Liquid Crystal'' Location:MATH 225 Abstract: We use dynamic simulations to explore the pairwise interaction and multi-particle assembly of droplets suspended in a nematic liquid crystal. The computation is based on a regularized Leslie-Ericksen theory that allows orientational defects. The homeotropic anchoring on the drop surface is of sufficient strength as to produce a satellite point defect near the droplet. Based on the position of the defects relative to the host droplet and the far-field molecular orientation, we have identified five types of pairwise attractive and repulsive forces. In particular, long-range attraction between two droplets with their line of centers along the far-field nematic decays as $R^{-4}$ with the center-to-center separation $R$. This agrees with prior static calculations and a phenomenological model that treats the attraction as that between two dipoles. For interaction in shorter ranges, our simulations agree qualitatively with experimental measurements and static calculations. However, there is considerable quantitative discrepancy among the few existing studies and our simulation. We suggest that this is partly due to the dynamic nature of the process, which has never been taken into account in prior calculations. Multi-drop simulations show the formation of linear chains through pairwise interactions between nearby droplets. Parallel chains repel or attract each other depending on the relative orientation of the drop-to-defect vector. These are consistent with experimental observations of chain formation and two-dimensional self-assembly in bulk nematics and smectic-C films. Time and Date: 4:00--5:00 p.m., Thursday, October 25, 2007 ON OCT. 22nd, THIS SEMINAR WAS CANCELLED. Event: PIMS-MITACS Math Finance Seminar Speaker: Jia-an Yan, Professor of Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing Subject:Risk Measures with Comonotonic Subadditivity or Convexity and Respecting Stochastic Orders'' Location:WMAX 216 Abstract: Taking subadditivity as a main axiom Artzner et.al.(1997, 1999) introduced the coherent risk measures. Song and Yan (2006) introduced risk measures which are comonotonically subadditive or convex. Recently we introduced risk measures which are not only comonotonically subadditive or convex, but also respect the (first) stochastic dominance or stop-loss order, and gived their representations in terms of Choquet integrals w.r.t. distorted probabilities. This talk is based on a joint work with Yongsheng Song. Time and Date: 3:00--4:30 p.m., Friday, October 26, 2007 Event: Mathematics Colloquium Speaker: Ian Frigaard, UBC Subject: Cementing oil & gas wells and other tales ...'' 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 29, 2007 Event: IAM Seminar Series Speaker: John Grue, Mechanics Division, Department of Mathematics, University of Oslo, Norway Subject:Fully nonlinear model for ocean surface waves and calculation of very large (rogue) wave events with comparison to experiments'' Location: Room 301, LSK Bldg. Abstract: We highlight the most essential steps of a fully nonlinear method for the computation of ocean surface waves in three dimensions, where solution of the Laplace equation, expressed in terms of an integral equation, is inverted analytically by means of Fourier transform. This leads to an iteration procedure for the fully nonlinear wave field with rapid convergence, where the leading terms are obtained in a rapid fashion using FFT. Class I and II instabilities, and formation of very large (rogue) wave events are exemplified and compared with experiments. The method is used to predict orbital velocities in nonlinear waves over appreciable regions measured in the field. Time and Date: 3:00--4:30 p.m., Monday, October 29, 2007 Event: Algebraic Geometry Seminar Speaker: Arend Bayer, University of Utah Subject:Polynomial Bridgeland stability conditions and the large-volume limit'' Location: WMAX 110 (PIMS Facility) Abstract: We introduce polynomial stability conditions, a generalization of Bridgeland's notion of a stability condition on a derived category. Whereas the existence of Bridgeland stability conditions is only known for surfaces and some special cases, we can construct a family of polynomial stability conditions for any projective variety, including a stability condition that should be the large-volume limit of Bridgeland stability conditions. Time and Date: 12:30--2:00 p.m., Tuesday, October 30, 2007 Event: UBC SCAIM Seminar Speaker: Dinesh Pai, Computer Science, UBC Subject:Computational Challenges in Sensorimotor Biology'' Location: WMAX 216 Abstract: Humans and other animals utilize spectacularly sophisticated sensorimotor systems to perceive and interact with their dynamic environment. Computational models are essential for understanding how these complex systems actually work. I will describe recent work in my group on building mathematical and computational models of these systems, focusing on three topics: (1) Numerical simulation of complex three dimensional musculoskeletal systems with neural activation; (2) Reconstruction of subject specific models from medical images and other measurements; and (3) Modeling the human hand and its interaction with external objects. Time and Date: 2:30--3:30 p.m., Tuesday, October 30, 2007 Event: DG-MP-PDE Seminar Speaker: Kenji Nakanishi, Kyoto University Subject:Scattering for 2D nonlinear Klein-Gordon equation in the energy critical case'' Location: WMAX 110 Abstract: We study large-time behavior for the wave equation with an exponential nonlinearity in two space dimensions, and prove asymptotic completeness of the linear evolution on the closed ball of the energy space with the same threshold as in the Moser-Trudinger inequality. A striking difference from the Sobolev-critical problem in higher dimensions is that Strichartz-type estimates on the nonlinearity do not uniformly hold, depending on how much the energy concentrates. Hence we have to classify behavior of the concentration radius to apply appropriate combination of nonlinear estimates. (Joint work with Slim Ibrahim, Mohamed Majdoub and Nader Masmoudi). Time and Date: 3:30--4:30 p.m., Tuesday, October 30, 2007 Event: Discrete Mathematics Seminar Speaker: Alexander E. Holroyd, UBC Subject:Partition identities old, new, and yet to be found '' Location: WMAX 216 Abstract: Integer partitions and their curious properties have fascinated mathematicians since Euler. For example, an identity of MacMahon relates partitions of n into parts no two of which are consecutive to partitions of n into parts not congruent to 1 or 5 modulo 6. I'll talk about some generalizations of this identity, and some clues to others which ought to exist. No prior knowledge will be assumed. Time and Date: 3:00--4:00 p.m., Wednesday, October 31, 2007 Event: Probability Seminar Speaker: Pierluigi Falco, Department of Mathematics, UBC Subject:Renormalization Group Approach to Fermionic Systems with Vanishing Beta Funtion' I: An Application'' Location: WMAX 216 Abstract: Certain 2-dimensional models of classical statistical mechanics, quantum statistical mechanics and quantum field theory can be written as a 'path integral' for fermionic fields with a quartic self-interaction. In the first seminar I will review how to write the Ising and related spin models in terms of fermions. In the second, I will describe very elementary facts, of analytical and combinatorial flavour, on which the renormalization group approach relies. Time and Date: 3:30--4:30 p.m., Wednesday, October 31, 2007 Event: Algebra/Topology Seminar Speaker: Jeff Smith, UBC Subject:Commutative cochains in finite characteristic'' Location: WMAX 110 Time and Date: 11:00 a.m.--12:00 p.m., Thursday, November 1, 2007 Event: Mathematics Colloquium Speaker: Richard Craster, Imperial College Subject: Checkerboard composites and the Motola-Steffe conjecture'' Location: LSK 200 (Leonard S. Klinck Bldg., 6356 Agricultural Rd. UBC) Time and Date: 2:00--3:00 p.m., Thursday, November 1, 2007 Event: Mathematical Biology Seminar Speaker: Joel Heath, PDF, UBC Subject:Behavioural Dynamics of Arctic wintering eider ducks '' Location: WMAX 216 Time and Date: 4:00--5:30 p.m., Thursday, November 1, 2007 Event: Complex Fluids Seminar CANCELLED AS OF OCT 31ST 11:45AM Speaker: Shilpa A. Ghadge, Department of Mathematics, UBC Subject:Dynamics of visco-plastic films with wall slip'' Location: MATH 225 Abstract: Visco-plastic fluids are usually multi-phase fluids, for example, kaolin suspensions, aqueous polymer solutions, slurries, etc. Rheological measurements of such fluids while keeping them in their natural state is particularly challenging as these fluids tend to slip near the wall in some geometries. This could be due to shear induced particle migration near the wall and may be due to surface chemistry. We have demonstrated this effect using dam break experiments. In this talk, a mathematical analysis to explain this phenomenon will be presented. Time and Date: 4:00--5:00 p.m., Thursday, November 1, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Traian Pirvu, UBC Subject:On Securitization, Market Completion and Equilibrium Risk Transfer'' Note: (This is joint work with Ulrich Horst and Goncalo Dos Reis.) Location: WMAX 216 Abstract: We propose an equilibrium framework within to price financial securities written on non-tradable underlyings such as temperature indices. We analyze a financial market with a finite set of agents whose preferences are described bya convex dynamic risk measure generated by the solution to a backward stochastic differential equation. The agents are exposed to financial and non-financial risk factors. They can hedge their financial risk in the stock market and trade a risk bond whose payoff depends on both financial and external risk factors. We prove an existence and uniqueness of equilibrium result for bond prices and characterize the equilibrium market price of risk in terms of a solution to a non-linear BSDE. Time and Date: 2:00--3:00 p.m., Friday, November 2, 2007 Event: Applied Mathematics Seminar Speaker: Richard Craster, Imperial College Subject:Topics in scattering theory, and guided modes, in elasticity and acoustics'' Location: WMAX 110 Abstract: Non-destructive testing and other detection applications are important in many practical situations (i.e. crack detection within railtracks for public safety implications) that involve waves in elastic media. Similar applications occur in electromagnetism for radar scattering and in acoustics. A common situation is practice is that a scattering problem must be solved many times over for many different incoming fields and the scattered far-field then identified for each case. These tasks can take considerable time and recently it has become clear that one can, instead, solve a vastly reduced number of "master" problems (only once) and then subsequently manipulate their far fields to generate the far-field behaviour for the physical problems really of interest. The entire computational effort can then be concentrated upon these "embedded" master problems, this is one example where Mathematical ideas can make a real impact upon practical calculations. If time allows other related issues will be described, for instance, guided modes can become trapped at specific frequencies in bent structures or by topography and thereby localize energy. This can be rather undesirable, a theory that encapsulates the dominant physics has been developed and will be outlined. Time and Date: 3:00--4:30 p.m., Friday, November 2, 2007 Event: Mathematics Colloquium Speaker: Don Saari, UC Irvine Subject: Mathematical complexity of decisions and multi-scale analysis'' 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 5, 2007 Event: IAM Seminar Series Speaker: Fernando Rochinha, Department of Mechanical Engineering, Federal University of Rio de Janeiro, Brazil Subject: Building Reliable Finite Element Formulations for Acoustics'' Location: Room 301, LSK Bldg. Abstract: Wave propagation phenomena are present and explored in a variety of applications, ranging from medical imaging to radar detection. Such sophisticated applications require accurate modeling in order to optimize the procedures involved. For that, classical analytical techniques do not seem to be viable, which leads to the need of resorting to numerical methods. As a first step towards developing reliable numerical models of wave propagation, the Helmholtz equation, which governs time-harmonic acoustic, elastic and electromagnetic waves, is tackled. Numerical approximation of this equation is particularly challenging, as vastly reported in literature. The oscillatory behavior of the exact solution and the quality of its numerical approximation depend on the wave number k. To approximate the Helmholtz equation with acceptable accuracy, the resolution of the mesh should be adjusted to the wave number according to a rule of thumb that prescribes a minimum number of elements per wavelength. It is well known that, despite adopting this rule, the performance of the Galerkin Finite Element method deteriorates as k increases. This misbehavior, known as pollution of the finite element solution, can only be avoided through a drastic refinement of the mesh, which normally entails significant barriers for the numerical analysis of the Helmholtz equation at moderate and high frequencies. A great effort has been devoted to the alleviation of the pollution effects. In particular, the GLS (Galerkin Least-Squares) method is able to completely eliminate the phase lag in one-dimensional problems. However, in two dimensions, this method is not pollution-free for any direction of the plane wave. In fact, in two spatial dimensions, there is no finite element method with piecewise linear shape functions free of pollution effects. Stencils with minimal pollution error are constructed by using the Quasi Stabilized Finite Element Method (QSFEM). QSFEM is really a finite difference rather than a finite element method, as the modifications of the discrete operator are made on the algebraic level, and no variational formulation is associated with its original form. In the present talk, some enhanced finite element formulations recently developed by the author and collaborators are discussed. These formulations rely on either discontinuous interpolations or projections of residual values of the balance equations. The talk also addresses the important issue of uncertainty propagation when finite element formulations are employed in the numerical simulation of acoustic problems. Time and Date: 3:00--4:00 p.m., Monday, November 5, 2007 Event: Algebraic Geometry Seminar Speaker: Michael Rose, UBC Subject:Mirror symmetry and 1-adic Chen-Ruan cohomology'' Location: WMAX 110 (PIMS Facility) Abstract: The Weil conjectures provide a technique to translate certain classical mirror theorems (for instance, the reflection of hodgenumbers) into the context of arithmetic algebraic geometry. I will demonstate this strategy and give a survey of results in this direction. Time and Date: 4:00--5:00 p.m., Monday, November 5, 2007 Event: CRM/Fields/PIMS Prize Distinguished Lecture 2007 Speaker: Joel Feldman, UBC Subject:A Functional Integral Representation for Many Boson Systems'' Location: WMAX 110 Note: Reception to precede talk at 3:30 p.m. in the PIMS Lounge. Abstract: Functional integrals have long been used, formally, to provide intuition about the behaviour of quantum field theories. For the past several decades, they have also been used, rigorously, in the construction and analysis of those theories. I will talk about a rigorous variant of a standard functional integral representation for the (cutoff) partition function of a many Boson system that provides a suitable starting point for its construction. Time and Date: 12:30--2:00 p.m., Tuesday, November 6, 2007 Event: UBC SCAIM Seminar Speaker: Fadil Santosa, School of Mathematics, University of Minnesota (visiting SFU) Subject:Design of a high quality optical resonator'' Location: WMAX 216 Abstract: We consider resonance phenomena for the scalar wave in an inhomogeneous medium. Resonance can be described as a solution to to the wave equation that is spatially localized while its time dependence is (mostly) harmonic except for decay due to radiation. The reciprocal of the decay rate is referred to as the quality of the resonator. We will discuss the problem of designing resonators which has high quality where the design variable is the index of refraction of the medium. We will start with an introduction to resonance and its computation, and describe a continuation approach that allows one to maximize quality. Numerical examples of high quality resonators will be presented. Time and Date: 2:30--3:30 p.m., Tuesday, November 6, 2007 Event: DG-MP-PDE Seminar Speaker: Micah Warren, University of Washington Subject:Hessian estimates for special Lagrangian equations'' Location: WMAX 110 Abstract: We review some recent results on Hessian estimates for solutions of special Lagrangian equations in dimensions two and three, including the sigma-2 equation in dimension three. The gradient graph of such a solution is a minimal Lagrangian surface. In the 1950\uffff~@~Ys Heinz proved an implicit Hessian estimate for the sigma-2 (Monge-Amp\ere) equation in dimension two. In the 1970\uffff~@~Ys, Pogorelov constructed his famous counterexamples, showing that Hessian estimates for the the sigma-3 (Monge-Amp\ere) equation do not exist. This is joint work with Yu Yuan. Time and Date: 3:30--4:30 p.m., Tuesday, November 6, 2007 Event: DG-MP-PDE Seminar Speaker: Xiuxiong Chen, University of Wisconsin Subject:Geometric flows in Kaehler geometry and the moduli space of extremal Kaehler metrics'' Location: WMAX 110 Abstract: An unpublished work of G. Perelman proved that the Kaehler Ricci flow always converges to a Kaehler Einstein metric in any compact Kaehler Einstein manifold. In 2005, We proved that the Calabi flow will deform any Kaehler metric near an extremal Kaehler metric to an extremal kaehler metric. What happen if we don't assume the existence of an extremal Kaehler metric? In this talk, we will report recent progress made in this direction. Time and Date: 3:30--4:30 p.m., Tuesday, November 6, 2007 Event: Discrete Mathematics Seminar Speaker: Kurt Luoto, University of Washington Subject:A matroid-friendly basis for quasisymmetric functions'' Location: WMAX 216 Abstract: Matroids were developed by Whitney to generalize the notion of linear independence. Matroid base polytope decompositions arise in the work of certain algebraic geometers. In 2006, Billera, Jia, and Reiner invented a new invariant F(M) for matroids in the form of a quasisymmetric function. One motivating application of this invariant is to the study of matroid base polytope decompositions. The mapping of matroids to the algebra of quasisymmetric functions (QSym) behaves as a valuation on matroid base polytopes, and leads to a necessary algebraic condition on their decompositions. Billera, Jia, and Reiner pose a number of questions regarding this relationship. We address some of these questions, obtaining a full characterization for the rank two case. Along the way, we obtain a novel Z-basis for QSym that has especially nice properties. For instance this basis has nonnegative integer structure constants and reflects, in addition to the usual grading of QSym by degree, a second grading of QSym that on (the images of) loopless matroids coincides with their matroidal rank. No familiarity with quasisymmetric functions or matroids are assumed for this talk. Time and Date: 4:00--5:00 p.m., Wednesday, November 7, 2007 Event: Probability Seminar. NOV. 6TH: THIS SEMINAR HAS BEEN CANCELLED. Speaker: Marek Biskup, UCLA, Microsoft Subject:Non-convexity of surface tension in a class of anharmonic crystals'' Location: WMAX 216 Abstract: I will discuss a class of gradient models with anharmonic potentials that defy a number of results that are known to hold in the convex case. This includes the possibility of having multiple ergodic measures for a given tilt or failure of convexity of the surface tension as a function of the tilt. Other results --- e.g., convergence of fluctuations to Gaussian Free Field in the usual scaling limit --- in turn hold (but with a distinct limit for each coexisting ergodic gradient Gibbs measure). The key step in understanding these models will be the characterization of ergodic measures by means of a Gibbs variational principle. This, in turn, boils down to homogenization theory for the random conductance model. Time and Date: 3:00--4:00 p.m., Wednesday, November 7, 2007 Event: Mathematics Colloquium Speaker: Xiuxiong Chen, University of Wisconsin Subject: A recent update on the existence of extremal Kaehler metrics in Kaehler surfaces'' Location: WMAX 110 Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge). Time and Date: 3:00--3:50 p.m., Thursday, November 8, 2007 Event: PIMS/SFU/UBC Number Theory Seminar Note: The two seminars will be simulcast: SFU Campus, Room ASB 10900 (IRMACS) and UBC Campus, Room WMAX 110 (PIMS). Speaker: Patrick Ingram, University of Toronto Subject:Diophantine approximation in arithmetic dynamics'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: In 1978, Lang conjectured a lower bound on the canonical height of a non-torsion point on an elliptic curve which depends on various data related to the curve. This conjecture remains open (although there are several partial results). Much more recently, Silverman posited a more general conjecture about lower bounds on canonical heights in “arithmetic dynamical systems” (that is, systems defined by a morphism mapping a variety to itself), which at least roughly reduces to Lang's Conjecture when the underlying system is that defined by the multiplication-by-n map on an elliptic curve (n > 1). We'll discuss the first result towards Silverman's conjecture in which the underlying structure is not that of an abelian variety. Some other problems related to heights and diophantine approximation in arithmetic dynamics will come up along the way. Time and Date: 4:00--5:30 p.m., Thursday, November 8, 2007 Event: Complex Fluids Seminar Speaker: Monica F. Naccache, Department of Mechanical Engineering, Pontificia Universidade Catolica, Rio de Janeiro, Brazil Subject:Yield-stress fluids flow through axissymmetric expansions-contractions'' Location: MATH 225 Abstract: The internal flow of yield-stress fluids through an abrupt axissymmetric expansion followed by an abrupt contraction is analyzed. This situation is representative of numerous flows found in industrial processes, such as extrusion, mold filling and liquid displacement in porous media. The yield stress strongly affects the flow pattern, as well as the pressure drop along the channel. Numerical results for steady flow and low Reynolds numbers were obtained using the Generalized Newtonian Fluid equation, and the finite volume method. Some results using a viscoelastoplastic equation are also presented. Yield surfaces obtained with flow visualization experiments using Carbopol aqueous solutions are also shown. Time and Date: 4:10--5:00 p.m., Thursday, November 8, 2007 Event: PIMS/SFU/UBC Number Theory Seminar Speaker: O-Yeat Chan, Dalhousie University Subject:Effective computation of Bessel functions'' Location: SFU Campus, Room ASB 10900 (IRMACS) Abstract: Bessel functions are some of the most important functions in mathematical physics and the theory of special functions, and the ability to compute their values is equally important. The standard method of evaluating the Bessel functions has been to use an ascending series for small argument, and the asymptotic (but divergent) series for large argument. In this talk, we describe a new series that is geometrically convergent in the number of summands, with explicitly computable error estimates for the tails. This is joint work with David Borwein and Jonathan Borwein. Time and Date: 3:00--4:30 p.m., Friday, November 9, 2007 Event: Mathematics Colloquium Speaker: Marek Biskup, UCLA, Microsoft Subject: Parabolic Anderson Model: eigenvalue order statistics and path localization'' 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, November 13, 2007 Event: UBC SCAIM Seminar Speaker: Fernando Alves Rochinha, COPPE, Brazil Subject: Improving Numerical Models through Inverse Analysis: A Viscoelastic Constitutive Equation with Internal Variables'' Location: WMAX 216 Abstract: The capability of producing and deeper understanding advanced materials engenders a new trend in modern engineering consisting of designing tailored systems through exploring specific characteristics of those materials. For instance, this is the case of devices build on viscoelastic materials that enhance damping levels in vibrating structures often found in automotive, space and energy industries. On the other hand, there is the need of accelerating the design of new systems which can be achieved through intensive use of numerical simulation substituting the role played by prototypes. The numerical models are developed to enhance the capability of predicting the behavior of engineered systems when submitted to operational conditions. A key issue on using simulated predictions relies on the trustability of those, which means that mathematical models and numerical methods should be reliable and reproduce, within a certain level of confidence, the physics reality. Indeed, numerical simulation often face two shortcomings concerning the reliability of the results: numerical pitfalls inherent to approximation methods, and uncertainties associated to non modeled dynamics and to parameters values. This last drawback can be alleviated by System Identification, which consists of the process of improving a mathematical model for a real system by combining physical principles with experimental or field data. The main idea is to identify a set of parameters such that, over a desired range of operating conditions, the model outputs are close, in some well-defined sense, to the system outputs, when both are submitted to the same inputs. Due to the incompleteness of available information and unavoidable measurement errors, system identification only achieves an approximation of the actual system. The present work is motivated by the need of improving the capability of predicting the mechanical response of damping materials when applied to control the level of vibrations in structures or mechanical components. Usually those materials present a viscoelastic behavior, which is the main focus of the present work. A constitutive equation for viscoelastic materials, in time domain, is proposed based on the concepts of internal variables and the thermodynamics of irreversible processes. The proposed constitutive equation is capable of dealing with common viscoelastic response such as creep and relaxation phenomena .The introduction of internal variables in the modeling entails the need of obtaining constitutive parameters which are not directly measurable due to its intrinsic nature. In order to cope with this difficulty, an inverse formulation combining experimental results and a minimization algorithm is applied to a composite structure consisting of metallic sandwich beam endowed with a viscoelastic polymeric layer. The parameters are estimated through the solution of an associated inverse problem which was formulated in frequency domain. The inverse problem has been solved by means of the Levenberg-Marquardt technique. Time and Date: 3:00--4:00 p.m., Wednesday, November 14, 2007 Event: Probability Seminar Speaker: Pierluigi Falco, UBC Subject:Renormalization group approach to fermionic systems with vanishing beta function' II: elements of the technique'' Location: WMAX 216 Abstract: Certain 2-dimensional models of classical statistical mechanics, quantum statistical mechanics and quantum field theory can be written as a 'path integral' for fermionic fields with a quartic self-interaction. In the first seminar I will review how to write the Ising and related spin models in terms of fermions. In the second, I will describe very elementary facts, of analytical and combinatorial flavour, on which the renormalization group approach relies. Time and Date: 12:30--1:30 p.m., Thursday, November 15, 2007 Event: Mathematics Colloquium Speaker: Bruce Reed, CRC Tier 1 Chair, Computer Science, McGill University Subject: Rooted Routing Via Graph Minors'' Location: MATX 1100 Note: Refreshments will be served at 12:15 p.m. (Math Lounge, MATX 1115). Time and Date: 2:00--3:00 p.m., Thursday, November 15, 2007 Event: Mathematical Biology Seminar Speaker: Jianhong Wu, York University Subject:Neural Computation with Attractors: Memory, Dynamics and Time Lags'' Location: WMAX 216 Abstract: This talk addresses the issue how to design and compute a network with feedback, that exhibits complex but desired dynamical behaviors for some particular cognitive tasks. We illustrate the linkage between neural computation with attractors and the memory storage/retrieval using the additive network of neurons, and discuss the simplicity-capacity dilemma arising from the requirement for a network to posses a large number of stable patterns and to be easily implemented. We then propose a novel approach based on signal processing delay and show the interaction of delay, feedback and refractoriness in a simple inhibitory network of two neurons can generate three basic types of oscillations and these three basic oscillations can then be pinned together to form a large number of interesting coexisting periodic patterns. Therefore, a simple and small network with delayed feedback can process a large amount of information. How connection topology of a large network enhances the network's capacity for memory storage and retrieval remains to be an interesting task. Time and Date: 4:00--5:30 p.m., Thursday, November 15, 2007 Event: Complex Fluids Seminar Speaker: Richard Craster, Department of Mathematics, Imperial College, London, U.K. Subject:Flow down a vertical fibre'' Location: MATH 225 Abstract: The vertical flow of a fluid, under the influence of gravity, down the exterior of a rigid fibre is a flow accompanied by rich dynamics that manifests itself via the formation of droplets, or beads, driven by a Rayleigh mechanism modulated by the presence of gravity. These droplets propagate down the fibre and undergo coalescence with preceding droplets. Different flow regimes are possible depending on system parameters such as the fibre radius, liquid flow rate and physical properties. We derive an evolution equation for the interface in the long-wavelength approximation, which captures the flow characteristics of the system; this model is similar to those previously used to investigate the dynamics of slender viscous threads in the absence of the fibre. Analytical and numerical solutions of the evolution equation yield information regarding the shape and propagation speeds of the droplets, which is in good agreement with available experimental data as well as those obtained as part of the present work. Connections with models already available in the literature are also established. Time and Date: 4:00--5:00 p.m., Thursday, November 15, 2007 Event: PIMS-MITACS Math Finance Seminar Speaker: Ali Lazrak, Sauder School of Business Subject:Leverage Choice and Credit Spread Dynamics when Managers Risk Shift'' Location: WMAX 216 Abstract: We provide new insights that link compensation terms to credit spreads and leverage by structurally modeling the financial and operating decisions of a risk-averse manager paid with cash and stock. Optimal debt balances tax benefits with the utility cost resulting from ex-post asset substitution. When cash-stock ratios are low (high), initial leverage is high and debt is safe (risky), while moderate cash-stock ratios are associated with low initial leverage. High credit spreads can be generated even when leverage and equity volatility are low. Using a large cross-section of 646 US based corporate credit default swaps (CDS) covering 2001-2006, we find strong evidence that the °exibility provided by the compensation terms is important for explaining CDS rates. With parameters estimated to match moments based on stock volatility and CDS rates, our model outperforms a similarly calibrated version of the Merton (1974) model, explaining an additional 10% of the variation in CDS rates and reducing average bias by over 50%. This is joint work with Murray Carlson (UBC). Time and Date: 1:00--2:00 p.m., Friday, November 16, 2007 Event: DG-MP-PDE Seminar Speaker: Gunther Uhlmann, University of Washington Subject: Travel time tomography'' Location: WMAX 110 Abstract: The scattering relation measures the exit points of a medium and directions of ray paths (geodesics) of waves, given its entrance point and entrance direction as well as the travel time. The broken scattering relation measures the exit point and direction of once broken (reflected) ray paths and the travel time. The inverse problems we consider consist of determining the index of refraction of the medium by knowing the scattering relation or the broken scattering relation. In this talk we will describe some recent results obtained about both inverse problems. Time and Date: 2:00--3:00 p.m., Friday, November 16, 2007 Event: Discrete Mathematics Seminar Speaker: Bruce Reed, CRC Tier 1 Chair, Computer Science, McGill University Subject:Graph Colouring Via the Probabilistic Method'' Location: WMAX 110 Abstract: One way of colouring graphs is to pick colour classes from a probability distribution on the stable sets of the graph. We discuss a variety of optimal and near optimal colourings which can be obtained using this approach. We begin with a straightforward example and then add various bells and whistles such as: the Lovasz Local Lemma, structural decomposition, hardcore distributions, concentration inequalities, and Edmond's Characterization of the Stable Set Polytopes of line graphs. Time and Date: 3:00--4:00 p.m., Friday, November 16, 2007 Event: Mathematics Colloquium Speaker: Gunther Uhlmann, University of Washington Subject: Invisibility and transformation media'' Location: MATX 1100 Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge). Time and Date: 4:00--5:00 p.m., Friday, November 16, 2007 Event: Special Probability Seminar Speaker: Tom Kurtz, U. Wisconsin Subject:Filtered martingale problems and Markov mapping theorems'' Location: WMAX 216 Abstract: The filtered martingale problem was originally introduced as a step in proving uniqueness for the stochastic partial differential equations arising in nonlinear filtering. Applications beyond the original goal include a general Markov mapping theorem and results on the equivalence of stochastic equations and martingale problems. Recent extensions treat Markov processes with boundary conditions and enable general results on the Markov property for solutions of filtering problems. Time and Date: 10:00 a.m., Monday, November 19, 2007 Event: Special PIMS Seminar Speaker: Yasha Eliashberg, Stanford University Subject: Orderability of groups of contact transformations and related topics'' Location: WMAX 110 Abstract: There is a natural candidate for a partial order on the universal cover G(M,\xi ) of the group of contact diffeomorhisms of a contact manifold (M,\xi ). Namely, we say that f>g if f can be generated by a bigger Hamiltonian than g. It is not clear, however, whether this order is non-trivial. In fact, this answer very much depends on the contact manifold, and recently there were discovered large classes of orderable and non-orderable contact manifolds. It turns out that the orderability problem is tightly related with many other interesting contact-geometric problems, and in particular, with a contact analog of Gromov’s famous non- squeezing theorem. Interestingly, the analogous contact non-squeezing phenomenon exists on large scales, but it disappears on small scales. In the talk there will be discussed these results as well as connections with other problems, such as existence of quasi-morphims on the group G(M,\xi ). Time and Date: 3:00--4:00 p.m., Monday, November 19, 2007 Event: IAM Seminar Series Speaker: Christian Schoof, Department of Earth and Ocean Sciences, UBC Subject:Free Boundary Problems in Ice Sheet Dynamics'' Location: Room 301, LSK Bldg. Abstract: Ice caps such as those covering Greenland and Antarctica behave as slowly flowing thin viscous films spreading under their own weight. Mathematical models for their dynamics often give rise to free and moving boundary problems. An obvious example of a moving boundary is the edge of a land-based ice sheet, where ice thickness and flux vanish. For an isothermal ice sheet with a flat base, the motion of this free boundary can be described by a parabolic obstacle problem, and a relatively complete analysis of the evolution problem is possible. The physics describing the motion of the edge of an ice sheet becomes more complicated if the base of the ice is below sea level, in which case the flow of the land-based part of the ice sheet, which can be described by a diffusion model, must be coupled to that of a floating ice tongue, which can be described by a system of hyperbolic PDEs. Here I describe how matched asymptotic expansions allow appropriate jump conditions to be derived at the free boundary that marks the location where the ice sheet begins to float. The land-based part of the ice sheet can then be described by a Stefan-type problem in which ice thickness takes the role of temperature, with the added complication that ice thickness at the free boundary (the equivalent of the phase transition temperature in the Stefan problem) depends on the location of the free boundary. This leads to the possibility of multiple steady states, some of which may be unstable. I will discuss appropriate stability criteria and the possibility of hysteresis under parameter variations that describe changes in snowfall and sea levels, and discuss the possibility that the past behaviour of the West Antarctic ice sheet may indeed manifest hysteresis. Time allowing, I will discuss physical complications to this model that will need to be addressed by future work, among them the appearance of internal free boundaries in ice sheets that mark sharp transitions in thermal behaviour in the ice. Time and Date: 4:00--5:30 p.m., Monday, November 19, 2007 Event: Mathematics Colloquium Speaker: Eric Zaslow, Northwestern University Subject: Ideas in mirror symmetry'' 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, November 20, 2007 Event: UBC SCAIM Seminar Speaker: Michael Overton, Computer Science, Courant Institute, NYU, PIMS and UBC Subject:Semidefinite Programming and a New Preconditioner'' Location: WMAX 216 Abstract: Semidefinite Programming has become an important paradigm in Optimization. We explain what it is all about, what the linear algebra bottleneck is, and how one might deal with it. Time and Date: 3:00--4:00 p.m., Tuesday, November 20, 2007 Event: Algebraic Geometry Seminar Speaker: Eric Zaslow, Northwestern University Subject:Constructible Sheaves and the Fukaya Category'' Location: MATH 203 Abstract: I will describe an equivalence between these two categories, focusing on simple examples and applications (as time permits). The talk is based on work of Nadler and joint work with Nadler. Time and Date: 3:00--4:00 p.m., Wednesday, November 21, 2007 Event: Probability Seminar Speaker: Frank den Hollander, Leiden University and EURANDOM, The Netherlands Subject:A quenched large deviation principle for words in a letter sequence'' Location: WMAX 110 (rooms 216 and 110 switched for prob and agl/topolgy seminars) Abstract: When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In this talk, we consider the quenched LDP, i.e., we condition on a typical letter sequence. The rate function of the quenched LDP turns out to be a sum of two terms, one being the annealed rate function, the other being proportional to the specific relative entropy of the observed law of letters, obtained after a randomised concatenation'' of words, w.r.t. the reference law of letters. The proportionality constant equals the tail exponent of the renewal process. We show how the annealed and the quenched LDP can be combined to prove that the domain of convergence of the moment generating function of the collision local time of two transient random walks on Z^d, d \geq 1, strictly increases when we condition on one of the random walks. The presence of this gap implies the existence of an intermediate phase for the long-time behaviour of a class of branching processes, respectively, a class of interacting diffusions. Joint work with M. Birkner (Berlin) and A. Greven (Erlangen). Time and Date: 3:30--4:30 p.m., Wednesday, November 21, 2007 Event: Algebra/Topology Seminar Speaker: Jose Maria Cantarero-Lopez, UBC Subject:The completion theorem for groupoid actions'' Location: WMAX 216 (room switch was announced) Abstract: In this talk I will introduce an invariant for spaces with an action of a groupoid which generalizes equivariant K-theory and orbifold K-theory. An analogue of the completion map of Atiyah and Segal will be constructed, and in some cases, shown to be an isomorphism. Time and Date: 2:00--3:00 p.m., Thursday, November 22, 2007 Event: Mathematical Biology Seminar Speaker: Rafael Meza, Fred Hutchinson Cancer Research Center, Seattle, WA Subject:Mathematical Modeling of Colon Carcinogenesis'' Location: WMAX 216 Abstract: Mathematical modeling of carcinogenesis offers the opportunity to study in greater detail the effects of specific interventions that affect critical biological processes involved in cancer development. In this talk, I will present a mathematical model of colorectal carcinogenesis and discuss some applications. Careful mathematical analysis shows that the age-specific incidence of cancer predicted by the model exhibits 'phases' that reflect the carcinogenic process in reverse, with early events showing up late, and late events influencing the incidence at young age. In particular, calibration of our model to the colorectal cancers (CRC) in the SEER registry makes it evident that the age-specific incidence increases mostly linearly above age 60-65, reflecting the incidence (onset) of adenomatous polyps (adenomas) in the population, while it increases exponentially for mid ages due to "clonal expansion" of adenoma cells. Adenomas are the premalignant lesions associated with the large majority of colorectal cancers. These results contradict the long-held view that the cancer age-specific incidence increases as a power of age. Our findings have important implications for the design and analysis of CRC screening strategies. In particular, they allow us to use our model, which was only fitted to cancer incidence and not to adenoma data, to simulate the natural history of CRC and evaluate the effect of screening for adenomas on CRC risk. If time permits, I'll discuss some of the mathematical, computational and practical issues related to our analyses of CRC screening, and present evidence that current screening guidelines may be far from optimal. Time and Date: 2:00--2:50 p.m., Thursday, November 22, 2007 Event: PIMS/SFU/UBC Number Theory Seminar (1 of 3 seminars) Speaker: Soroosh Yazdani, McMaster University Subject:Level lowering and Szpiro's conjecture'' Location: UBC Campus, Room WMAX 110, (PIMS) Abstract: Let E/ \mathbf Q be an elliptic curve over the rationals. One can associate two rational integers that measure the ramification of this elliptic curve over various primes, the conductor N_E and the minimal discriminant \Delta_E. The Szpiro's conjecture states that for any \varepsilon >0 there exists a constant C_\varepsilon >0 such that |\Delta_E| < C_\varepsilon (N_E)^{6+\varepilson}. This conjecture is equivalent to the ABC-conjecture and, if true, would imply solutions to many Diophantine equations. A consequence of Szpiro's conjecture is that we can bound v_p(\Delta_E) for the largest prime p dividing \Delta_E. In this talk I will show how a generalization of Ken's level-lowering result can be used to bound v_p(\Delta_E). Time and Date: 3:00--3:50 p.m., Thursday, November 22, 2007 Event: PIMS/SFU/UBC Number Theory Seminar (2 of 3 seminars) Speaker: Sander Dahmen, Universiteit Utrecht Subject: Modular methods applied to Diophantine equations'' Location: UBC Campus, Room WMAX 110, (PIMS) Abstract: Deep results about elliptic curves, modular forms and Galois representations have successfully been applied to solve FLT and other Diophantine equations. Most of such applications broadly proceed along the following lines. To a hypothetical solution is associated a certain elliptic curve, called a Frey curve, and it is shown that the mod l Galois representation \rho_l associated to the l-torsion points of the Frey curve (with l, say, an odd prime occurring as exponent in the Diophantine equation) is irreducible. Then by modularity and level lowering, one obtains that \rho_l is modular of some explicitly known level (weight 2 and trivial character). Finally, the modular forms of this level provide (possibly in a non trivial way) information about the original Diophantine equation. In this talk I will first describe the above mentioned method in some more detail and then focus on the problem of finding Frey curves and proving irreducibility of \rho_l for small primes l. Time and Date: 4:00--5:30 p.m., Thursday, November 22, 2007 Event: Complex Fluids Seminar Speaker: Bernd R. Noack, Berlin University of Technology Subject:A finite-time thermodynamics for modeling and control of shear flows'' Location: MATH 225 Abstract: Turbulent fluid has often been conceptualized as transient thermodynamic phase. A statistical physics description of turbulence has been a long-term endeavour since the early 20th century. Here, a finite-time thermodynamics (FTT) formalism (Andresen, Salamon & Berry 1977) is proposed to compute the mean flow and fluctuation levels of unsteady, incompressible, shear flows. That formalism yields a definition for a thermodynamic degree of freedom of the velocity fluctuation, conditions for local thermal equilibrium (LTE), as well as a Fickian law of energy re-distribution for non-equilibrium conditions. In general, the dynamics of unsteady flow is shown to be in partial LTE, a state governed by finite time scales of energy transfer. Mathematically, this partial LTE arises from a continuous interpolation between a linear instability of few degrees of freedom and statistical physics of the whole system. The FTT model has been successfully applied to shear flows with simple to complex dynamics. Presented examples include the 1D Burgers equation, 2D vortex shedding and 3D homogenous shear turbulence. In addition, the FTT formalism opens the first path to a fully nonlinear, infinite-horizon control theory. Corresponding efforts of shear flow control in experiment and simulations will be presented. Time and Date: 4:10--5:00 p.m., Thursday, November 22, 2007 Event: PIMS/SFU/UBC Number Theory Seminar (3 of 3 seminars) Speaker: Paul Mezo, Carleton University Subject:A Paley-Wiener theorem and Arthur's trace formula'' Location: UBC Campus, Room WMAX 110, (PIMS) Abstract: Modular forms may be recast and generalized as automorphic representations, which are objects of abstract harmonic analysis. The trace formula is a theorem in harmonic analysis which allows one to compare automorphic representations. The Paley-Wiener theorem is also a theorem in harmonic analysis. It characterizes the Fourier transform of smooth compactly-supported functions, and is essential in the proof of Arthur's trace formula. We shall expand on each of these statements, highlighting new results. This is joint work with P. Delorme. Time and Date: 3:00--4:30 p.m., Friday, November 23, 2007 Event: Mathematics Colloquium Speaker: Frank den Hollander, Leiden University and EURANDOM, The Netherlands Subject: Metastability under stochastic dynamics'' 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 26, 2007 Event: IAM Seminar Series Speaker: Nilima Nigam, Department of Mathematics, McGill University Subject:High-Order Conforming Finite Elements for a Pyramid'' Location: Room 301, LSK Bldg. Abstract: Pyramidal elements can arise in hybrid meshes as "gluing" elements between hexahedral and tetrahedral structures. A long-outstanding problem has been how to design high-order conforming finite elements on the pyramid which are compatible on their faces and edges with existing elements from neighbouring tetrahedra or hexahedra. We present high-order elements which satisfy the exact sequence property for H^1, H(curl), H(div) and L^2, and which also have the required compatibility features. The use of projection-based interpolation allows for a commuting diagram property. Along the way, we describe the (surprising) result that such finite elements cannot be comprised of polynomial functions alone. Time and Date: 3:00--4:30 p.m., Monday, November 26, 2007 Event: Algebraic Geometry Seminar Speaker: Patrick Brosnan, UBC Subject:Perverse weak Lefschetz with applications to admissible normal functions'' Location: WMAX 110 Abstract: I will discuss one aspect of joint work with H. Fang, Z. Nie and Greg Pearlstein. In it, we use a relative weak Lefschetz theorem for families of hyperplane sections to get a deeper understanding of work of Griffiths and Green on singularities of normal functions. I plan to talk more about the perverse weak Lefschetz than about the normal functions. Time and Date: 4:00--5:30 p.m., Monday, November 26, 2007 Event: Mathematics Colloquium Speaker: Matania Ben-Artzi, Hebrew University of Jerusalem Subject: Dispersive evolution equations (and why Newton is still relevant)'' 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, November 27, 2007 Event: UBC SCAIM Seminar Speaker: Felix Herrmann, Earth and Ocean Sciences, UBC Subject:Seismic imaging meets compressive sampling'' Location: WMAX 216 Abstract: Seismic imaging involves the solution of an inverse-scattering problem during which the energy of (extremely) large data volumes is collapsed onto the Earth's reflectors. We show how the ideas from 'compressive sampling' can alleviate this task by exploiting the curvelet transform's 'wavefront-set detection' capability and 'invariance' property under wave propagation. First, a wavelet-vaguelette technique is reviewed, where seismic amplitudes are recovered from complete data by diagonalizing the Gramm matrix of the linearized scattering problem via the curvelet domain. Next, we show how the recovery of seismic wavefields from incomplete data can be cast as a compressive sampling problem, followed by a proposal to compress wavefield extrapolation operators via compressive sampling. As part of the first problem, we show how jitter sampling creates favorable conditions for recovery by curvelet sparsity promotion. The second approach uses the modal domain as the measurement basis, effective reducing the size of the wavefield extrapolation operator. Time and Date: 2:30--3:30 p.m., Tuesday, November 27, 2007 Event: DG-MP-PDE Seminar Speaker: Matania Ben-Artzi, Hebrew University Subject:Nonlinear conservation laws on manifolds'' Location: WMAX 110 Abstract: We define a class of nonlinear scalar hyperbolic equations on Riemannian varieties (compact, without boundary). Proofs of existence and uniqueness are obtained by a combination of dissipative estimates and Young measures. Suitable entropy conditions are introduced. We show the convergence of a class of finite-volume schemes and present some numerical results. The numerical scheme used is the GRP (Generalized Riemann Problem) scheme, an analytic high-resolution extension of the Godunov scheme. (Joint work with J. Falcovitz and Ph. LeFloch). Time and Date: 3:30--4:30 p.m., Tuesday, November 27, 2007 Event: Discrete Mathematics Seminar Speaker: Eric Fusy, SFU Subject:Transversal structures on triangulations: combinatorial study and algorithmic applications'' Location: WMAX 216 Abstract: We study the combinatorial properties and algorithmic of planar maps (planar graphs embedded in the plane). The techniques are illustrated on a particular family, namely plane triangulations with no separating triangle (called irreducible). These triangulations can be endowed with specific edge bicolorations, called transversal structures, which makes it possible to count the triangulations bijectively, generate them at random, encode them and draw them on a grid. Simulations indicate that the grid used by the drawing has with high probability a size close to 11n/27 * 11n/27, where n is the number of vertices. As we will see, this can be proved rigorously using tools from bijective combinatorics as well as analytic combinatorics. Time and Date: 3:00--4:00 p.m., Wednesday, November 28, 2007 Event: Probability Seminar Speaker: Alexander E. Holroyd, UBC Subject:Slow convergence in bootstrap percolation'' Location: WMAX 216 Abstract: Bootstrap percolation is a simple cellular automaton model for nucleation and growth. Sites in an L by L square are initially infected with probability p, and a healthy site becomes infected if it has at least 2 infected neighbours. Asymptotically for large L, the model is known to undergo a phase transition as the parameter p log L crosses the threshold pi ^2/18. However, simulation predictions for this threhold are typically smaller by more than a factor of two! I'll talk about some attempts to understand this discrepancy. The main result is that the asymptotic value differs from the actual threshold by at least const/sqrt(log L). (In contrast, the critical window has width only const/log L.) For a variant model we can prove that to get within 1% of the asymptotic value, L must be at least 10^{3000}! This is joint work with Janko Gravner. Time and Date: 2:00--3:00 p.m., Thursday, November 29, 2007 Event: Mathematical Biology Seminar Speaker: Lazar Krsmanovic, National Institutes of Health, USA Subject:Pulsatile Gonadotropin-Releasing Hormone Secretion: Roles of G Protein-Coupled Receptors, Second Messengers and Ion Channels'' Location: WMAX 216 Abstract: The integrated activity of the hypothalamic gonadotropin-releasing hormone (GnRH) neuronal network, and the pulsatile release of GnRH at the median eminence, is essential for the episodic mode of pituitary gonadotropin secretion and for the maintenance of normal gonadal function. GnRH receptor was found to be expressed in GnRH neurons and their immortalized counterparts (GT1-7 cells). This suggested that GnRH released from hypothalamic GnRH neurons could exert autocrine actions upon its cells of origin and contributes to the pulsatile secretion of GnRH. Patch clamp recording from identified GnRH neurons showed irregular action potential (AP) firing with transition between narrow, high spike amplitude rhythmic firing, and intervals of broader, lower spike-amplitude, burst-like AP firing. Treatment of hypothalamic GnRH neurons with 10 nM GnRH increased the occurrence of high-frequency broad APs with unchanged decay constants for fast afterhyperpolarization (fAHP) and medium (mAHP). In contrast, treatment of hypothalamic GnRH neurons with 1 M GnRH abolished mAHP current, but did not affect the occurrence of fAHP current. That was followed by subthreshold afterdepolarization potential (ADP) and significant reduction of the frequency of AP firing. These data indicate that spontaneous firing of APs in hypothalamic GnRH neurons determines the profile of afterhyperpolarization currents and consequently mediates firing frequency and the spike-profile. Constitutive and agonist-induced hetero-oligomerization of GnRH receptor and G protein-coupled receptor 54 (GPR54), stimulation of GnRH secretion by kisspeptin, and the opposing effects of GnRH on kisspeptin secretion, indicates that GnRH receptor/GnRH and GPR54/kisspeptin autoregulatory systems are integrated by negative feedback to regulate GnRH and kisspeptin secretion from GnRH neurons. Time and Date: 3:00--4:00 p.m., Thursday, November 29, 2007 Event: Algebra/Topology Seminar Speaker: Yongbin Ruan, University of Michigan Subject:Symplectic birational geometry'' Location: WMAX 110 Abstract: In the talk, I will outline a joint program with Tian-Jun Li towards a birational classification of symplectic manifolds. Time and Date: 4:00--5:30 p.m., Thursday, November 29, 2007 Event: Complex Fluids Seminar Speaker: Neville Dubash, Department of Mathematics, UBC Subject:Behaviour of a conducting drop in an electric field'' Location: MATH 225 Abstract: The general behaviour of a conducting drop in a uniform electric field is to deform and elongate in the direction of the field. Depending on the physical parameters the drop may reach and equilibrium state or it may undergo some form of breakup. Here, both these cases are examined for an axisymmetric conducting drop that is suspended in a very viscous insulating fluid. Numerical simulations using boundary integral methods, as well as a simple spheroidal model are used. For the more interesting case of drop breakup, it is found that different type of breakup can occur. These different types of breakup, and when each occurs, are also presented. Time and Date: 3:30--4:30 p.m., Monday, December 3, 2007 Event: Algebra/Topology Seminar Speaker: Tullia Dymarz, MSRI Berkeley Subject:Large scale geometry of certain solvable groups'' Location: WMAX 216 Abstract: Finitely generated groups can be viewed as metric spaces when endowed with a word metric, which is unique up to quasi-isometry. A group theoretic property is said to be geometric if it is invariant under quasi-isometries. Gromov initiated a program of investigating which algebraic properties of finitely generated groups are geometric, by showing that (virtual) nilpotence is a geometric property. Recently, Eskin-Fisher-Whyte conjectured that being (virtually) polycyclic is also a geometric property and developed tools to approach this problem. I will give a proof of quasi-isometric rigidity for one class of polycyclic groups. This will involve, among other things, ideas from hyperbolic geometry and quasiconformal analysis. Time and Date: 2:30--3:30 p.m., Tuesday, December 4, 2007 Event: DG-MP-PDE Seminar Speaker: Yannick Sire, Universite Aix-Marseille III Subject:KAM theory for lattices and PDEs'' Location: WMAX 110 Time and Date: 10:00--11:00 a.m., Thursday, December 6, 2007 (Only the time has been revised.) Event: PIMS-MITACS Math Finance Seminar Speaker: Ron Giammarino, Sauder School of Business, UBC Subject:Leaders, Followers and Risk Dynamics in Industry'' Location: WMAX 216 Abstract: We examine a model where two firms compete in a duopolistic product market. Firms produce a homogeneous product and face stochastic industry demand. Each firm has a single option either to expand or contract capacity, and hence output. In this setup we analyze the risk characteristics of industries as well as single firms and look at corresponding asset price dynamics. We focus on sequential exercise of options. We find that strategic competition in the product market is risk reducing. Time and Date: 2:00--3:00 p.m., Thursday, December 6, 2007 Event: Mathematical Biology Seminar Speaker: Joel Miller, BC Centre for Disease Control (recently, Los Alamos) Subject:Predicting the size and probability of epidemics on networks'' Location: WMAX 216 Abstract: Many diseases periodically emerge into human populations. Many of these diseases have animal hosts, while others are diseases which have been eliminated from some parts of the world and are occasionally reintroduced by travelers. As a classic example, HIV probably began as a transmission from an infected monkey to a hunter or cook in West Africa around 1930. Perhaps many such introductions happened over the centuries, and there is evidence that they continue, but this was the first instance in which the disease managed sustained spread. When a disease emerges or is likely to emerge, public health responses need to devote limited resources to containing the spread. In this talk we will address three important questions: 1) How likely is an introduction to lead to an epidemic? 2) If an epidemic occurs, how quickly will it grow? 3) How many people will be infected by an epidemic. All of these questions depend on both the characteristics of the disease and the structure of the population. We will develop a relatively simple mathematical theory and show how its predictions compare with an epidemic spreading in a simulated urban population. Time and Date: 2:30--3:30 p.m., Thursday, December 6, 2007 Event: DG-MP-PDE Seminar Speaker: Jean-Michel Roquejoffre, Paul Sabatier University, Toulouse III Subject:Nontrivial large-time behaviour in reaction-diffusion equations'' Location: WMAX 110 Abstract: It is well-known (Fife, Mc Leod, 1977) that solutions of bistable reaction-diffusion equations, posed on the whole real line, will converge to travelling waves. When the same equation is posed on the plane, or in the N-dimensional space, sufficiently well-prepared initial data will still give raise to convergence to 1D travelling waves (Levermore-Xin; Kapitula). We will explain in this talk why, when the initial datum is slightly less well-prepared than in the Levermore-Xin setting, the solution will not converge to a single 1D wave; it will instead undergo some diffusive behaviour. We will also discuss what happens when the level sets of the initial datum are conical-shaped. If time permits, we will describe what happens for KPP equations, when nontrivial behaviour occurs even in one space dimension. Time and Date: 4:00--5:30 p.m., Thursday, December 6, 2007 Event: Complex Fluids Seminar Speaker: Jun Zhang, Courant Institute and Physics Department, NYU Subject:The unidirectional flight of flapping wings'' Location: MATH 225 Abstract: The locomotion of most fish and birds is realized by flapping their wings or fins transverse to the direction of travel. Here, we study experimentally the dynamics of a symmetric wing that is "flapped" up and down but is free to move in the horizontal direction. In this table-top prototypical experiment, we show that flapping flight occurs abruptly at a critical flapping frequency as a symmetry-breaking bifurcation. We then investigate the separate effects of the flapping frequency, the flapping amplitude, the wing geometry and the influence from the solid boundaries nearby. Through dimensional analysis, we found that there are two dimensionless parameters well describe this intriguing problem that deals with fluid-solid interaction. The first one is the dynamical aspect ratio that combines four length scales, which includes the wing geometry and the flapping amplitude. The second parameter, the Strouhal number, relates the flapping efforts in the vertical direction to the resultant forward flight speed. We also investigated the effect of flexibility and passive pitching of the wings. We find that these help to increase the flight speed significantly, as observed in our experiments. Time and Date: 10:00 a.m., Monday, December 17, 2007 Event: Discrete Mathematics Seminar Speaker: Joel Friedman, Mathematics & Computer Science, UBC Subject:Solution to the Road Colouring Problem'' Location: MATH 202 Abstract: We outline Trahtman's recent solution to the road colouring problem, which asks if every directed graph of outdegree k has a k colouring of its edges that is synchronizing. This graph theory or automata theory question has received a lot of attention since it appeared in 1977 [Adler-Goodwyn-Weiss], in the context of symbolic dynamics. The solution introduces a number of new ideas, while utilizing many of the previous ideas: eigenvalue weights and inverse images [Friedman 1990], stability and congruence [Culik-Karhumaki-Kari, Kari 2001]. Time and Date: 2:30 p.m., Tuesday, December 18, 2007 Event: DG-MP-PDE Seminar Speaker: Werner Kirsch, Ruhr-University Bochum, Germany Subject:Mathematics and Politics: What is a fair distribution of power in a supranational organization?'' Location: WMAX 110

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