2009 Seminars

2009 Seminars

Time and Date: 3:00 p.m., Friday, January 9, 2009
Event: Mathematics Colloquium
Speaker: Chuck Cadman, Department of Mathematics, UBC
Subject: ``The geometry of root stacks and gerbes''
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 12, 2009
Event: IAM-PIMS-MITACS Distinguished Colloquium Series
Speaker: Lisa Fauci, Department of Mathematics and Center for Computational Science, Tulane Univ., Louisiana
Subject:``Understanding Swimming at Low Reynolds Numbers: Successes and Challenges''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: Microorganisms such as bacteria and spermatozoa move in a world where viscous forces completely dominate inertial forces, and the time evolution of their motion may be thought of as a sequence of steady-state snapshots. In this world, what motility strategies give rise to efficient locomotion? The study of the fluid dynamics of microorganism motility began with the classic work of G. I. Taylor in 1951, and has been an active area of research in the last decades. Current modelling challenges include the collective dynamics of microorganisms and their interactions with surrounding physical and chemical environments, coupling of their internal force-generating mechanisms with external fluid dynamics, as well as their motion through viscoelastic fluids. We will present recent work, both analytical and computational, that sheds light on these complex systems.

Time and Date: 10:00 a.m., Wednesday, January 14, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Baptiste Calmes, University of Cambridge
Subject:``Formal group laws and flag varieties''
Location: WMAX 110 (PIMS)
Abstract: The purpose of this talk is to explain how to adapt and extend the classical topological computations of the cohomology of flag varieties to the world of algebraic geometry and oriented cohomology theories (in particular algebraic cobordism).

The classical situation in algebraic topology is as follows. Let G be a compact Lie group, with maximal torus T. The flag variety G/T is a fundamental object, and it is important to understand its (say, singular) cohomology H^*(G/T). To compute the ring structure of H^*(G/T), one classically considers the cohomology of the classifying space H^*(BT) (a power series ring) and the so-called characteristic map c from H^*(BT) to H^*(G/T). This ring map is surjective when the coefficients are the rational numbers, and its kernel is the ideal generated by elements fixed by the Weyl group and in positive degree. Since H^*(G/T) with integer coefficients has no torsion, this is enough to give a concrete description of the ring structure on H^*(G/T).

Instead, in algebraic geometry, G becomes a split semi-simple linear algebraic group with a Borel subgroup B, the flag variety is G/B and we want to replace singular cohomology by any oriented cohomology theory h. The first task will be to replace the characteristic map (since there is no algebraic BT). Then, we will explain how to compute the ring structure of h^*(G/B) using the formal group law associated to h. On the way, we will encounter Schubert varieties and their desingularizations, together with Demazure and Gelfand operators.

Time and Date: 12:30--1:30 p.m., Wednesday, January 14, 2009
Event: Complex Fluid Seminar
Speaker: Cherif Nouar, LEMTA, UMR 7563, CNRS, France
Subject:``Transitional flow of a shear-thinning fluid in a pipe.
Experimental evidence of a chaotic flow induced by the shear-thinning behavior''
Location: CHBE 204 (2360 East Mall)
Abstract: In the last decades considerable advances have been made in understanding the transition mechanisms from laminar to turbulent flow of newtonian liquids in pipes. For non-newtonian liquids however, perhaps unsurprisingly, given the inherent additionnal complexities involved, little is known. Aside from a handful papers, there is practically no data about the transitional of such non-newtonian liquids. Although limited, the existing literature for the transitional pipe-flow of non-newtonian liquids reveals an interesting and yet unexplained effect: above a certain Reynolds number the flow develops a stable asymmetry. For laminar and turbulent regimes, the velocity profiles are perfectly symmetric. In the present work, we provide a three- dimensional description of this asymmetry. The experimental results suggest the existence of a robust nonlinear coherent structure characterized by two weakly modulated counter-rotating longitudinal vortices. The statistical analysis of the velocity fluctuations, show that this non linear asymmetric state corresponds to a weak turbulent flow.

Time and Date: 3:00-4:00 p.m., Wednesday, January 14, 2009
Event: Probability Seminar
Speaker: Allan Sly, Berkeley
Subject:``Mixing in Time and Space''
Location: WMAX 216
Abstract: For Markov random fields temporal mixing, the time it takes for the Glauber dynamics to approach it's stationary distribution, is closely related to the spatial mixing properties of the measure such as uniqueness and the reconstruction problem. Such questions are of importance in probability, statistical physics and theoretical computer science. I will discuss some recent progress in understanding the mixing time of the Glauber dynamics for the Ising model and for random colourings of graphs.

Time and Date: 12:30--1:30 p.m., Thursday, January 15, 2009
Event: Mathematics Graduate Student Seminar
Speaker: Scott Sitar, Mathematics, UBC
Subject:``Solving Diophantine Equations: The Modular Method''
Location: MATH 225
Abstract: The resolution of Fermat's Last Theorem has seen the introduction of a powerful new tool into the study of Diophantine equations. In this talk, I will define and outline the basic objects and strategies of this new method: elliptic curves, modular forms, Galois representations, Frey curves, and level lowering. Using these tools, I will give a proof of Fermat's Last Theorem (which is easy!), as well as survey some other successes of the new method.

Time and Date: 2:00--3:00 p.m., Thursday, January 15, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: Alex Mogilner, UC Davis
Subject:``Multiscale Modeling of the Motile Keratocyte Cell''
Location: WMAX 216
Abstract: Fish keratocytes, when plucked out of the fish scales and placed on a flat surface, move rapidly and persistently keeping a characteristic fan-like shape. This movement is powered by the lamellipod . flat meshwork of dynamic actin filaments enveloped by the cell membrane. Rapid treadmill of these filaments, restrained by the membrane and cell adhesion to the surface and assisted by myosin-generated contraction, governs the shape and speed of the motile cells. I will introduce a number of mathematical models at various spatial-temporal scales, including a model of viscoelastic contractile gel, that explain the rules behind the keratocyte motility.

Time and Date: 3:00--3:50 p.m., Thursday, January 15, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Michael Coons, SFU
Subject:``Transcendence and functional equations''
Location: SFU Campus, Room ASB 10900 (IRMACS)
Abstract: We discuss various transcendence results regarding generating functions of sequences which satisfy two very different types of functional equations. We apply these results to improve some results of W. Schwarz.

Time and Date: 4:10--5:00 p.m., Thursday, January 15, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Peter Borwein, SFU
Subject:``Approximation and the Riemann zeta function''
Location: SFU Campus, Room ASB 10900 (IRMACS)
Abstract: We explore the location of the zeros and poles of the Pade approximations to the Riemann Zeta function. The patterns are striking and the computations difficult. Little is proved but much is suggested. This, of course, is intimate to the Riemann hypothesis.

Time and Date: 4:00 p.m., Tuesday, January 20, 2009
Event: Discrete Mathematics Seminar
Speaker: Omer Angel, UBC
Subject:``Do four colours really suffice?''
Location: WMAX 216 (PIMS)
Abstract: We consider the problem of colouring the planar map given by the Voronoi tessellation corresponding to a Poisson process in R². We seek deterministic colouring rules that are independent of the coordinate system (formally: isometry covariant and are factors of the Poisson process). We prove that 6 colours suffice. I shall also discuss other dimensions. With Benjamini, Gurel-Gurevich, Meyerovitch, Peled.

Time and Date: 12:00--1:00 p.m., Wednesday, January 21, 2009
Event: Complex Fluids Seminar
Speaker: Bulent Guzel, Dept. of Mechanical Engineering, UBC
Subject:``Observation of laminar-turbulent transition of a yield stress fluid in Hagen-Poiseuille flow''
Location: CHBE 202 (2360 East Mall)
Abstract: The main focus of this work is to investigate experimentally the transition to turbulence of a yield stress shear thinning fluid in Hagen-Poiseuille flow. By combining direct high speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations, and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution, and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equals or exceeds the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behavior of the yield stress fluid is somewhat similar to a (simpler) shear thinning fluid. We have also observed the shape of slugs during transition and find that their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined. Finally we present a new phenomenological approach for quantifying laminar-turbulent transition in pipe flow. This criterion is based on averaging a local Reynolds number to give ReG. Our localised parameter shows strong radial variations that are maximal at approximately the radial positions where puffs first appear during the first stages of turbulent transition.

Time and Date: 3:00--4:00 p.m., Wednesday, January 21, 2009
Event: Algebra/Topology Seminar
Speaker: Dale Rolfsen, UBC
Subject:``Fox calculus and fibred manifolds''
Location: WMAX 110 (PIMS)
Abstract: This talk is dedicated to the memory of Bernard Perron, who recently passed away. We collaborated on work involving automorphisms of a free group: he showed me how to understand the induced automorphisms on the lower central series quotients, using the Fox free calculus.

My talk will discuss this, with applications to the orderability of fundamental groups of certain manifolds which fibre over the circle.

Time and Date: 3:00-4:00 p.m., Wednesday, January 21, 2009
Event: Probability Seminar
Speaker: Ben Graham, UBC
Subject:``Influence and statistical mechanics''
Location: WMAX 216
Abstract: Statistical mechanics is the branch of physics that seeks to explain the properties of matter that emerge from microscopic scale interactions. Probabilistic models such as percolation help describe various physical phenomena. The models are generally not exactly solvable; simple local interactions produce complex long range behaviour.

The technology of influence provides a way to study these processes. We will look at applications of influence to percolation, directed and undirected first passage percolation, the Ising model, and the random-cluster model.

Joint work with Geoffrey Grimmett.

Time and Date: 4:00--5:00 p.m., Thursday, January 22, 2009
Event: Teaching Resources Seminar
Speaker: Mclean Edwards, Department of Mathematics, UBC
Subject:``The Computer Labs of Math 102/103: A Practical Look at an Efficient Complementary System for Student Instruction''
Location: MATH 204
Abstract: The Labs for Math 102 and 103 are a successful application of information technology towards student instruction. I will first show how the student is able to explore calculus in an alternative and meaningful way, followed by a demonstration of how streamlined the process of preparing for the labs has become. Finally, the history and implementation details will be covered, paving the way for a discussion of further possibilities.

Time and Date: 10:00--10:50 a.m., Friday, January 23, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Travis Schedler, MIT
Subject:``Cyclic homology and the Gauss-Manin connection''
Location: WMAX 110
Abstract: Cyclic homology is a generalization of de Rham cohomology which makes sense for associative algebras (viewed as functions on a ``noncommutative space") and coincides with the latter on commutative algebras. I will explain a construction of cyclic homology in the spirit of equivariant de Rham cohomology, a relationship which becomes precise on the level of representations of the algebra. As an application, I will explain a simple construction of the Gauss-Manin connection on cyclic homology, which generalizes the well-known connection in the commutative case. This simplifies complicated formulas of Getzler. This work is joint with V. Ginzburg.

Time and Date: 12:00 p.m., Friday, January 23, 2009
Event: PIMS/WMAX Postdoctoral Colloquium
Speaker: Jose Manuel Gomez, UBC
Subject:``Almost commuting elements in Lie Groups''
Location: WMAX 216
Abstract: In this non technical talk I will show how one can use the space of almost commuting elements in a compact Lie group G to study the space of commuting elements in G. The exposition will be based on interesting examples trying to keep the technical details to a low level.
Note: Attendees may bring their lunches.

Time and Date: 3:00 p.m., Friday, January 23, 2009
Event: Mathematics Colloquium
Speaker: Travis Schedler, MIT
Subject: ``Noncommutative geometry and the McKay correspondence''
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 26, 2009
Event: Joint IAM Seminar Series and Mathematics Departmental Colloquium
Speaker: John Lowengrub, University of California at Irvine
Subject: ``Controlling the shapes of micro- and nano- scale structures''
Location: Room 301, Leonard S. Klinck Bldg.
Note: Refreshments will be served at 2:30 p.m. in the IAM Lounge, Room 306, please bring your own mug.

Time and Date: 12:30--2:00 p.m., Tuesday, January 27, 2009
Event: Scientific Computing and Applied & Industrial Mathematics (SCAIM) Seminar
Speaker: John Lowengrub, UC Irvine
Subject:``Multiscale models of solid tumor growth and angiogenesis''
Location: WMAX 216 (PIMS)
Abstract: We present and investigate models for solid tumor growth that incorporate features of the tumor microenvironment including tumor-induced angiogenesis. Using analysis and nonlinear numerical simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We account for variable cell-cell/cell-matrix adhesion in response to microenvironmental conditions (e.g. hypoxia) and to the presence of multiple tumor cell species. We focus on glioblastoma and quantify the interdependence of the tumor mass on the microenvironment and on the cellular phenotypes. The model provides resolution at various tissue physical scales, including the microvasculature, and quantifies functional links of molecular factors to phenotype that for the most part can only be tentatively established through laboratory or clinical observation. This allows observable properties of a tumor (e.g. morphology) to be used to both understand the underlying cellular physiology and to predict subsequent growth or treatment outcome, thereby providing a bridge between observable, morphologic properties of the tumor and its prognosis.

Time and Date: 3:00-4:00 p.m., Wednesday, January 28, 2009
Event: Probability Seminar
Speaker: Martin Barlow, UBC
Subject:``Convergence of random walk in random environment to fractional kinetic motion''
Location: WMAX 216
Abstract: I will consider a random walk in random environment obtained by putting iid bond weights \mu_e on the bonds in the lattice Z^d. (Here d\ge 3). We assume \mu_e \ge 1, but have heavy tails: P(\mu_e > t) \sim t^{-\alpha} with \alpha \in (0,1). This process, when suitably rescaled, converges to a non Markovian process, called 'fractional kinetic motion'. This is joint work with J. Cerny.

Time and Date: 2:00--3:00 p.m., Thursday, January 29, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: Pik-Yin Lai, National Central University of Taiwan
Subject:``Synchronization of cardiac cells growing in culture''
Location: WMAX 216
Abstract: Synchronization of heterogeneous systems consisted of oscillatory and passive elements are studied in cardiac myocytes (CM)/fibroblasts (FB) co-cultures. It is found that beating clusters of CM surrounded by FB will be formed. The beatings of the CM clusters are not correlated at early times but get synchronized as the cultures mature. This synchronization can be understood by a Kuramoto model with a time increasing coupling strength. Our findings show that the growth of the coupling strength between clusters is linear while the overall wave dynamics of the system is controlled by the passive FB in the system which presumably is growing exponentially. The variations of the frequencies towards synchronization are also modeled b y the "frequency enhancement" effect for coupled excitable/oscillatory elements.

Time and Date: 3:00--3:50 p.m., Thursday, January 29, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Mark Watkins, University of Sydney
Subject:``A survey of L-function computations''
Location: UBC Campus, Room WMAX 216 (PIMS)
Abstract: This talk will be in two parts. The first will give an idea of what computations are possible with L-functions, and what uses they have. The second part will give more explicit details for some of the work being done under a Focused Research Group grant from the NSF. In particular, we will describe work concerning the number of rank 4 twists of the congruent number curve (still in progress), and some eta-quotient expressions for various Waldspurger lifts of modular forms.

Time and Date: 4:10--5:00 p.m., Thursday, January 29, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Scott Sitar, Department of Mathematics, UBC
Subject:``Erdos-Turan with a moving target, equidistribution of roots of reducible quadratics, and Diophantine quadruples''
Location: UBC Campus, Room WMAX 216 (PIMS)
Abstract: A Diophantine m-tuple is a set of positive integers such that the product of any two distinct elements, increased by 1, is a perfect square. We will derive an asymptotic formula which counts the number of Diophantine quadruples with elements bounded by N by modifying the Erdös-Turán inequality and a result of Hooley on the equidistribution of solutions to polynomial congruences. This is joint work with Greg Martin.

Time and Date: 10:00--10:50 a.m., Friday, January 30, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Lior Silberman, UBC
Subject:``Diophantine Geometry in Algebraic Groups''
Location: WMAX 110
Abstract: Let G be an algebraic group over the rationals, and let S be a finite subset of elements of G(Q) which lie close to a (small) subgroup of G(R). Under what conditions can we conclude that S in fact lie on a (small) subgroup of G(Q)?

Time and Date: 2:00--3:00 p.m., Friday, January 30, 2009
Event: Algebra/Topology Seminar Note special day and time of seminar.
Speaker: Gyo Taek Jin, KAIST, Korea
Subject:``Prime Knots with arc index up to 11 and an upper bound arc index for non-alternating knots''
Location: WMAX 110
Abstract: Every knot can be embedded in the union of finitely many half planes with a common boundary line in such a way that the portion of the knot in each half plane is a properly embedded arc. The minimal number of such half planes is called the arc index of the knot. We have identified all prime knots with arc index up to 11. We also proved that the crossing number is an upperbound of arc index for non-alternating knots. As a result the arc index is determined for prime knots up to twelve crossings.

Time and Date: 3:00 p.m., Friday, January 30, 2009
Event: Mathematics Colloquium
Speaker: James Carrell, UBC
Subject: ``Seeking the Smooth Schubert 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, February 2, 2009
Event: IAM Seminar Series
Speaker: Benedetto Piccoli, Istituto per le Applicazioni del Calcolo, Roma, Italy
Subject:``Traffic flow and intelligent motions of large groups''
Location: Room 301, Leonard S. Klinck Bldg.
Note: Refreshments will be served at 2:30 p.m. (LSK 306 Lounge)
Abstract: In recent years, a growing interdisciplinary interest has showed up in the moving groups of intelligent agents, which include vehicular traffic, pedestrian flows, movement of robots and movement of animal groups. We first review various results and applications about the modelling of vehicular traffic via conservation laws, with special focus on networks. Then we discuss an alternative mathematical framework, based on time-evolving measures, which can be applied to pedestrian flows and to animal/robot groups. The latter is still macroscopic but takes into account microscopic issues.

Time and Date: 4:10--5:10 p.m., Monday, February 2, 2009
Event: Algebraic Geometry Seminar
Speaker: Lothar Gottsche, Abdus Salam International Centre for Theoretical Physics
Subject:``Sections of line bundles on moduli spaces of sheaves on rational surfaces and Le Potier's strange duality''
Location: WMAX 110 (PIMS)
Abstract: Let X be a (smooth, projective) rational surface, with an ample line bundle H. We consider the moduli spaces M_n of H-stable rank 2 torsion- free sheaves on X with second Chern class n. For a line bundle L on X there is an associated line bundle L_n on M_n, and we study the generating function of the holomorphic Euler charcteristics of these line bundles. We prove that it is always a rational function in, which can be determined explicitly in many cases, and has some nice symmetry properties.

The rationality and the symmetry properties find their natural explanation in Le Potiers strange duality conjecture, which relates sections of L_n on M_n to sections of line bundles on a moduli space of pure sheaves supported on curves in the linear system associated to L. In some cases we prove the strange duality conjecture.

Time and Date: 12:30--2:00 p.m., Tuesday, February 3, 2009
Event: SCAIM Seminar
Speaker: Benedetto Piccoli, Istituto per le Applicazioni del Calcolo, Roma, Italy
Subject:``Traffic flow on networks''
Location: WMAX 216
Abstract: Recent results proposed a systematic use of conservation laws models on networks for urban vehicular traffic. We first describe modelling issues and relative analysis. Then we discuss numerics and challenges raising in real cases, addressing convergence, data sources and computational costs. Similar models are illustrated for the case of data networks and supply chains. Finally, ode-pde systems for single vehicle trajectory are presented.

Time and Date: 2:30-3:30 p.m., Tuesday, February 3, 2009
Event: Probability Seminar
Speaker: Michael Goldstein, University of Toronto
Subject:``Fluctuations and growth of the magnitude of the Dirichlet determinants of Anderson Model at all disorders''
Location: WMAX 216
Abstract: We consider the Schrodinger operator of the Anderson model

\bigl[\hlv \psi\bigr](n) := \Delta_\Lambda\psi(n) + v_n \psi_n\ ,\quad v = (v_n)

in a quasi-one-dimensional domain \Lambda = [1, N]\times [1, K]\subset \IZ2, K\le N^{1-\delta}, with Dirichlet boundary condition on \partial\Lambda. We study the function

\cU_\Lambda(v, E) = \log \big |\det\bigl(\hlv - E\bigr) |=\sum_j \log |E_{\Lambda,j}(v)-E|

where E_{\Lambda,j} are the eigenvalues of \hlv in \Lambda, E \in \IC, with v_n being i.i.d. which common distribution dP_0(v_0) has a bounded density. We prove that

\la \cU_\Lambda(., E) \ra \ge {K} N

where the constant \beta_0 >0 can be effectively evaluated in terms of the main parameters of the density of v_0. This, in particular, gives an effective, finite number of factors lower bound \gamma_1(E)\ge \frac {\beta_0}{K} for the upper Lyapunov exponent \gamma(E) of the product of the corresponding 2K\times 2K symplectic matrices. We explain the mechanism responsible for {\sl exponentially large magnitude of the Dirichlet determinant\/} \det \bigl(\hlv - E\bigr). The central part of this mechanism consists of the fact that \cU_\Lambda(., E) {\sl has large fluctuations.} Namely, its variants obeys \var\left(\cU_\Lambda(., E)\right)\ge c_1 |\Lambda|, c_1 > 0. The later fact holds for any finite domain \Lambda \subset \znu and any dimension \nu.

Time and Date: 4:00--5:00 p.m., Tuesday, February 3, 2009
Event: Discrete Maths Seminar
Speaker: Joel Friedman, UBC
Subject:``A Spectral Approach to the Moore Bound''
Location: WMAX 216
Abstract: The so called "Moore Bound" is one of the great puzzles of graph theory. It is an upper bound on the girth of a d-regular graph on n vertices; it is almost immediate, and appeared in publication roughly 50 years ago. However, this bound has only been improved by an additive factor of -1 or -2 for any d > 2 and n.

We focus on the problem of fixing d and letting n tend to infinity. The Moore Bound gives an upper bound of roughly 2 log(n)/log(d-1), whereas the highest girth known is roughly (4/3) log(n)/log(d-1) (for the LPS expanders, for certain values of d and n; random graphs do worse). We describe a spectral approach to improving the Moore Bound with abelian lifts. Our main result is to describe a edge colouring problem, such that a significant improvement over a greedy colouring result would lead to an asymptotic improvement in the Moore Bound. (Unfortunately, we have no results on the colouring problem at present...). This is joint work with Nati Linial.

Time and Date: 3:00--4:00 p.m., Wednesday, February 4, 2009
Event: Mathematics Colloquium
Speaker: G.M. Homsy, Department of Mechanical Engineering, University of California at Santa Barbara
Subject: ``Chaotic Advection in Drops Driven by Electrohydrodynamics: Enhancement of Heat and Mass Transport''
Location: WMAX 110 (PIMS)
Note: Refreshments will be served at 2:45 p.m. (PIMS Lounge).

Time and Date: 4:00--5:00 p.m., Wednesday, February 4, 2009
Event: Topology Seminar
Speaker: Sadok Kallel, University of Lille & PIMS
Subject:``Topological Aspects of Finite subset spaces''
Location: WMAX 110
Abstract: For any positive integer n and any space X, Sub{n}(X) denotes the space of all finite subsets of X of cardinality at most n. This is almost like a configuration space but not quite. It appears in various contexts in algebraic and differential geometry. We review in this talk some known (and attractive) results due to Borsuk, Bott or more recently Tuffley.

Then we build on this to give more detailed results on the connectivity of Sub{n}X for general X and on the top homology group when X is a manifold. This is joint work with Denis Sjerve (UBC).

Time and Date: 4:30 p.m., Wednesday, February 4, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: David Drubin, University of California at Berkeley
Subject:``A mechanochemical model for endocytic vesicle formation''
Location: WMAX 216
Note: Refreshments at 4:00 p.m. in PIMS 2nd flr lounge.
Abstract: Formation of endocytic vesicles is a complex, dynamic process that couples sequential protein recruitment and lipid modifications with dramatic shape transformations of the plasma membrane. How the proper timing and coordination of these events is achieved, and the vesicle scission mechanism, are not understood. We address these questions by constructing an integrated mathematical model based on four key ideas: (1) membrane curvature and PI(4,5)P2 hydrolysis are mechanochemically coupled; (2) curvature-sensing and curvature-deforming activities constitute a positive feedback loop for BAR domain protein recruitment; (3) the mechanochemical coupling of events ensures the proper and robust temporal and spatial sequence of endocytic events; and (4) vesicle scission is the result of an interfacial force that develops at a lipid phase boundary. The model quantitatively recapitulates the endocytic events in budding yeast in a coherent manner, and explains key aspects of endocytosis in mammalian cells.

Time and Date: 2:00--3:00 p.m., Thursday, February 5, 2009
Event: Special Applied Mathematics Seminar
Speaker: G.M. Homsy, Department of Mechanical Engineering, UC Santa Barbara
Subject:``Some Heat Pipe Problems''
Location: LSK Bldg. Room 460
Note: Refreshments at 4:00 p.m. in PIMS 2nd flr lounge.
Abstract: Heat pipes are engineering devices designed to transport energy at very high fluxes (power densities) without moving parts. They exploit evaporation/condensation cycles in which capillarity is used to pump liquid against a thermal gradient, moving it from colder regions where it condenses to hotter regions where it evaporates. With the advent of microfabrication techniques, so-called ‘micro heat pipes’, with their well-defined geometries, open the way for physically based and predictive modeling, and insight into mechanisms. This talk will cover our recent work based on lubrication theory and a class of contact line models that results in thin film equations that can be integrated semi-analytically. We follow with a discussion of optimal design of micro heat pipes, novel architectures, new physical mechanisms, and if time allows, a brief mention of some open problems in the field.

Time and Date: 10:00--10:50 a.m., Friday, February 6, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Burt Totaro, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
Subject:``The torsion index of a complex reductive group''
Location: WMAX 110
Abstract: We survey the known calculations of the Grothendieck torsion index of a reductive group. The torsion index of G measures the maximum complexity of all G-torsors over all fields. Grothendieck showed that the torsion index is determined by the cohomology ring of the flag manifold G/B. Using this, the torsion index has been computed for all simply connected groups.

Time and Date: 3:00 p.m., Friday, February 6, 2009
Event: Mathematics Colloquium
Speaker: Burt Totaro, Department of Pure Mathematics and Mathematical Statistics, Cambridge
Subject: ``Algebraic surfaces and hyperbolic 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, February 9, 2009
Event: IAM Seminar Series
Speaker: Robert Beardmore, Department of Mathematics, Imperial College London, UK
Subject:``Biodiversity across Environments: A Problem in Bifurcation Theory''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: The Geographic Mosaic Theory of Coevolution (GMC) proposes conditions under which diversity both changes and is invariant across different environments. We use mathematical models of evolving in-chemostat experimental microbial systems to investigate the dependence of diversity on external system parameters. The basic prediction of the GMC is that so-called GxE (gene-by-environment) interactions do not yield changes in diversity across environments, whereas GxGxE interactions do. We illustrate these ideas by examining chemostat models that include terms to describe evolutionary adaptation in the following three contexts: adaptation to a single, limiting resource; bacteria-phage coevolution; and, time-permitting, adaptation of cross-feeding interactions.

Time and Date: 3:10--4:10 p.m., Monday, February 9, 2009
Event: Algebraic Geometry Seminar
Speaker: Dave Anderson, University of Michigan
Subject:``Positivity and transversality in the equivariant K-theory of flag varieties''
Location: WMAX 110 (PIMS)
Abstract: The torus-equivariant K-theory of a (generalized) flag variety G/P is an algebra over a Laurent polynomial ring. This algebra has a natural basis consisting of structure sheaves of Schubert varieties. The structure constants for multiplication with respect to this basis are Laurent polynomials, and a fundamental problem is to determine them explicitly. Based on a wealth of evidence, Griffeth--Ram and Graham--Kumar conjectured that the coefficients of these polynomials are positive (with respect to a certain choice of generators for the polynomial ring). Their conjectures generalize theorems of Graham and Brion, treating equivariant cohomology and non-equivariant K-theory, respectively.

In joint work with Stephen Griffeth and Ezra Miller, we prove these positivity conjectures. I will explain our methods, which combine earlier work of Brion with new equivariant transversality techniques.

Time and Date: 12:30--2:00 p.m., Tuesday, February 10, 2009
Event: SCAIM Seminar
Speaker: Danny Kaufman, Computer Science, UBC
Subject:``Coupled Principles for Contacting Systems''
Location: WMAX 216
Abstract: Numerical methods for the solution of multibody, frictional contact problems are in demand in a wide variety of application areas that include structural engineering, robotics, computer animation, interactive medical simulation, biomechanics, and granular flow. While pioneering research in applied mathematics, mechanics, and graphics have helped us to understand many of the unique challenges imposed by contacting systems, robust, accurate and efficient methods for solving frictional contact problems have remained elusive.

In particular, classical complementarity formulations of frictional contact, when discretized for numerical integration, generally lead to challenging optimization problems. We've found that, in practice, standard optimization methods such as Lemke's algorithm, Projected Gauss-Seidel, and interior point methods, that have generally been presumed suitable for solving these contact-related optimization problems, fail entirely for many important examples of frictional contact.

To address and understand these difficulties we present a generalized approach for formulating numerical methods to solve frictionally contacting systems. This leads us to an investigation of the properties of both rigid and elastic contacting systems which cause difficulties and to propose principled methods for obtaining and approximating their solutions in practical settings. Finally, we validate the proposed methods by obtaining accurate solutions to a wide range of frictionally contacting systems that were previously impractical to solve, as well as robust and stable simulations of elastic-frictional composites, friction-dependent masonry, stick-slip oscillation, and other complex frictional contact behaviors.

Time and Date: 12:00--1:00 p.m., Wednesday, February 11, 2009
Event: Complex Fluids Seminar
Speaker: Mya Warren, Department of Physics & Astronomy, UBC
Subject:``Non-equilibrium dynamics in the glassy state''
Location: CHBE 202 (2360 East Mall)
Abstract: Glass is not an equilibrium state of matter. One consequence is that glasses undergo aging, whereby the material properties depend on the time since vitrification. While thermodynamic variables such as the energy and enthalpy decrease only logarithmically, measures of the dynamics such as the diffusion constant and mechanical response change much more rapidly as structural relaxations become increasingly sluggish with age. In this talk, I’ll discuss some results of molecular dynamics simulations in the glassy state, and their implications for a microscopic description of aging.

Time and Date: 3:00--4:00 p.m., Wednesday, February 11, 2009
Event: Topology Seminar
Speaker: Daniel Mullner, University of Bonn
Subject:``Orientation reversal of manifolds''
Location: WMAX 110
Abstract: An orientable manifold is called amphicheiral if it admits an orientation-reversing self-map and chiral if it does not. Many familiar manifolds like spheres or orientable surfaces are amphicheiral but chiral manifolds have also been known for many decades, e.g. the complex projective spaces CP^{2n} and some lens spaces in dimensions congruent 3 mod 4. Interestingly, however, this phenomenon had not been studied systematically. In my talk, I will report on results concerning both chirality and amphicheirality of manifolds. The focus lies on the existence of simply-connected chiral manifolds in all possible dimensions.

Time and Date: 12:30--1:30 p.m., Thursday, February 12, 2009
Event: Mathematics Graduate Student Seminar
Speaker: Jerome Lefebvre, Department of Mathematics, UBC
Subject:``Introduction to p-adic fields and a toy model for SL2(R)''
Location: MATH 225
Abstract: As a general rule of thumb "number sets grow when a mathematician and an equation love each other very much". The p-adic numbers are very much part of that story. As p-adic numbers are rarely talked about at an undergraduate level, I'll try to introduce them through their topology and give some of their basic properties. This talk will be very elementary, requiring only basic ideas of metric spaces and ring theory. As a bonus mini-talk, I'll show how one of the models that are lying around the graduate student offices can be used to visualize SL(2,R), the group of two by two matrices with real entries and determinant equal to 1.

Time and Date: 2:00 p.m., Thursday, February 12, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: Nessy Tania, University of Utah
Subject:``Mathematical models of calcium regulation in cardiac cells''
Location: WMAX 216
Abstract: Calcium is a ubiquitous signaling molecule involved in the regulation of a wide range of processes. In cardiac cells, calcium plays a key role in mediating the electrical-excitation and contraction processes. Three mathematical models of calcium regulation are derived and analyzed. Using a simplified model, we first show that release localization, diffusion, and single-channel activity modulate the onset of calcium oscillations. These factors are of particular importance in cardiac cells where calcium release is spatially inhomogeneous and inherently stochastic. However, models that take these effects into account are computationally expensive to simulate. Using a variety of asymptotic approximations, we derive a simplified yet reliable model of stochastic calcium flux through a release unit. Finally, we use a whole-cell model to explore the role of calcium oscillations in the generation of periodic action potentials based on recent experimental studies on the sinoatrial node and embryonic cardiac cells.

Time and Date: 3:30--4:30 p.m., Thursday, February 12, 2009
Event: DG-MP-PDE Seminar
Speaker: Felix Shulze, Freie Universitat Berlin
Subject:``Stability of non-compact manifolds under curvature flows''
Location: WMAX 110
Abstract: In this talk we present two stability results. Firstly we present a stability result for graphical, rotationally symmetric, translating solutions to mean curvature flow. There we obtain that for initial data that converge spatially at infinity to such a soliton, the flow converges for large times to that soliton, without imposing any decay rates. Secondly we discuss Ricci flow of initial metrics which are asymptotically Euclidean. For small perturbations of the metric of Euclidean space, we show that the Ricci harmonic map heat flow converges to Euclidean space for large times. We also investigate the convergence of the diffeomorphisms relating Ricci harmonic map heat flow to Ricci flow. The first result is joint work with J. Clutterbuck and O.C. Schnuerer, the second result is joint work with M. Simon and O.C. Schnuerer.

Time and Date: 3:00--3:50 p.m., Thursday, February 12, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Karen Yeats, SFU
Subject:``Weight drop in Phi^4 transcendentals''
Location: SFU Campus, Room ASB 10900 (IRMACS)
Abstract: Primitive Feynman graphs in Phi^4 theory give rise to transcendental numbers which, from the work of people like David Broadhurst, are multiple zeta values in known examples. Very little is known in general. Even how to predict the weight of the zeta value from the graph without doing the integrations is not known in general. I will discuss one special case of predicting weight drop, some interesting conjectures from the known data, and what very little I can prove so far.

Time and Date: 4:10--5:00 p.m., Thursday, February 12, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Daniel Fiorilli, Universite de Montreal
Subject:``The Chebyshev's Bias phenomenon from the point of view of probability theory and asymptotic formulas''
Location: SFU Campus, Room ASB 10900 (IRMACS)
Abstract: The study of certain error terms arising in number theory can lead to very interesting results. For example, it was a great surprise when Littlewood discovered in 1914 that pi(x)-Li(x) changes sign infinitely often. Since then, finer questions have been asked about this error term, for example, what is the proportion of x such that pi(x)-Li(x) is positive. A similar phenomenon was observed by Chebyshev who noted that there seems to be more primes of the form 4n+3 than of the form 4n+1. Rubinstein and Sarnak gave a framework to study these questions in a groundbreaking article in 1994. We will push further their results, and show how one can compare different 'two-way prime number races' together, that is different error terms of the form pi(x;q,a)-pi(x;q,b), and see which is more often positive (or negative). The main tool is an asymptotic formula derived from the characteristic function of a random variable we will define. Here it is very interesting that these results are derived from a probabilistic model.

Time and Date: 10:00--10:50 a.m., Friday, February 13, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Angelo Vistoli, Scuola Normale Superiore, Pisa
Subject:``Group actions and moduli problems: some examples''
Location: WMAX 110
Abstract: The talk would aim at explaining the idea of a quotient stack in very concrete terms, giving some elementary, but non-trivial, examples.

Time and Date: 3:00 p.m., Friday, February 13, 2009
Event: Mathematics Colloquium
Speaker: Angelo Vistoli, Scuola Normale Superiore, Pisa
Subject: ``Parabolic sheaves''
Location: MATX 1100
Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).

Time and Date: 3:00--4:00 p.m., Monday, February 16, 2009
Event: Mathematics Colloquium
Speaker: Douglas Lind, University of Washington
Subject: ``Noncommutative Mahler Measure''
Location: WMAX 110 (PIMS)
Note: Refreshments will be served at 2:45 p.m. (PIMS 1st Flr Lounge).

Time and Date: 2:00 p.m., Thursday, February 19, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: Anmar Khadra, Humboldt University, Berlin
Subject:``Investigating the role of IGRP-specific low avidity T cells in the protection against T1D''
Location: WMAX 216
Abstract: Recent experimental observations have revealed that during the onset of autoimmune Type 1 Diabetes (T1D), different clones of T cells with various T cell avidities and protein specificities are naturally generated in diabetic animal models. One particular protein, IGRP, is considered to be the most dominant autoantigen, responsible for activating low and high avidity IGRP-specific T cells via APCs. Although high avidity T cells destroy ~90% of beta cell repertoire, leading to the abolishment of insulin secretion crucial for glucose metabolism, low avidity T cells appear to play a protective role. Several hypotheses concerning the kinetics of these low avidity T cells and the effects of certain drug treatments on this populations have been suggested. In this talk, we shall present series of mathematical models that investigate these hypotheses and the outcome of certain drug treatments. We shall examine the experimental data available so far and explain certain features exhibited by the various clones of T cells.

Time and Date: 3:00--4:00 p.m., Monday, February 23, 2009
Event: IAM Seminar Series
Speaker: Amy Shen, Department of Mechanical Engineering, University of Washington
Subject:``Microfluidics-Enhanced Synthesis for Biocompatible Nanoporous Materials''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: The flow of complex fluids in confined geometries produces rich and new phenomena due to the interaction between the intrinsic length-scales of the fluid and the geometric length-scales of the device. In this talk, I will focus on a micellar solution system that yields a novel route to synthesizing biocompatible nanoporous sol-gels. Through a combination of experiment and modeling I will show how self-assembly, confinement, and flow can be utilized to control fluid microstructure and system phase transitions, and thus to enhance the controlled synthesis of new biocompatible materials.

Time and Date: 12:30--2:00 p.m., Tuesday, February 24, 2009
Event: SCAIM Seminar
Speaker: Betsabeh Madani, Director, Business Development at MITACS
Subject:``The MITACS-Accelerate Internship Programme''
Location: WMAX 216 (PIMS)
Abstract: An overview of the MITACS ACCELERATE Graduate Research Internship Program is given. This program connects companies with university researchers. Some examples of past internships will be given as well as the administrative details of how an internship in the program works. The benefits of an internship to students, their professors, and the industry partners are extolled.

Time and Date: 4:00--5:00 p.m., Tuesday, February 24, 2009
Event: Discrete Maths Seminar
Speaker: Alexander Schonhuth, PIMS and SFU
Subject:``A simple and efficient solution of the identifiability problem for hidden Markov sources and quantum random walks''
Location: WMAX 216
Abstract: A solution of the identifiability problem (IP) for hidden Markov models (HMMs), based on a novel algebraic theory for random sources, is presented. It gives rise to an efficient and practical algorithm that can be easily implemented. Extant approaches are exponential in the number of hidden states and therefore only applicable to a limited degree. The algorithm can be equally applied to solve the IP for quantum random walks (QRWs) that have recently been presented as an analogon of Markov chains in quantum information theory. Moreover, the algorithm can be used to efficiently test HMMs and QRWs for ergodicity, which had remained an open problem so far.

Time and Date: 10:00--10:50 a.m., Wednesday, February 25, 2009
Event: Seminar on Algebraic groups, Galois cohomology and related topics
Speaker: Stefan Gille, University of Munich
Subject:``Rost cycle modules and sheaves with transfers''
Location: WMAX 110
Abstract: In this talk I will explain the relation between Voevodky's sheaves with transfers and the cycle modules of Rost. This relation is useful to compute the Zariski cohomology of sheaves with transfer. We will illustrate this by the example of such sheaves over split semisimple algebraic groups. On the way I will also define Voevodky's category of effective motives, and (if time permits) give an example of the different behaviour of the Zariski cohomology of sheaves without transfer over split semisimple algebraic groups.

Time and Date: 12:00--1:00 p.m., Wednesday, February 25, 2009
Event: Complex Fluids Seminar
Speaker: Amy Shen, Department of Mechanical Engineering, University of Washington
Subject:``Combing self-assembly, confinement, and flow to synthesize novel materials''
Location: CHBE 202 (2360 East Mall)
Abstract: The flow of complex fluids in confined geometries produces rich and new phenomena due to the interaction between the intrinsic length- scales of the fluid and the geometric length-scales of the device. In this talk, I will choose two model systems to illustrate the idea. First, I will focus on a micellar solution system that yields a novel route to synthesizing bio-compatible nanoporous sol-gels. Through a combination of experiment and modeling I will show how self-assembly, confinement, and flow can be utilized to control fluid microstructure and system phase transitions, and thus to enhance the controlled synthesis of bio-compatible new materials. Second, I will illustrate how confinement and flow can modify the self-assembly of supramolecular hydrogels and their subsequent thermal properties.

Time and Date: 3:00-4:00 p.m., Wednesday, February 25, 2009
Event: Probability Seminar
Speaker: Ronnie Pavlov, Department of Mathematics, UBC
Subject:``Estimating the entropy of a Z^d shift of finite type with probabilistic methods''
Location: WMAX 216
Abstract: In symbolic dynamics, a Z^d shift of finite type (or SFT) is the set of all ways to assign elements from a finite alphabet A to all sites of Z^d, subject to rules about which elements of A are allowed to appear next to each other. A simple example of an SFT is the Z^d golden mean shift, which is the set of all ways to assign zeroes and ones to sites of Z^d such that no two ones are adjacent (for d=2, this example is also known as the hard square model.)

Any Z^d SFT has an associated topological entropy (or entropy), which is a real number measuring the exponential growth rate, as n goes to infinity, of the number of configurations in A^({1,...,n}^d) which satisfy the SFT adjacency rules. For d=1, the entropy of any SFT is easy to compute: it is always the log of the largest eigenvalue of an easily defined integer-valued matrix associated with the SFT; for the golden mean shift, the entropy is the log of the golden mean. For d>1, the computation is much more difficult. For instance, there is no known explicit closed form for the entropy of the Z^2 golden mean shift. And the standard ways to approximate the entropy of a Z^d SFT appear to converge very slowly.

For the Z^2 golden mean shift, we give a sequence of computable upper and lower bounds which converge exponentially fast to the entropy. Empirical data suggested that these particular numbers approach the entropy some time ago, but it has been an open problem to prove the convergence. Surprisingly, the methods we use to solve this combinatorially defined problem come mostly from measure theory and probability. We use concepts and techniques from the theory of interacting particle systems, including stochastic domination of measures and uniqueness of Gibbs states. Some results from percolation theory are also used to prove the exponential rate of convergence.

Time and Date: 3:00--4:00 p.m., Wednesday, February 25, 2009
Event: Topology Seminar
Speaker: Alexandra Pettet, University of Michigan
Subject:``Dynamics of Out(F): twisting out fully irreducible automorphisms''
Location: WMAX 110
Abstract: The outer automorphism group Out(F) of a free group F of finite rank shares many properties with the mapping class group of a surface, however the techniques for studying these groups are generally quite different. Analogues of the pseudo-Anosov elements of the mapping class group are the so-called fully irreducible automorphisms, which exhibit north-south dynamics on Culler-Vogtmann's Outer Space. We will explain a method for constructing these automorphisms and suggest why this construction should be useful. This is joint work with Matt Clay (University of Oklahoma).

Time and Date: 12:30--1:30 p.m., Thursday, February 26, 2009
Event: Graduate Student Seminar
Speaker: Adam Clay, UBC
Subject:``An introduction to orderable groups''
Location: MATH 225
Abstract: This talk will be an introduction to the theory of orderable groups, with emphasis on examples. The main goal will be to introduce "the space of all orderings of a group", a new object of study which has proven very useful in addressing several long-standing open problems. Time permitting, I will also explain those open problems that have been resolved using the space of all orderings of a group, as well as outline directions for future research.

Time and Date: 3:00--3:50 p.m., Thursday, February 26, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Yuk Kam Lau, University of Hong Kong
Subject:``Moments of the error term in the Dirichlet divisor problem''
Location: UBC Campus, Room WMAX 216 (PIMS)
Note: 3:50 -- 4:00 p.m. Tea Break
Abstract: In 1849, Dirichlet showed that sum_{n le x} d(n) = x(log x+2gamma-1)+Delta(x) with Delta(x) ll sqrt{x} where d(n) counts the number of divisors of n and gamma is the Euler constant. An interesting problem is to study the behaviour of Delta(x), for instance, its true order of magnitude and oscillations. We shall explore the various moments of this error term.

Time and Date: 4:00--4:50 p.m., Thursday, February 26, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Felipe Voloch, University of Texas
Subject:``Rational points on curves and cryptography''
Location: UBC Campus, Room WMAX 216 (PIMS)
Note: 4:50--5:10 p.m. another break
Abstract: I'll discuss some connections between algorithms for finding rational points on curves and some cryptosystems. Akiyama and Goto have proposed a cryptosystem based on rational points on curves over function fields (stated in the equivalent form of sections of fibrations on surfaces). It is easy to construct a curve passing through a few given points, but finding the points, given only the curve, is hard. In this talk I will show how to break their original cryptosystem by using algebraic points instead of rational points and discuss the possibility of changing their original system to create a secure one.

Time and Date: 5:10--6:00 p.m., Thursday, February 26, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Amanda Beeson, University of California-San Diego
Subject:``Groups of special units''
Location: UBC Campus, Room WMAX 216 (PIMS)
Abstract: We will introduce briefly the philosophy of the Stark conjectures about special values of L-functions, the work of Sinnott regarding unit groups, and Anderson's construction of the maximal almost abelian extension of the rational numbers. We will see that these three areas tie neatly together in the form of groups of special units, out of which we will produce new and surprising trigonometric and L-function identities.

Time and Date: 1:30 p.m., Friday, February 27, 2009
Event: PIMS/WMAX Postdoctoral Colloquium
Speaker: Hamid Usefi, UBC
Subject:``Isomorphism problem for group algebras and enveloping algebras''
Location: WMAX 216
Abstract: The celebrated work of Roggenkamp & Scott and Weiss implies that every finite nilpotent group is determined by its integral group ring. The (still open) modular isomorphism problem (MIP) asks whether a finite p-group G is determined by its modular group algebra FG. Although open for more than 50 years, no serious progress is made about MIP. In this talk, I will review these problems and their connections with the isomorphism problem for enveloping algebras of Lie algebras.

Time and Date: 2:00--3:00 p.m., Friday, February 27, 2009
Event: Special Complex Fluids Seminar
Speaker: Reghan J. Hill, Department of Chemical Engineering, McGill University
Subject:``Dynamics of lipopolymers in supported phospholipid bilayer membranes''
Location: CHBE 204 (2360 East Mall)
Abstract: Supported phospholipid bilayers have been widely adopted as model biological membranes and as novel platforms for biosensing and biomolecular separations. We have been studying the electromigration of polyethylene glycol chains tethered to charged phospholipids in otherwise uncharged supporting membranes. Our goal is to understand and quantify the influence of the polymer chains on electroosmotic flow. In particular, want to know if the lipopolymer charge and self-diffusion coefficient ¯as measured by fluorescence recovery after photobleaching (FRAP) experiments¯are sufficient to predict the electromigrative velocity and, thus, to ascertain the correct timescale for electric-field-induced organization of these intriguing two-dimensional fluids. This talk will outline the experimental diagnostics we have developed to measure the electrophoretic mobilty and self-diffusion coefficient of fluorescently labelled lipopolymers as a function of their surface grafting density. The complex interplay of electrical and hydrodynamic forces makes this seemingly simple system challenging to study both experimentally and theoretically. As a first step, we will present a theoretical interpretation of the experiments based on a continuum electrokinetic theory.

Time and Date: 3:00 p.m., Friday, February 27, 2009
Event: Mathematics Colloquium
Speaker: Felipe Voloch, University of Texas
Subject: ``Local-global principles for diophantine equations and arithmetic 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, March 2, 2009
Event: IAM-PIMS-MITACS Distinguished Colloquium Series
Speaker: Edgar Knobloch, Department of Physics, University of California at Berkeley
Subject:``Spatially Localized Structures''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: Spatially localized structures occur widely across the physical sciences. Classic examples include localized buckling of slender structures, localized oscillations in vertically vibrated granular media (oscillons) and localized convection in fluid dynamics (convectons). In this talk I will describe the basic mathematics – and the physics – behind the formation of these often unexpected structures, with a view to providing a unified picture of their origin and properties.

Time and Date: 12:30--2:00 p.m., Tuesday, March 3, 2009
Event: SCAIM Seminar
Speaker: Guido Kanschat, Texas A & M University
Subject:``Divergence-Conforming Finite Element Methods for coupled free and groundwater flow''
Location: WMAX 216 (PIMS)
Abstract: We present a family of mixed finite elements suitable for discretization of the Navier-Stokes and Darcy equations. It is inf-sup stable and consistent for both equations, such that arbitrarily high order approximations can be achieved by increasing the polynomial degree. Furthermore, the discrete velocities are pointwise divergence free in the free flow region. We will discuss interface conditions between the regions and present numerical results.

Time and Date: 3:00--4:00 p.m., Wednesday, March 4, 2009
Event: Topology Seminar
Speaker: Kee Y Lam, UBC
Subject:``A synthesis of results on the geometric dimension problem''
Location: WMAX 110
Abstract: Consider a vector bundle E of rank k over a finite CW complex X. Assume k>dimX for simplicity. If E is not trivial, then it will contain various trivial sub-bundles of maximal rank r. The geometric dimension of E is simply defined to be gd(E)=k-r. It provides a (crude) measure of E's deviation from triviality.

In this talk I'll present some new observations concerning gd(E) when X is a sphere or projective space. These will culminate in a new proof that for X=S^8m+1 or S^8m+2, gd(E) is always equal to 6. [Joint work with D. Randall].

Time and Date: 4:00--5:00 p.m., Thursday, March 5, 2009
Event: Teaching Resources Seminar (postponed from last week)
Speaker 1: (4:00--4:15) Richard Froese, UBC
Subject:``The CWSEI course materials archive''
Abstract: The CWSEI archive is now available to the Math Department to store course materials. Richard will give a short demonstration.
Speaker 2: Anthony Peirce, UBC
Subject:``Spreadsheet PDE demonstrations in Math 257''
Abstract: Anthony will show us his in-class demonstrations that use ordinary spreadsheets to solve the heat equation and compute Fourier series.
Location: MATH 204

Time and Date: 10:00--10:50 a.m., Friday, March 6, 2009
Event: Seminar on algebraic groups, Galois cohomology and related topics
Speaker: Masoud Kamgarpour, Department of Mathematics, UBC
Subject:``Group cohomology and extensions''
Location: WMAX 110
Abstract: It is well-known that the second group cohomology is related to central extensions. After reviewing this fact, I will discuss the interpretation of the third cohomology group in terms of "hyper-extensions".

Time and Date: 3:00 p.m., Friday, March 6, 2009
Event: Mathematics Colloquium
Speaker: Shmuel Friedland, University of Illinois, Chicago
Subject: ``Counting matchings in graphs with applications to the monomer-dimer models''
Location: MATX 1100
Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).

Time and Date: 3:00--4:00 p.m., Monday, March 9, 2009
Event: IAM Seminar Series
Speaker: Stefan Llewellyn Smith, Department of Mechanical and Aerospace Engineering, University of California at San Diego
Subject:``Vortex Rings with Swirl''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: Vortex rings have been a source of fascination in fluid mechanics since the time of Helmholtz. Asymptotic results for the velocity of axisymmetric vortex rings exist in the limit of narrow cores, including the effect of swirl (flow "around" the ring). Exact solutions, however, are more difficult to find, in particular for the unsteady case. Axisymmetric vortex rings with azimuthal vorticity proportional to distance from the axis of symmetry have a contour dynamical formulation as shown by Pozrikidis and Shariff, and steadily-propagating solutions had been found earlier by Norbury. We consider the effect of adding swirl. Taking the swirl inversely proportional to distance from the axis so that the swirl is irrotational leads again to a contour dynamics formulation, but it becomes necessary to add a vortex sheet at the boundary of the rings. The steady case requires an extra constraint. Steady and unsteady results are discussed.

Time and Date: 3:10--4:10 p.m., Monday, March 9, 2009
Event: Algebraic Geometry Seminar
Speaker: Yimu Yin, University of Pittsburgh
Subject:``Fourier transform in algebraically closed valued fields''
Location: WMAX 110 (PIMS)
Abstract: I will discuss the Hrushovski-Kazhdan integration theory, which is a major development in the theory of motivic integration. I will first present the fundamental constructions in this theory (homomorphisms between various Grothendieck rings). Then i will define the Fourier transform and discuss its basic properties. The theory of definable distributions will also be discussed. In the end, as an application, I will show that the Weil representation exists on the Schwartz space.

Time and Date: 3:30--4:30 p.m., Tuesday, March 10, 2009
Event: DG-MP-PDE Seminar
Speaker: Jingyi Chen, UBC
Subject:``Mean Curvature flow of entire Lagrangian graphs''
Location: WMAX 110
Abstract: In this joint work with Albert Chau and Weiyong He, we prove existence of longtime smooth solution to mean curvature flow of entire Lagrangian graphs without assuming curvature bounds on initial manifold. We also obtain a Bernstein type result for translating solitons.

Time and Date: 12:00--1:00 p.m., Wednesday, March 11, 2009
Event: Complex Fluids Seminar
Speaker: Sardar Malek, Department of Mechanical Engineering, UBC
Subject:``Experimental study of displacement flows in an annulus; The Effects of viscosity, buoyancy and eccentricity on the interface shape''
Location: CHBE 202 (2360 East Mall)
Abstract: In this project displacement flows in an eccentric annulus are studied experimentally. Displacement flows occur in the oil and gas industry when the drilling mud should be displaced by cement slurry. To remove mud effectively, it is vital to design the fluid rheology so that a steady displacement can be achieved in an annulus. Many industrial studies have been carried out in this area, however further fundamental experimental work is needed to understand the fluid mechanics behind this type of flow. In our research the effects of viscosity, density and eccentricity of inner pipe on the interface dynamics have been studied. An experimental matrix is devised in a manner to capture the boundary between steady and unsteady displacements for a specific series of fluids. The interface is analyzed by image processing and a method developed by the authors. This method describes the relative steadiness of displacement by defining a statistical parameter, deviation over mean. Using this parameter, for each set of fluids a contour plot is created to show the relative importance of buoyancy, eccentricity and viscosity in displacement flows. The contour plots confirm that higher viscosity ratios help displacement while little eccentricity makes the displacement unsteady. Secondary flows are observed in our displacement experiments. These secondary flows have not been studied carefully so far and more sophisticated models are needed to predict this type of flow.

Time and Date: 3:00-4:00 p.m., Wednesday, March 11, 2009
Event: Probability Seminar
Speaker: Robert Masson, Department of Mathematics, UBC
Subject:``Second moment estimates for the growth exponent of loop-erased random walk''
Location: WMAX 216
Abstract: The loop-erased random walk Y^n is the process obtained by running a random walk in Z^d from the origin to the first exit time of the ball of radius n and then chronologically erasing its loops. If we let X_n denote the number of steps of Y^n then the growth exponent a is defined to be such that E[X_n] grows like n^a. The value of a (or even its existence) depends on the dimension d. In this talk I'll focus on d=2 where it's been shown that a = 5/4. What we want to know is how close is X_n to its mean? By the Markov inequality one gets that P(X_n > bE[X_n]) < b^{-1}. The goal of this talk will be to show a similar lower bound: P(X_n < bE[X_n]) < b^{c} for some c>0.

Time and Date: 3:00 p.m., Wednesday, March 11, 2009
Event: Mathematics Colloquium
Speaker: Yongbin Ruan, University of Michigan
Subject: ``Integrable hierarchies and singularity theory''
Location: WMAX 110 (PIMS)
Note: Refreshments will be served at 2:45 p.m. (1st Flr Lounge at PIMS).

Time and Date: 3:00--3:50 p.m., Thursday, March 12, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Tsz Ho Chan, University of Memphis
Subject:``On the congruence equation xy=c (mod q)''
Location: SFU Campus, Room ASB 10900 (IRMACS)
Abstract: A famous congruence equation question is the solvability of x y = c (mod q) with x, y in intervals of length q^{1/2 + epsilon}. In this talk, we will discuss its history and recent developments. We will show that it is solvable for almost all pairs of intervals on x and y. Then, out of the blue, it leads to a new attack on the problem through 'higher moments'.

Time and Date: 4:10--5:00 p.m., Thursday, March 12, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Nils Bruin, SFU
Subject:``Visibility of Sha[3] in genus-2 jacobians''
Location: SFU Campus, Note: Room K9509 for second talk.
Abstract: In [Mazur, Visualizing elements of order three in the Shafarevich-Tate group, Asian J. Math. 3 (1999), no. 1, 221-232], Mazur proves that any element in Sha[3](E/K) can be made visible in an abelian surface. Mazur did not comment on whether this surface can be taken to be a Jacobian of a genus 2 curve, however. His construction does not prove that it can, but with an easy observation, one can actually see that it is possible. In this talk, I will explain what Mazur proved and what the easy observation is. This is joint work with Sander Dahmen (SFU/UBC). Note that we will move to room K9509 for this second talk.

Time and Date: 10:00--10:50 a.m., Friday, March 13, 2009
Event: Seminar on algebraic groups, Galois cohomology and related topics
Speaker: Nicolas Guay, University of Alberta
Subject:``Double affine quantum algebras''
Location: MATX 1118
Abstract: Quantum toroidal algebras appeared about fifteen years ago, but still remain very mysterious mathematical objects. I will present new families of quantum algebras of double affine type which should be simpler to understand and which, one hopes, will eventually help shed some light on quantum toroidal algebras. These new algebras are related to Cherednik algebras and to the symplectic reflection algebras of P. Etingof and V. Ginzburg, which are analogs of Hecke algebras of double affine type.

I will briefly sketch one connection between some of those double affine quantum algebras on one hand, algebraic groups and cohomology on the other hand. This is the content of a recent paper of B. Feigin, M. Finkelberg et al. in which they showed how to construct an action of the affine Yangian in the equivariant cohomology of certain Laumon spaces.

Time and Date: 3:00 p.m., Friday, March 13, 2009
Event: Mathematics Colloquium
Speaker: Sadok Kallel, University of Lille, and PIMS
Subject: ``String Topology and Applications''
Location: MATX 1100
Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).

Time and Date: 3:00--4:00 p.m., Monday, March 16, 2009
Event: IAM Seminar Series
Speaker: Richard Craster, Department of Mathematics, Imperial College London, UK (currently at University of Alberta)
Subject:``Trapped Modes in Elastic/Acoustic Waveguides and their Relation to Slow-Sound/Light Modes in Pe riodic Structures''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: Trapped modes in elastic waveguides correspond to non-trivial eigenfunctions of the system and can be identified using asymptotic techniques. I shall review these and the associated long wave theory. Recently, the identification of slow modes or slow sound/light has also become of practical interest in periodic structures. A combination of numerical and asy mptotic methods are used to find these modes. Under some circumstances these modes can also be identified using long wave theory. If time permits, other wave systems allowing for localisation will be considered, such as surface Rayleigh waves guided along a ha lf space whose surface is perturbed.

Time and Date: 12:30--2:00 p.m., Tuesday, March 17, 2009
Event: SCAIM Seminar
Speaker: Francisco-Javier Sayas, University of Minnesota and Universidad de Zaragoza, Spain
Subject:``Boundary integral scattering''
Location: WMAX 216 (PIMS)
Abstract: I will give a transverse introduction to how Boundary Integral techniques (or their numerical versi on, the Boundary Element Method) have been and are being used for scattering problems. While in the beginning the field of boundar y integral equations dealt mainly with simple exterior problems, the study of the scattering of waves by penetrable obstacles offe rs a set of more realistic problems where BEM techniques have often to be coupled with better known methods for PDEs, such as the Finite Element Method. We will see how a method-oriented approach can be valid for wave problems in the frequency and time domains , and how the Laplace transform plays a surprising role for numerical discretization in the time domain.

Time and Date: 12:00--1:00 p.m., Wednesday, March 18, 2009
Event: Complex Fluids Seminar
Speaker: Karen C. Cheung, Electrical and Computer Engineering, UBC
Subject:``Hydrogel-based microfluidic system for cell culture''
Location: CHBE 202 (2360 East Mall)
Abstract: Bio-micro-electro-mechanical systems (BioMEMS) comprise a wide range of applications, including lab -on-a-chip devices and microfabricated implants. One project in our group investigates a hydrogel-based microfluidic device to cul ture and characterize breast cancer cells for screening of anti-cancer agents. By integrating traditional lab processes such as in cubation and assaying in a closed lab-on-a-chip device, a much smaller number of cells, as obtained in needle biopsies, can be exa mined. Such a system can be used to track and characterize individual cells, and reduce the costs and time for diagnostic and drug screening assays.

The BioMEMS group is part of the larger Microsystems and Nanotechnology (MiNa, www.mina.ubc.ca) Research Group at UBC, which inclu des 17 faculty members in departments spanning Electrical, Mechanical, Chemical, and Materials Engineering as well as Physics.

Time and Date: 3:00-4:00 p.m., Wednesday, March 18, 2009
Event: Probability Seminar
Speaker: Michael Kozdron, University of Regina
Subject:``Using multiple SLE to explain a certain observable in the 2d Ising model''
Location: WMAX 216
Abstract: The Schramm-Loewner evolution (SLE) is a one-parameter family of random growth processes that has b een successfully used to analyze a number of models from two-dimensional statistical mechanics. Currently there is interest in try ing to formalize our understanding of conformal field theory using SLE. Smirnov recently showed that the scaling limit of interfac es of the 2d critical Ising model can be described by SLE(3). The primary goal of this talk is to explain how a certain non-local observable of the 2d critical Ising model studied by Arguin and Saint-Aubin can be rigorously described using multiple SLE(3) and Smirnov's result. As an extension of this result, we explain how to compute the probability that a Brownian excursion and an SLE(k) curve, 0
Time and Date: 2:00 p.m., Thursday, March 19, 2009
Event: MITACS/PIMS Mathematical Biology Seminar
Speaker: Eldon Emberly, SFU
Subject:``Optimization of Mutual Information in Genetic Networks''
Location: WMAX 216
Abstract: Cellular decisions rely upon a cell making some measurement of its surroundings and then regulatin g its behaviour based on this measurement. For many cellular processes this decision is regulated by the transcriptional output of a gene which is regulated by a single input which may exist in several possible states. Given the noise inherent in the input sig nal and the chemical processes coupling the input to the output, how well can the input states be measured by the genetic network and is the genetic network optimized to maximize the likelihood of determining the correct input state? Recently, this problem has been analyzed in the context of mutual information. I will discuss the application of mutual information to the problem of morpho gen readout in developing organisms, and will compare the predicted optimal morphogen gradient for the early drosophila factor Bcd to its experimental profile. Lastly, I will show how optimizing mutual information for an organism that needs to infer a two stat e environment which varies, leads to an optimal transcriptional response with biologically realistic kinetic parameters.

Time and Date: 3:00--4:00 p.m., Thursday, March 19, 2009
Event: Topology Seminar (Note special day of the week.)
Speaker: Liam Watson, University of Quebec at Montreal
Subject:``On two-fold branched covers, L-spaces, and Khovanov homology''
Location: WMAX 110
Abstract: Khovanov homology gives rise to a simple invariant of knots and links taking values in the positive integers. Referred to as the width of a link, this invariant is a measurement of the homology's support. In general this quantity is not very well understood, though in relation to two-fold branched covers of the 3-sphere, situations arise wherein the width i s quite well behaved. This talk will give some applications of width resulting from this fact, and hint at some interaction with L -spaces, a class of interesting manifolds that arise in Heegaard-Floer homology.

Time and Date: 10:00--10:50 a.m., Friday, March 20, 2009
Event: Seminar on algebraic groups, Galois cohomology and related topics
Speaker: Jean Fasel, UBC
Subject:``Unimodular rows over smooth algebras''
Location: MATX 1118
Abstract: Let R be a smooth k-algebra of dimension d. A well known theorem by H. Bass and S. Schanuel states that stably free projective R-modules of rank strictly bigger than d are free. In general, there are some stably free non free pr ojective modules of rank d and it is a classical (and hard) problem to understand when such a module is free or not. In this talk, I will present the recent developments in the subject and give a complete answer to the problem in the case of real smooth ration al algebras.

Time and Date: 3:00 p.m., Friday, March 20, 2009
Event: Mathematics Colloquium
Speaker: Ethan Coven, Wesleyan University, Middletown, Connecticut
Subject: ``The Morse-Thue sequence, its friends, and its friends in disguise''
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 23, 2009
Event: IAM Seminar Series
Speaker: George Bluman, UBC
Subject:``Construction of Conservation Laws: How the Direct Method Generalizes Noether's Theorem''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: It is shown how to construct directly the local conservation laws for essentially any given system of differential equations (DEs). This comprehensive treatment is based on first finding conservation law multipliers. It is shown how this treatment is related to and subsumes the classical Noether’s theorem (which only holds for variational systems). In particular, multipliers are symmetries of a given DE system only when the system is variational as written. Many illustrative examples will be presented. This material is available in a preprint and will be included in the book “Advanced Symmetry Methods for Partial Differential Equations” by G. Bluman, A. Cheviakov and S. Anco – to appear in the Applied Mathematical Sciences series, Springer, New York, 2009.

Time and Date: 12:30--2:00 p.m., Tuesday, March 24, 2009
Event: SCAIM Seminar
Speaker: Roger Donaldson, Caltech, and Midvale Applied Mathematics Inc., Vancouver, BC
Subject:``Discrete Geometric Homogenization''
Location: WMAX 216 (PIMS)
Abstract: We consider homogenization of the operator u \mapsto -\text{div} (\sigma \nabla u), which is parameterized by symmetric \sigma \in \real^{2\times 2} for the special case where the domain \Omega \subset \real2. We refer to \sigma as the conductivity owing to is physical interpretation, and, in addition to conditions maintaining ellpticity, require only that \sigma \in L^{\infty}---that is, \sigma may vary on a continuum of scales. This is in contrast to classical homogenization, which typically requires that rapid variations in \sigma occur at length scales far below the dimensions of \Omega .

Following work of Owhadi and Zhang (2007, 2008), we represent \sigma in particular coordinates F : \Omega \rightarrow \Omega such that its push-forward Q = F_{\ast} \sigma is a divergence-free tensor. In \real2, the consequence of the divergence-free constraint is that we can represent Q using a scalar function s(x). We show that sampling s(x) at a coarse scale is equivalent to homogenizing \sigma at that scale. For example, the effective anisotropy of a laminated material predicted by classical homogenization theory is manifested when s(x) is sampled at a scale coarser than the pitch of laminations.

We discuss two applications of this new parameterization of conductivity: 1) We present the efficient computation of triangulations well-adapted to the effective anisotropy of \sigma, in turn developing a new geometric understanding of weighted Delaunay triangulations; and 2) We show how our parameterization can play a role in Electric Impedence Tomography, an inverse method which {\em determines} \sigma from boundary Dirichlet and Neumann data.

Time and Date: 4:00--5:00 p.m., Tuesday, March 24, 2009
Event: Discrete Maths Seminar
Speaker: Paul Ottaway, UBC
Subject:``How to Win and Lose Combinatorial Games''
Location: WMAX 216
Abstract: I will give an introduction to the mathematics of combinatorial games. We shall examine the similarities and differences between Normal Play rules where the last player wins and Mis\`ere Play rules where the last player loses. The complete analysis for both play conventions will be given for a simple coin-flipping game.

Time and Date: 12:00--1:00 p.m., Wednesday, March 25, 2009
Event: Complex Fluids Seminar
Speaker: Frank K. Ko, Advanced Fibrous Materials Laboratory AMPEL, Department of Materials Engineering, UBC
Subject:``Nanofiber Technology''
Location: CHBE 202 (2360 East Mall)
Abstract: Materials in fiber form are of great practical and fundamental importance. The combination of high specific surface area, flexibility and superior directional strength makes fiber a preferred material form for many applications ranging from clothing to surgical implants and reinforcements for aerospace structures. The availability of fibers in the nanoscale greatly expands the performance limit and application opportunities fibrous materials. We are witnessing the birth of a new nanofiber-based industry. Specifically, the significant role of fiber size has been recognized in the remarkable increase in surface area (1000 m2/g)]; in bio-reactivity (7X proliferation rate) ; electroactivity (>10X response rate); and in mechanical properties (exponential increase in strength as fiber diameter decreases). Motivated by the potential opportunities provided by nanofibers, there is an increasing interest in nanofiber technology. Amongst the processing technologies for nanofiber fabrication, including the template method, vapor grown, phase separation and electrospinning which has attracted the most intense interest. In this presentation the processing and structure of nanofibers produced by the electrospinning process will be reviewed. The technical challenges and opportunities will be discussed in terms of specific examples of recent developments in bioactive, electroactive and carbon nanotube reinforced composite nanofibres.

Time and Date: 3:00-4:00 p.m., Wednesday, March 25, 2009
Event: Probability Seminar Postponed until April 15/09.
Speaker: Shankar Bhamidi, UBC
Subject:``Branching processes and real world networks''
Location: WMAX 216
Abstract: The aim of this talk is to highlight the usefulness of continuous time branching process theory in understanding refined asymptotics about various random network models. We shall exhibit their usefulness in two different contexts:

(1) First passage percolation: Consider a connected network and suppose each edge in the network has a random positive edge weight. Understanding the structure and weight of the shortest path between nodes in the network is one of the most fundamental problems studied in modern probability theory. In the modern context these problems take an additional significance with the minimal weight measuring the cost of sending information while the number of edges on the optimal path (hopcount) representing the actual time for messages to get between vertices in the network. In the context of the configuration model of random networks we shall show how branching processes allow us to find the limiting distribution of the minimal weight path as well as establishing a general central limit theorem for the hopcount with matching means and variances.

(2) Spectral distribution of random trees: Many models of random trees (including general models embedded in continuous time branching processes) satisfy a general form of convergence locally to limiting infinite objects. In this context we find via soft arguments, the convergence of the spectral distribution of the adjacency matrix to a limiting (model dependent) non random distribution. For any \gamma we also find a sufficient condition for there to be a positive mass at \gamma in the limit.

Joint work with Remco van der Hoftsad, Gerard Hooghiemstra, Steve Evans and Arnab Sen.

Time and Date: 12:30--12:45 p.m., Thursday, March 26, 2009
Event: Mathematics Graduate Student Seminar
Speaker: Maria Khomenko, Department of Mathematics, UBC
Subject:``Fluid Instability Propagation with Stiff Boundary Conditions in Case of Low Reynolds Number. (a.k.a. What can golden syrup and latex do for you?)''
Location: MATH 225
Abstract: This is the classic problem of a viscous fluid forming instabilities as it flows down an inclined plane. In this case the flow takes place under a sheet of latex. There are a number of physical parameters that can be measured experimentally. And then to some extent compared with theory. Note to Cameron: Ethical issues aside, just because you sold your body to science, that does not give you the right to perform perverse social experiments on your peers. (please refer to potential Dr. Christou's last week's abstract for details). The experimental results will be accompanied by mathematical formulation of the problem.

Time and Date: 1:30 p.m., Thursday, March 26, 2009
Event: PIMS/WMAX Postdoctoral Colloquium
Speaker: Mark MacDonald, Department of Mathematics, UBC
Subject:``Chow Motives of Quadrics''
Location: WMAX 110
Abstract: A Chow motive of an algebraic variety may be thought of as an attempt to define a universal cohomology theory for algebraic varieties, through the use of the Chow ring. The Chow ring in algebraic geometry is an analog of the cohomology ring of a topological space.

In this talk I will define and describe Chow motives of algebraic varieties, with a focus on quadrics - which are the zero sets of degree 2 homogeneous polynomials. The reason for the focus on quadrics is because their Chow motives may be nicely decomposed and this decomposition can be easily visualized with a helpful diagram. Also, I may have time to mention some new results, where I have explicitly decomposed the Chow motives of a particular class of quadrics.

Time and Date: 10:00--10:50 a.m., Friday, March 27, 2009
Event: Seminar on algebraic groups, Galois cohomology and related topics
Speaker: Alexander Duncan, Department of Mathematics, UBC
Subject:``Finite groups of essential dimension 2 over C''
Location: MATX 1118
Abstract: I will outline the classification of finite groups of essential dimension 2. We shall see that a finite group G has essential dimension 2 if and only if it has a versal action on one of the following four surfaces: \mathbb{P}2, \mathbb{P}1 \times \mathbb{P}1, or a Del Pezzo surface of degree 5 or 6.

In the first part of the talk, I will discuss some geometric techniques for studying the essential dimension of finite groups: compressions, versal varieties and the going-down theorem. In the second part, I will describe Manin and Iskovskikh's classification of minimal rational G-surfaces and its relation to essential dimension.

Time and Date: 3:00 p.m., Friday, March 27, 2009
Event: Mathematics Colloquium
Speaker: John Heywood, UBC
Subject: ``On a conjectured estimate for solutions of the three-dimensional Stokes equations, with a constant that is optimal and independent of the domain''
Location: MATX 1100
Note: Refreshments will be served at 2:45 p.m. (MATX 1115, Math Lounge).

Time and Date: 3:00--4:30 p.m., Friday, March 27, 2009
Event: MITACS/PIMS Mathematical Biology Seminar, Diabetes Double Bill
Speaker: Vipul Periwal, NIH/NIDDK (1st speaker)
Subject:``Dynamics of Adipose Tissue Growth''
Location: WMAX 216
Abstract: Adipose tissue grows by two mechanisms: hyperplasia (cell number increase) and hypertrophy (cell size increase). Genetics and diet affect the relative contributions of these two mechanisms to the growth of adipose tissue in obesity. To address adipose tissue growth precisely, we developed a mathematical model describing the evolution of the adipose cell-size distributions as a function of the increasing fat pad mass, instead of the increasing chronological time. Our model describes the recruitment of new adipose cells and their subsequent development in different strains, and with different diet regimens, with common mechanisms, but with diet- and genetics-dependent model parameters. Hyperplasia is enhanced by high-fat diet in a strain-dependent way, suggesting a synergistic interaction between genetics and diet. Moreover, high-fat feeding increases the rate of adipose cell size growth, independent of strain, reßecting the increase in calories requiring storage. Additionally, high-fat diet leads to a dramatic spreading of the size distribution of adipose cells in both strains; this implies an increase in size ßuctuations of adipose cells through lipid turnover.

Time and Date: 3:00--4:30 p.m., Friday, March 27, 2009
Event: MITACS/PIMS Mathematical Biology Seminar, Diabetes Double Bill
Speaker: Will Heuett, NIH/NIDDK (2nd speaker)
Subject:``Modeling Metabolism in Pancreatic Beta-Cell Mitochondria''
Location: WMAX 216
Abstract: Pancreatic beta-cells sense the ambient blood-glucose concentration and secrete insulin to signal other tissues to take up glucose. Mitochondria play a key role in this response as they metabolize nutrients to produce ATP and reactive oxygen species (ROS), both of which are involved in insulin secretion signaling. I will present a model of beta-cell mitochondrial respiration, ATP synthesis, and ROS production in response to glucose and fatty acid stimulation, based on available data in the literature and mathematical models derived from first principles. The model explains experimental observations of the non-ohmic rise in the passive proton-leak rate at high membrane potential and its dependence on increased ROS production. It also predicts that glucose-stimulated insulin secretion is inhibited by long-term fatty acid exposure, but can be enhanced by inhibiting uncoupling protein activation and promoting mitochondrial biogenesis. Using glucose and fatty acid profiles from individuals, I will show that there is a negative correlation between the amount of ROS produced per ATP, as predicted by the model, and the individual insulin sensitivities. Finally, I will discuss how the model can be used to predict the c-peptide and insulin secretion rate and provide a quantitative description of beta-cell function for a single individual.

Time and Date: 3:00--4:00 p.m., Monday, March 30, 2009
Event: IAM-PIMS-MITACS Distinguished Colloquium Series
Speaker: Bernardo Cockburn, University of Minnesota
Subject:``The Hybridizable Discontinuous Galerkin Methods''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: The success of the application of discontinuous Galerkin methods to nonlinear hyperbolic problems in the 1990s fueled the recent exploration of new and old DG methods for elliptic problems. Although the DG methods are clearly ideal for adaptive strategies, the method has been criticized, especially within the structural mechanics community, for having significantly more degrees of freedom than the continuous Galerkin method (for the same mesh) and for producing less accurate solutions than certain mixed methods. The hybridizable discontinuous Galerkin methods appeared as a response to this criticism. In this talk, we introduce these methods in the framework of second-order elliptic problems, show why they can be efficiently implemened and prove that they are actually more accurate than all previously known discontinuous Galerkin methods. Numerical comparisons with the continuous and with some mixed methods will be presented.

Time and Date: 3:10--4:10 p.m., Monday, March 30, 2009
Event: Algebraic Geometry Seminar
Speaker: Qendrim Gashi, Max Planck Institute, Bonn, Germany
Subject:``A vanishing result for toric varieties associated with root systems''
Location: WMAX 110 (PIMS)
Abstract: We prove a conjecture of Kottwitz and Rapoport formulated in terms of root systems and use it to imply the vanishing of higher cohomology groups for certain line bundles on toric varieties associated with root systems. During the proof, we will also discuss the so-called numbers game with a cutoff. These results are also relevant to a converse to Mazur's inequality, which will be discussed on Friday at the Algebraic Groups, Galois Cohomology and Related Topics Seminar. (The part of the talk about the numbers game is joint work with T. Schedler.)

Time and Date: 3:30--4:30 p.m., Tuesday, March 31, 2009
Event: DG-MP-PDE Seminar
Speaker: Marco Castrillon Lopez, Universidad Complutense de Madrid
Subject:``Hamilton equations for Gauge-invariant problems''
Location: WMAX 110
Abstract: Hamiltonian and Lagrangian formalisms in Field Theories are equivalent when the Lagrangian is regular. Nevertheless, there are many interesting instances where the regularity is not guaranteed. This is the case of those variational problems on connections invariant under tha action of the gauge group. The Yang-Mills Lagrangian is the best known example of this situation. The goal of the talk is to show in this situation the fiber nature of the set of solutions of the Hamilton equation over the set of solutions of the Euler-Lagrange equations. Moreover, this structure is studied for the Jacobi fields and the moduli spaces under the gauge groups. Some physical considerations will be also analyzed.

Time and Date: 3:00-4:00 p.m., Wednesday, April 1, 2009
Event: Probability Seminar
Speaker: Eugene Kritchevski, Department of Mathematics, UBC
Subject:``Localization of the eigenfunctions of the one-dimensional Schrodinger operator in the presence of random potentials''
Location: WMAX 216
Abstract: We consider the one-dimensional discrete Schrödinger operator (Hf)(x)=f(x-1)+f(x+1)+v(x)f(x), on the interval {1,2,...,N} with Dirichlet boundary conditions f(0)=f(N+1)=0. We assume that v(x) are independent random variables for a very small fraction of the sites x and nonrandom for the remaining sites. We discuss a mechanism responsible for the following localization phenomenon: for large N, outside a set of realizations of the potentials of very small probability, each eigenfunction of H decays exponentially. Our approach to localization is based on a recent method of Goldstein.

Time and Date: 3:00--3:50 p.m., Thursday, April 2, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Shanta Laishram, University of Waterloo
Subject:``Irreducibility of generalised Hermite-Laguerre polynomials''
Location: UBC Campus, Room WMAX 110
Abstract: Let a, a_0, a_1, ..., a_m be integers with a nonnegative, and define f_a(x) = sum_{j=0}^m a_j x^j / (j+a)!. Schur (in 1929) proved that f_0(x) with |a_0| = |a_n| = 1 is irreducible for all m. Schur's result has been generalized by many authors by using p-adic methods of Coleman and Filaseta. In this talk, I will give a survey of the some of these results and prove some results on the irreducibility of generalised Hermite-Laguerre polynomials by combining p-adic methods with the greatest prime factor of the product of terms of an arithmetic progression.

Time and Date: 4:10--5:00 p.m., Thursday, April 2, 2009
Event: PIMS/SFU/UBC Number Theory Seminar
Speaker: Alia Hamieh, UBC
Subject:``On computing a basis for the space of half integer weight modular forms''
Location: UBC Campus, Room WMAX 110
Abstract: I will give an expository talk about half integer weight modular forms. Definitions and basic properties of this space will be given. Then, the Shimura correspondence will be discussed. Roughly speaking, this associates to a modular form of half integer weight some modular form of integer weight. This will be followed by a discussion of several improvements on this result, the most important of which is due to Waldspurger. In his work Waldspurger used representation theory to establish an explicit relation between the square of the coefficients in the q-expansion of a form f of half integer weight k/2 and the central values of 'twist' L-series for a form g of integer weight k-1 corresponding to f via the Shimura map.

Time and Date: 10:00--10:50 a.m., Friday, April 3, 2009
Event: Seminar on algebraic groups, Galois cohomology and related topics
Speaker: Qendrim Gashi, Max Planck Institute, Bonn, Germany
Subject:``A converse to Mazur's Inequality''
Location: MATX 1118
Abstract: Given an isocrystal N and a lattice M in it, Mazur proved that the Hodge vector of M lies on or above the Newton vector of N. This can be viewed as a statement for the group GL_n and it is known that it can be generalized to other reductive groups. The converse to Mazur's inequality is the assertion that given a vector v that lies above the Newton vector of N (and satisfies certain obvious properties), there exists a lattice M whose Hodge vector is equal to v. We prove the generalized converse to Mazur's inequality for (connected, reductive) split and quasi-split groups; this was previously known for split classical groups. These results can also be interpreted to give a necessary and sufficient condition for the non-emptiness of certain affine Deligne-Lusztig varieties.

Time and Date: 3:30 p.m., Friday, April 3, 2009
Event: CRM-Fields-PIMS Prize Lecture
Speaker: Martin Barlow, UBC
Subject: ``The Ant in the Labyrinth: Random Walks and Percolation''
Location: WMAX 110 (PIMS)
Note: Cookies and tea will be served.

Time and Date: 3:00--4:00 p.m., Monday, April 6, 2009
Event: IAM Seminar Series
Speaker: John Stockie, SFU
Subject:``Porous Immersed Boundaries''
Location: Room 301, Leonard S. Klinck Bldg.
Abstract: Porous, deformable membranes are encountered in a wide range of applications, including red blood cells, vesicles, porous wave makers, and parachutes. The "immersed boundary method" has already proven to be a versatile and robust approach for simulating the interaction of impermeable, elastic structures with an incompressible fluid flow. We demonstrate how to extend the method to handle porous boundaries by incorporating an explicit porous slip velocity that is determined by Darcy's law. We derive a simple, radially-symmetric exact solution, which is then used to validate numerical simulations of porous membranes in two dimensions.

Time and Date: 3:10--4:10 p.m., Monday, April 6, 2009
Event: Algebraic Geometry Seminar
Speaker: Sebastian Casalaina-Martin, University of Colarado
Subject:``The moduli space of cubic threefolds via degenerations of the intermediate Jacobian''
Location: WMAX 110
Abstract: A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this talk I will discuss the possible degenerations of these abelian varieties, and thus give a description of the compactification of the moduli space of cubic threefolds obtained in this way. The relation between this compactification and those constructed in the work of Allcock-Carlson-Toledo and Looijenga-Swierstra will also be considered, and is similar in spirit to the relation between the various compactifications of the moduli spaces of low genus curves. This is joint work with Radu Laza.

Time and Date: 12:30--2:00 p.m., Tuesday, April 7, 2009
Event: SCAIM Seminar
Speaker: Richard Bartels, Computer Science, University of Waterloo
Subject:``Constructing Multi-resolutions from Regular Geometric Subdivisions''
Location: WMAX 216
Abstract: We consider regular geometric subdivisions. These combine the refinement of a regular lattice with a regular pattern of affine transformations applied to geometric data associated with the nodes of the lattice. Such subdivisions are used in computer aided geometric design for surface modeling and in the film industry for scene and character design and animation. A multi-resolution combines subdivision-based approximation with efficient representation of the approximation error, and in this form has application to image compression. This talk will outline an approach to the constriction of a multi-resolution from a given subdivision. The construction is purely geometric and linear-algebraic in form and makes repeated use of the singular values decomposition. In brief, given the matrix of affine transformations, P, that maps the points c of a lattice to the points f of a refined lattice, the construction provides a reverse mapping Af = c that consists of an oblique projection founded on a geometric argument. If the points f are not the exact products of a subdivision; e.g. are measured data, Pc will not equal f, and the construction provides mappings B and Q such that d=Bf and Qd represents the error in Pc. Any matrix representing such a P will be regular and banded, and it is a requirement that the construction provide matrices representing A, B, and Q that are of similar character. In particular this requirement proceeds from the fact that, in a multi-resolution, the data c and d must occupy no more storage than the data f, which puts significant restrictions on the construction. Nevertheless, these restrictions provide the impetus for organizing the construction entirely in terms of the interaction between the short intervals of the nonzeros in the rows of one matrix with the columns of another matrix. The construction never has to deal with any matrix in its entirety.

Time and Date: 4:00--5:00 p.m., Tuesday, April 7, 2009
Event: Discrete Maths Seminar
Speaker: Eric Fusy, UBC/LIX Laboratoire d'Informatique de l'Ecole Polytechnique, Paris
Subject:``Schnyder woods generalized to higher genus surfaces''
Location: WMAX 216
Abstract: Schnyder showed in 1989 that every plane triangulation has a partition of its (inner) edges into 3 trees spanning all (inner) vertices. The so-called Schnyder woods are a powerful combinatorial structure with many applications: new planarity criterion, straight-line drawing, coding, bijective counting... In this talk, we show that the definition of Schnyder woods admits a generalization to surfaces of any genus, and that such a Schnyder wood can be computed efficiently. As an application we extend a simple coding procedure to higher genus.

This is joint work with Luca Castelli Aleardi and Thomas Lewiner.

Time and Date: 12:00--1:00 p.m., Wednesday, April 8, 2009
Event: Complex Fluids Seminar
Speaker: Rodrigo Velez, Department of Chemical and Biological Engineering, UBC
Subject:``Study of the properties of non Newtonian bubbly flows''
Location: CHBE 202 (2360 East Mall)
Abstract: It has been postulated that the rise velocity of a swarm of bubbles in shear-thinning fluids is mainly influenced by the reduction in local viscosity and the population of bubbles, i.e., gas hold up. On the other hand, while many authors have studied the elastic force effects in the abrupt change of velocity and shape in single bubbles, little has been done in bubble columns. By using a high speed camera and digital image analysis we measured the rise velocity of bubbles in inelastic and elastic shear-thinning fluids in a bubble column. Great care was taken to produce nearly mono-dispersed bubble swarms. Results show that the convex-to-concave shape can also be observed in bubble swarms immersed in a Boger type fluid. This change of shape, which is associated with the so-called single bubble velocity discontinuity and the negative wake appearance, has a significant influence in the general behavior of the bubbly flow, especially in cluster formation. Bubbles immersed in shear-thinning fluids also form aggregations. It seems that a critical Morton number (0.001) separates cluster and non-cluster formation regimes.

Time and Date: 3:00-4:00 p.m., Wednesday, April 8, 2009
Event: Probability Seminar
Speaker: Ori Gurel-Gurevich, Microsoft Research
Subject:``Choice-memory tradeoff in allocations''
Location: WMAX 216
Abstract: Consider the classical balls-and-bins setup: n balls are thrown independently and uniformly into n bins. The most loaded bin then has log n/log log n balls with high probability. What happens when instead of throwing balls completely by random, there is an allocation algorithm which is given k uniformly and independently selected bins to choose from for the location of each ball? A well known result of Azar, Broder, Karlin & Upfal states that one can then achieve a maximal load of log_k log n, simply by putting each ball in the less loaded of the k optional bins. In order to implement this simple algorithm, one needs to keep track of the status of the entire array of n bins, which requires about n bits of memory.

The problem of what can be achieved with less memory was raised by Itai Benjamini. The main result in this talk is that, generally speaking, there is a tradeoff between the number of choices, k, and the memory, m. That is, when km>>n one can achieve a constant maximal load, while for km< A key ingredient in the proofs of the lower bounds is a large deviation inequality, which relates the sum of a sequence of bounded dependent random variables with the sum of their conditional expectations. This inequality may prove useful in other combinatorial or algorithmic problems.

Joint work with Noga Alon and Eyal Lubetzky.