Scientific Lectures

  • 19-Oct-06

Fluid Mathematical Models of Traffic Flow

I will start with a few basic facts on other types of description (microscopic, kinetic ...) Then I will talk about fluid models, of 'first order': Lighthill-Whitham-Richards (LWR) , i.e. a scalar conservation law, robust and (too ?) simple. The f   more››

University of British Columbia

  • 19-Oct-06

Impact of Travel Between Patches for Spatial Spread of Disease

A patch model is proposed to study the impact of travel on the spatial spread of disease between patches. The basic reproduction number for the i-th patch in isolation, is obtained along with the basic reproduction number of the system, $mathcal{R   more››

University of British Columbia

  • 18-Oct-06

Arithmetic Fuchsian groups of genus two

A hyperbolic 2- or 3-orbifold M is called arithmetic if M = H^2/G or H^3/G where G is an arithmetic Fuchsian or Kleinian group, respectively. Considerable work has been done in the last two decades classifying these groups. I will explain how arit   more››

University of British Columbia

  • 16-Oct-06

Frozen boundaries and log-fronts

In this talk, based on a joint work with Richard Kenyon and Grisha Mikhalkin, Andrei Okounkov will discuss some simple binary operation on plane curves which 1) generalizes classical duality for plane curves, 2) arises naturally in probabilistic c   more››

University of British Columbia

  • 16-Oct-06

Integral cohomology of singular toric varieties

The singular cohomology and Chow cohomology, with Q-coefficients, of projective toric varieties with at worst orbifold singularities are well-understood, but interesting problems remain for toric varieties with more serious singularities and for c   more››

University of British Columbia

  • 13-Oct-06

Applied Math Show and Tell

The first annual applied math show and tell will be an opportunity graduate students and other faculty to learn about what faculty in the applied math group are doing. Each speaker will have under five minutes to give a one paragraph intro to their r   more››

Simon Fraser University

  • 12-Oct-06

Implicit Immersed Boundary Methods with Boundary Mass

The immersed boundary method is a general framework used to handle fluid-structure interactions. One computational bottleneck of the immersed boundary methods is that the elastic structures are often very stiff, necessitating the use of a very fin   more››

University of British Columbia

  • 11-Oct-06

Effect of noise on front propagation in KPP equations

We study random traveling waves in KPP equations with appropriate additive noise. We prove a very explicit conjecture of Brunet and Derrida concerning the dramatic slowdown of these fronts by the noise. This is joint work with Carl Mueller and Leo   more››

University of British Columbia

  • 11-Oct-06

Aspects of Khovanov homology

Khovanov's construction of a homology theory for knots allows us to view the Jones polynomial as an Euler characteristic, provides a stronger knot invariant, and is the main tool for Rasmussen's combinatorial proof of the Milnor conjecture. In thi   more››

University of British Columbia

  • 11-Oct-06

The 290-Theorem and Representing Numbers by Quadratic Forms

This talk will describe several finiteness theorems for quadratic forms, and progress on the question: "Which positive definite integer-valued quadratic forms represent all positive integers?". The answer to this question depends on sett   more››

University of British Columbia

  • 10-Oct-06

Three challenges of Claude Shannon

In 1948/1949 Claude Shannon wrote two papers~[Sha48,Sha49] which became the foundation of modern information theory. The papers showed that information can be compressed up to the `entropy', that data can be transmitted error free at a rate below   more››

University of British Columbia

  • 10-Oct-06

Common Agency with Informed Principals: an Economics Lecture

The provision of public goods under asymmetric information has generally been viewed as a mechanism design problem under the aegis of an uninformed mediator. This paper focuses on institutional contexts where no such mediator is available. Contrib   more››

University of British Columbia

  • 10-Oct-06

Regularity criteria for Navier-Stokes equations

In the talk I will first review various known regularity criteria and partial regularity theory for 3D incompressible Navier-Stokes equations. I will then talk about a joint work with Gustafson and Kang on regularity criteria based on scaled space   more››

University of British Columbia

  • 6-Oct-06

Formal proofs in geometry

Traditional mathematical proofs are written in a way to make them easily understood by mathematicians. Routine logical steps are omitted. An enormous amount of context is assumed on the part of the reader. Proofs, especially in topology and geomet   more››

University of Calgary

  • 6-Oct-06

Three-dimensional Turing patterns: Stability, implications in biological modeling, and equilibrium

Turing patterns are structures that can form spontaneously in systems of reacting and diffusing chemicals. Since the 1950s, when Alain Turing first put forth the theoretical considerations, there has been a vast amount of literature on the subject. I   more››

Simon Fraser University

  • 5-Oct-06

Functional equations for Mahler measures of genus-one curves

The Mahler measure of an n -variable polynomial P is the integral of log | P | over the n -dimensional unit torus T n with the Haar measure. Consider a family of two-variable polynomials whose coefficients depend on one parameter. Then the Mahler mea   more››

University of British Columbia

  • 4-Oct-06

Computer-assisted proofs in geometry

In recent years, computer-assisted proofs have become relatively common. For example, in 2002, W. Tucker published a proof of problem 14 (concerning strange attractors) on Smale's list of problems for the new century. Other recent computer-assiste   more››

University of Calgary

  • 3-Oct-06

Semilinear elliptic systems with exponential nonlinearities in two dimensions

We study the existence of nontrivial solutions for the following system of two coupled semilinear Poisson equations: left{ begin{array}{rlllllll} -Delta u &=& g(v), & v & > & 0 & extrm{in} Ω, \ -Delta v &=&   more››

University of British Columbia

  • 3-Oct-06

Exponential integrators

Numerical schemes for ordinary differential equations, using matrix exponentials, were introduced in the 1960's as a way to overcome the stability restrictions of explicit methods. However, such methods were not considered as a practical mean of s   more››

University of British Columbia