Pacific Institute for the Mathematical Sciences - PIMS

Open problems related to certain mathematical models for MEMS

University of British Columbia

A knot theoretic equivalent to Kervaire's conjecture for groups

University of British Columbia

Open problems related to certain mathematical models for MEMS devices, (Part II)

University of British Columbia

Some mathematical challenges in nuclear medical imaging problems

We give a brief description of some of the challenging problems in medical imaging, particularly those related to nuclear medicine. We will describe some recent progress made in dual-isotope SPECT image reconstruction - obtaining two images from a   more››

University of British Columbia

Gaussian processes, kinematic formulae and Poincare's limit

The main aim of this talk will be to prove the specific result that the mean invariant measures of the excursion sets f^{-1}(D) of the vector-valued isotropic Gaussian process f on the n-sphere have a specific form, highly reminiscent of the Kinem   more››

University of British Columbia

New geometric and functional analytic ideas arising from problems in symplectic geometry

The study of moduli spaces of holomorphic curves in symplectic geometry is the key ingredient for the construction of symplectic invariants. These moduli spaces are suitable compactifications of solution spaces of a first order nonlinear Cauchy-Ri   more››

University of British Columbia

The quantum McKay correspondence in dimension two

Let G be a finite subgroup of SU(2). The classical McKay correspondence describes the cohomology ring of Y the minimal resolution of C2/G in terms of the representation theory of G. We give a description of the quantum cohomology of Y in terms of   more››

University of British Columbia

Going with the (Information) Flow: on efficient computations & boundary value problems.

The direction of information propagation can be used to de-couple certain systems of nonlinear equations. This fundamental principle is the basis of Dijkstra's classical method for finding shortest paths on graphs. We will use the continuous analogue   more››

Simon Fraser University

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

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

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

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

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

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

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

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

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

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

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

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