Pacific Institute for the Mathematical Sciences - PIMS

A Galois correspondence for reductive groups and applications to the First Fundamental Theorems

Following some unpublished ideas of Lex Schrijver we will explain a new approach to the First Fundamental Theorems (FFTs) from classical invariant theory. It uses the tensor product of the two tensor algebras $T(V)$ and $T(V^*)$ with the aim to se   more››

University of British Columbia

Open problems related to certain mathematical models for MEMS: The dynamical case

University of British Columbia

SL(2,C) Character Varieties of 3-Manifold Groups

In continuation of the intro from last time, I will give an overview of some applications of SL(2,C) character varieties to 3-manifold topology. We will then discuss possible topics for the following seminars and will assign speakers.   more››

University of British Columbia

Random walk in random environment on a strip

I am going to define the model, discuss briefly an interesting particular case of it, and present some limit theorems recently obtained for RWRE on strips. I am going to build my talk around the comparison of this model to the well-studied RWRE on   more››

University of British Columbia

Finite subset spaces of the circle and a theorem of Bott

By considering the circle as the boundary of the hyperbolic plane we are able to describe the first three unordered configuration spaces of the circle by considering them as particular quotients of the group of isometries of the hyperbolic plane.   more››

University of British Columbia

Galloping instability of viscous shock waves

This is joint work with Kevin Zumbrun (Indiana University). Motivated by physical and numerical observations of time oscillatory galloping, spinning, and cellular instabilities of detonation waves, we study Poincare--Hopf bifurcation of traveling-   more››

University of British Columbia

Glacier and ice sheet dynamics

Glaciers and ice sheets are thin viscous gravity currents subject to mass sources and sinks due to surface snow accumulation and melting. Mathematically, the evolution of glacier geometry poses interesting free boundary problems. Land-based glaciers   more››

Simon Fraser University

Dynamic Asset Allocation: a Portfolio Decomposition Formula and Applications

This paper establishes a new decomposition of the optimal portfolio policy in dynamic asset allocation models with arbitrary vNM preferences and Ito prices. The formula rests on a change of num'{e}raire which consists in taking pure discount bonds   more››

University of British Columbia

A stochastic two-state signalling module with negative feedback

Motivated by the negative feedback calcium exerts on the gating dynamics of a calcium-conducting ion channel in olfactory receptor neurons, we develop an abstract two-state (open/closed) signalling module with negative feedback. The coupling betwe   more››

University of British Columbia

Stochastic control and optimal design of a heat mill.

University of British Columbia

Perfect Matchings under Vertex Deletion

University of British Columbia

A History of the Trace Formula

The trace formula is a far reaching generalization of the Poisson summation formula. It relates spectral data of deep arithmetic significance to explicit but complicated geometric data. With its applications to the Langlands programme, some alread   more››

University of Toronto

Hedging Under Jump Diffusion with Transaction Costs

In this talk, we consider the problem of hedging a contingent claim, where the underlying asset follows a jump diffusion process. The no-arbitrage value of the claim is given by the solution of a Partial Integro-Differential Equation (PIDE), which   more››

University of British Columbia

Optimal Drug Therapy for Chronic Myelogenous Leukemia

Drug therapy is introduced as a control in a mathematical model for chronic myelogenous leukemia (CML). The cancer is modeled as a system of ODE's representing the dynamics between the immune systen in the body and cancer cells. We introduce two cont   more››

Simon Fraser University

A Polymer Model Explains MinDE Dynamics in E. coli Cell Division

In Escherichia coli, the location of the site for cell division is regulated by the action of the Min proteins. These proteins undergo a periodic pole-to-pole oscillation that involves polymerization and ATPase activity of MinD under the controlling   more››

Simon Fraser University

Canonical metrics and collapsing manifolds

University of British Columbia

Heights of polynomials and random matrix theory

We will discuss a method for producing asymptotic estimates for the number of integer polynomials of degree N with bounded (but large) Mahler's measure. This method also produces a closed form for averages of class functions over ensembles of asym   more››

University of British Columbia

The Diophantine equation aX4-bY2=1

In a series of papers over nearly forty years, Ljunggren derived remarkably sharp bounds for the number of solutions to various quartic Diophantine equations, particularly those of the shape aX4-bY2=±1, typically via a sophisticated application o   more››

University of British Columbia

Invasion percolation on regular trees

We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behaviour of its connectivity functions, and of its volume both at a given height and below a given height. We find   more››

University of British Columbia

Some self-interacting random walks

We will discuss two different classes of self-interacting random walks. Firstly, in joint work with Akira Sakai, we consider a simple model of a random walk with reinforcement but with very short term spatial memory. The simplicity of these 'Senil   more››

University of British Columbia