## Past Events at the University of British Columbia

### Past Events

- 7-Nov-06

Perfect Matchings under Vertex Deletion

Scientific Event

- 6-Nov-06

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››

Scientific Event

- 3-Nov-06

Canonical metrics and collapsing manifolds

Scientific Event

- 2-Nov-06

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››

Scientific Event

- 2-Nov-06

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››

Scientific Event

- 1-Nov-06

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››

Scientific Event

- 1-Nov-06

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››

Scientific Event

- 25-Oct-06

Open problems related to certain mathematical models for MEMS

Scientific Event

- 25-Oct-06

A knot theoretic equivalent to Kervaire's conjecture for groups

Scientific Event

- 24-Oct-06

- 24-Oct-06

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››

Scientific Event

- 24-Oct-06

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››

Scientific Event

- 23-Oct-06

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››

Scientific Event

- 23-Oct-06

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››

Scientific Event

- 23-Oct-06

Wild fish, farmed fish and sea lice—a big-box model with spatial effects

The Anderson-May dynamical model for host-macroparasite systems is extended to include resource limitation and the distribution of both resource limitation effects and parasite pathogenicity over host mortality and natality. When the equilibrium h more››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event