Scientific Lectures

  • 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

  • 2-Oct-06

Sphere Packings and foams

Kepler's conjecture asserts that the densest possible arrangement of congruent balls in three dimensions is the familiar pyramid arrangement, which is used to stack oranges at the fruit stand. A 300-page proof of this theorem finally appeared in J   more››

University of Calgary

  • 2-Oct-06

Ehrhart analogue of the h-polynomial

In this talk I will explain how the Ehrhart problem of counting lattice points in a polyhedron is equivalent to a problem in orbifold cohomology. This equivalence can be used to prove a conjecture of Stanley that relates the Ehrhart generating pol   more››

University of British Columbia

  • 28-Sep-06

Perturbations Methods in Default Modeling

Stochastic volatility has played a central role in modeling equity derivative markets. In the recent years the market in credit-linked derivative products has grown tremendously and had generated a need for more sophisticated models of default. We   more››

University of British Columbia

  • 28-Sep-06

The integral geometry of random sets

In various scientific fields from astro- and high energy physics to neuroimaging, researchers observe entire images or functions rather than single observations. The integral geometric properties, notably the Euler characteristic of the level/excu   more››

University of Calgary

  • 25-Sep-06

Primitivity in twisted homogeneous coordinate rings

Given a projective k-scheme X, an automorphism sigma of X and an invertible sheaf L on X, one can form the twisted homogeneous coordinate ring bigoplus_{nge 0} H0(X,L_n), where L_n=Lotimes L^{sigma}otimes cdotsotimes L^{sigma^{n-1}. We study the q   more››

University of British Columbia

  • 19-Sep-06

Comparing sumsets and difference sets

Since addition is commutative but subtraction is not, the subset S+S of a finite set S is predisposed to be smaller than the difference set S-S. As Mel Nathanson wrote: Even though there exist sets S that have more sums than differen   more››

University of British Columbia

  • 18-Sep-06

A Mirror Theorem for Complete Intersection Orbifolds in Weighted Projective Spaces

The famous mirror formula for quintic threefolds, conjectured to Candelas, de la Ossa, Green, and Parkes, provides detail information on genus zero Gromov-Witten invariants of the quintic threefold. Mirror formula has been extended to larger class   more››

University of British Columbia

  • 18-Sep-06

Prediction of dispersal and establishment of aquatic nonindigenous species across Ontario lakes: Linking vector-based and habita

Prediction of range expansion of nonindigenous species is important, as it is often easier to prevent invasions than to mitigate impacts once invasions have occurred. A combination of models for propagule pressure (gravity models) and habitat matc   more››

University of Alberta

  • 14-Sep-06

Closed form solution for maximizing CRRA type utility

This paper studies the problem of optimal investment in incomplete markets when the agents have CRRA type utility. Closed form solutions are obtained up to some unhedgeble risk represented by a process orthogonal on the stock price. The   more››

University of British Columbia

  • 14-Sep-06

On classifications of links up to C_n-moves

A C_n-move (nin{Bbb N}) is a local move on links defined by Habiro, which can be regarded as a 'higher order crossing change'. The C_n-equivalence is an equivalence relation on links generated by C_n-move. The C_m-equivalence implies the C_n-equiv   more››

University of British Columbia

  • 14-Sep-06
  • 14-Sep-06

Nucleation of localised pattern in continuous media

The formation of patterns from quiescence under the continuous variation of a parameter has long been of interest across the physical and life sciences since the pioneering work of Alan Turing. We describe how spatially localised patches of patter   more››

University of British Columbia

  • 13-Sep-06

The loop-erased random walk and the uniform spanning tree on the four-dimensional discrete torus

Let x and y be points chosen uniformly at random from the four-dimensional discrete torus with side length n. We show that the length of the loop-erased random walk from x to y is of order n2 (log n)^{1/6}, resolving a conjecture of Benjamini and   more››

University of British Columbia

  • 13-Sep-06

Ionic and Metabolic Mechanisms in Pulsatile Insulin Secretion

Insulin is secreted in pulses with a period of about 5 minutes from the beta-cells of the pancreas. These pulses are in turn driven by oscillations of cytosolic calcium. Two parallel streams of investigation over more than two decades have studied   more››

University of British Columbia

  • 13-Sep-06

Subfactors and (1+1)-dimensional TQFTs (Part 2)

University of British Columbia

  • 12-Sep-06

Subfactors and (1+1)-dimensional TQFTs (Part 1)

In this joint work with Vijay Kodiyalam (IMSc, Chennai) and Vishwambhar Pati (ISI, Bangalore), we construct a certain 'cobordism category' D whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-man   more››

University of British Columbia

  • 11-Sep-06

Linearly reductive finite group schemes

I will report on joint work with Dan Abramovich and Martin Olsson. We classify linearly reductive finite group schemes in positive or mixed characteristic, and use this to define a good replacement for the notion of orbifold in positive or mixed c   more››

University of British Columbia

  • 5-Sep-06

Prime numbers, Riemann, and Langlands

Prime numbers have held a mystery over number theory since before Euclid. To introduce a powerful new tool to the subject, Riemann defined his analytic zeta function; with it, he described the Prime Number Theorem and conjectured Riemann's Hypothe   more››

University of British Columbia