## Scientific Lectures

- 23-Jan-07

New singular solutions of the Nonlinear Schrodinger equation (NLS)c

The study of singular solutions of the NLS goes back to the 1960s, with applications in nonlinear optics and, more recently, in BEC. Until recently, the only known singular solutions had a self-similar 'peak-type' profile that approaches a delta f more››

University of British Columbia

- 23-Jan-07

Mirkovic-Vilonen cycles on the affine Grassmannian

The geometric Satake correspondence relates representation theory to the geometry of the affine Grassmannian. In particular, certain subvarieties of the affine Grassmanian, called Mirkovic-Vilonen cycles, give bases for representations of complex more››

University of British Columbia

- 19-Jan-07

A Simple Technique for Solving Partial Differential Equations on Surfaces

Many applications require the solution of time dependent partial differential equations (PDEs) on surfaces or more general manifolds. Methods for treating such problems include surface parameterization, methods on triangulated surfaces and embeddi more››

Simon Fraser University

- 19-Jan-07

One of the most recurrent themes in Geometry, is the study of objects that locally look the same. I will explain, mainly via examples and in non-technical terms, how the concept of 'locally look the same' has evolved through time (mostly through s more››

University of British Columbia

- 18-Jan-07

In this talk I will present two pieces of work in progress. In the first half of the talk I will speak about the evolution of phenotype determining mechanisms. Many heterogeneous environments favour different phenotypes in different places or at d more››

University of British Columbia

- 17-Jan-07

MITACS Math Finance Seminar 2007

We study the existence of a numeraire portfolio for a discrete time financial market with proportional transaction costs. In an incomplete market without frictions, consistent prices for derivative securities can be obtained by taking the expectat more››

University of British Columbia

- 17-Jan-07

Normal subgroups of the braid groups and the Dehornoy ordering

The braid groups admit a left-ordering, known as the Dehornoy ordering, which has come up under many guises in recent years. I will show that normal subgroups interact with the Dehornoy ordering in such a way that 'nearly all' normal subgroups of more››

University of British Columbia

- 16-Jan-07

Cooperation in Social Dilemmas: The Role of Punishment and Volunteering

The emergence and maintenance of cooperative behavior that is beneficial to others but costly to the individual represents a major conundrum in evolutionary biology. Punishment represents an efficient mechanism to stabilize and maintain cooperatio more››

University of British Columbia

- 11-Jan-07

Inflation Indexed Swaps and Swaptions

This article considers the pricing of inflation indexed swaps, inflation indexed swaptions, and options on inflation indexed bonds. To price the inflation indexed swaps, we suggest an extended HJM model. The model allows both the forward rates and more››

University of British Columbia

- 11-Jan-07

Bergman metrics and geodesics in the space of Kahler metrics

The space of positively curved hermitian metrics on a positive holomorphic line bundle over a compact complex manifold is an infinite-dimensional symmetric space. It is shown by Phong and Sturm that geodesics in this space can be uniformly approxi more››

University of British Columbia

- 11-Jan-07

A multiphase flow model of calcium induced morphology changes in true slime mold

The true slime mold Physarum polycephalum is a single cell organism reaching up to meters in size. The cytoplasm shows periodic shuttle streaming through a network of tubular structures attaining velocities up to 1 mm/s. The motion is driven by th more››

University of British Columbia

- 11-Jan-07

On Some of the Differences Between Z and Z^2 in Dynamics

Around 1970 it was discovered that measure preserving actions of Z^2 on probability spaces can have remarkably different properties from Z-actions, i.e. from actions of single transformations. Many of these differences can be described as 'rigidit more››

University of Washington

- 10-Jan-07

New numerical techniques for some non-Newtonian fluid models and thin film heteroepitaxial growths

In this talk, we shall discuss the construction of discrete analogues of continuous theories and their vital roles in two research areas, fluid dynamics and material sciences. For the simulation of rate-type non-Newtonian fluid flows more››

University of British Columbia

- 10-Jan-07

Heatball localizations of monotone functionals on evolving manifolds

Monotone functionals give important information for the analysis of geometric evolution equations. I will describe a quite general mechanism for localizing such functionals. This construction results in what may be regarded as local mean-value, mo more››

University of British Columbia

- 10-Jan-07

We give a mathematical model with ordinary differential equations and the graph laplacian towards the problem: what decentralized mechanisms give rise to common features as language? A critical exponent plays a role in this deterministic setting. more››

University of Washington

- 9-Jan-07

Large data sets usually have some geometric core. We give some results toward understanding that core. more››

University of Washington

- 5-Jan-07

Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanic

During the last three years of his life Heinrich Hertz wrote a treatise on mechanics which was to be the last attempt to supply a satisfactory foundation to classical mechanics. It was published posthumously in 1894, the year of his death. more››

Simon Fraser University

- 18-Dec-06

Volume, twist number, and the Jones polynomial of hyperbolic knots

I will describe a few results that relate combinatorial data about a knot or link projection to geometric and topological information about the link complement. For a large family of knots and links, one single piece of diagrammatic data (the twis more››

University of British Columbia

- 12-Dec-06

Self-avoiding walk enumeration via the lace expansion

We introduce a new method for the enumeration of self-avoiding walks based on the lace expansion combined with another algorithmic improvement which we call the two step method. We have been able to significantly extend series for the simple cubic more››

University of British Columbia

- 12-Dec-06

Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

The critical dissipative quasi-geostrophic equation was proposed by several authors as a toy model to study the regularity of solutions to 3D Navier-Stokes equations. In this work, in collaboration with L. Caffarelli, we prove that drift-diffusion more››

University of British Columbia