Pacific Institute for the Mathematical Sciences - PIMS

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

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

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

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

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

Emergence and Flocking

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

Topology, data and vision

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

University of Washington

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

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

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

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

Time-Frequency Analysis: From Wireless Communications to Abstract Harmonic Analysis

In the talk I will discuss the relation between problems in wireless communications and time-frequency analysis. I will explain the basic principle of OFDM (orthogonal frequency division multiplexing) and its formulation in time-frequency analysis   more››

University of Calgary

PIMS Probability Seminar 2006

If we would -say- estimate the anthropogenic contribution to climate change, we would have to understand the range of natural variability. Now, the climate of the Earth is an experiment, which is only run once, so in order to assess this we have t   more››

University of Alberta

Introduction to Brownian snakes

Discrete models for an evolving population -such as branching random walks- arise in a variety of different contexts. In such models, individuals undergo both a branching phenomenon and a spatial displacement. Superprocesses are obtained as the we   more››

University of British Columbia

Homotopical group theory II: p-local finite groups

University of British Columbia

New constructions of volume-critical submanifolds of the sphere

Constant mean curvature hypersurfaces in S^n are critical points of the (n-1)-volume functional subject to an enclosed-volume constraint whereas contact-stationary Legendrian (CSL) submanifolds of S^{2n+1} are n-dimensional submanifolds tangent to   more››

University of British Columbia

Remarks on split graphs and related notions

A graph is split if its vertices can be covered by two sets A and B where A induces a complete graph and B induces an empty graph. This concept has many related notions. For example, the number of non-isomorphic set covers of a set of order n is t   more››

University of British Columbia

An alternative formulation for a delayed logistic equation

After a brief review of the history and dynamics of the classical logistic and delayed logistic equation models, an alternative expression for a delayed logistic equation is derived assuming that the rate of change of the population depends on thr   more››

University of British Columbia

Random Sorting Networks

See http://www.math.ubc.ca/~holroyd/sort for pictures. Joint work with Omer Angel, Dan Romik and Balint Virag. Sorting a list of items is perhaps the most celebrated problem in computer science. If one must do this by s   more››

University of British Columbia

Plagued by numbers: the mathematics of disease

The dynamics of disease have long fascinated mathematical researchers. From influenza to the bubonic plague, mathematical and computational models are used to evaluate factors governing disease outbreaks. Facts about a disease are put into models.   more››

University of British Columbia