Pacific Institute for the Mathematical Sciences - PIMS

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››

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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››

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Geometry, Topology, and their Interactions.

http://www.math.ohio-state.edu/~jlafont/MoreliaConf.html   more››

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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››

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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››

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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››

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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››

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Homotopical group theory II: p-local finite groups

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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››

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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››

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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››

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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››

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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››

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High dimensional convex bodies: phenomena, intuitions and results

Phenomena in large dimensions appear in a number of fields of mathematics and related fields of science, dealing with functions of infinitely growing number of variables and with objects that are determined by infinitely growing number of paramete   more››

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Mathematical models in radiation biology

In this talk, I will review concepts in radiation biology that allow us to model the effectiveness of radiation therapy in the treatment of cancer. In particular, I will focus on the Tumour Control Probability (TCP), which is the probability that   more››

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The action on a tree associated to an ideal point of the character variety

Let G be the fundamental group of a compact, orientable, irreducible 3-manifold M. I will discuss the correspondence between ideal points of a curve in the character variety X(G) and actions of G on a tree (following Culler-Shalen). This is a part   more››

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Homotopical group theory I: p-compact groups

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Hydrodynamic limits of spatially structured coalescents

We are motivated by a question arising in population genetics, and try to describe the effect of migratory fluxes and spatial structure on the genealogy of a population. This leads to the study of systems particles performing simple random walk on   more››

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L^2 decay estimates for oscillatory integral operators in several variables with homogeneous polynomial phases

Oscillatory integral operators mapping $L^2(mathbb R^{n_1})$ to $L^2(mathbb R^{n_2})$ play an important role in many problems in harmonic analysis and partial differential equations. We will briefly discuss the applicability of these operators in   more››

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Puzzles, Tableaux, and Mosaics

The Littlewood-Richardson numbers show up in a number of different areas of mathematics. They are structure constants of the ring of symmetric functions, which connects them to representation theory and cohomology of Grassmannians. There are now s   more››

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