Past Events

We introduce a Markov chain model to study evolution of a continuous trait based on population genetics. It corresponds to individual-based model which includes frequency dependent selection caused by m-player game interactions and stochastic...

Given two homotopy equivalent manifolds with different dimensions, it is natural to ask if the smaller one embeds in the larger one. We will discuss this problem in the case of four-manifolds homotopy equivalent to surfaces.

This is the first of a two part expository talk on the Balog-Szemerédi-Gowers theorem. This theorem, originally due to Balog and Szemerédi and later strengthened by Gowers, is one of the most important tools in additive combinatorics, with...

Self-similar solutions and translating solitons are not only special solutions of mean curvature flow (MCF) but a key role in the study of singularities of MCF. They have received a lot of attention. We introduce some examples of self-similar...

A lattice-indexed family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a stochastic reaction-diffusion system when we insert a local...

Although integers are ubiquitous in quantum physics, they have different mathematical origins. In this colloquium, I will give a glimpse of how integers arise as either topological invariants or as analytic indices, as is the case in the so-called...

I will present nonlinear dynamics for distributed decision-making that derive from principles of symmetry and bifurcation. Inspired by studies of animal groups, including house-hunting honeybees and schooling fish, the nonlinear dynamics describe a...

Mathematical models for population dynamics have a long history in biomathematics. They are tools to explore the effects of birth and death, species interaction, landscape quality and spatial movement on the persistence, spread and spatial...

The Heegaard Floer theory of a 4-ended tangle takes the form ofan immersed curve (with possibly non-trivial local system) on theboundary of the tangle minus the tangle ends. The Heegaard Floerhomology of a link can be computed as the Lagrangian...

Moving boundary problems are found in many contexts including coastlines and the seabed on the large scale to atherosclerosis and blood clotting on the micro scale. The coupling between the fluid flow and evolving solid bodies is an important...