Past Events

Mutation is a process that makes a non-trivial local change to a knot; the distinction between the resulting pair of knots is difficult to detect. I will present a vaguely historical account of why mutant pairs are difficult to distinguish. This will...

We consider the Dirichlet problem for a strongly-coupled nonlocal system of equations motivated by peridynamics, a model in continuum mechanics. The strain energy densities involve the magnitude of projected "directional" difference quotients of the...

When you load a webpage, watch a video, send an email, or do any other task on the internet, packets of information travel along a path from you to your destination. But where, physically, is this path? We answer this question by using traceroutes...

Improvements in sequencing technology mean that we have rich data on how infections evolve and spread. In this talk I will describe two settings where this calls for new mathematics. Trees -- in the sense of graphs with no cycles -- are a cornerstone...

What is the minimal possible diameter of a hyperbolic surface (i.e. with constant curvature equal to -1) of genus g? We will prove that it is asymptotic to log(g). While the lower bound follows from a simple volume growth argument, the upper bound is...

The second-order centered (leapfrog) time-stepping scheme is commonly used in numerical models of weather and climate. The unstable computational mode is damped by applying a Robert–Asselin filter, which introduces first-order numerical errors...

Among modern numerical methods to solve the optimal transport problem, dynamical optimal transport (a.k.a. fluid dynamic formulation or Benamou-Brenier formulation) is one of the oldest: it consists in rewriting the problem in terms of convex...

A diffusion-type operator biologically significant in neuroscience is a difference of Gaussian functions used as a spatial-convolution kernel (Mexican-Hat operator). We are interested in the dynamics inherent in a neural structure such as visual...

Which 3-manifolds smoothly embed in the 4-sphere? This seemingly simple question turns out to be rather subtle. Using Donaldson's theorem, we derive strong restrictions to embedding a Seifert fibered space over an orientable base surface, which in...

Inspired by a problem in joint source-channel coding, we introduce a new notion of similarity between graphs, termed graph information ratio. We discuss various properties of this measure, including in particular metric structure and partial ordering...