Past Events

We will discuss a graph that encodes the divisibility properties of integers by primes. We prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional...

The first cotangent cohomology module $T^1$ describes the first order deformations of a commutative ring. For Stanley-Reisner rings, this module has a purely combinatorial description: its multigraded components are given as the relative cohomology...

In 2017, Ron Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most the ceiling of n...

People interact with each other in social and communication networks, which affect the processes that occur on them. In this talk, I will give an introduction to dynamical proceses on networks. I will focus my discussion on opinion dynamics, and I...

Abelian networks a class of models from statistical physics introduced as models to help understand the complex behavior exhibited by forest fires and avalanches. In this talk we will introduce a few different Abelian networks including activated...

A point-line incidence is a point-line pair such that the point is on the line. The Szemer\'edi-Trotter theorem says the number of point-line incidences for n (distinct) points and lines in R^2 is tightly upperbounded by O(n^{4/3}). We advance the...

I will present some classes of fully nonlinear PDEs on: complex hermitian and Riemannian manifolds which are motivated (respectively) by hypercomplex and quaternionic geometry. In particular, I will formulate the generalization of the conjecture of...

A momentous legacy of twentieth-century mathematics is the realisation that deterministically evolving systems frequently exhibit, when observed for sufficiently extended periods of time, a statistical behaviour akin to the limiting behaviour of...

The classification of 2-dimensional TQFTs was obtained by cutting up surfaces into disks, cylinders, and pairs of pants. In higher dimension, such a decomposition of n-manifolds is not available. We need to cut up manifolds not only along codimension...

Membrane-enclosed fluid objects, or capsules, are everywhere in natural and industrial processes, from red blood cells and circulating tumor cells in the life sciences to encapsulated substances in the pharmaceutical, food and cosmetic industries. A...