Past Events

In the late 70s, in a series of three seminal papers, Keane and Smorodinsky proved a finitary version of the Ornstein isomorphism theorem, first for Bernoulli schemes and then for Markov shifts. For Markov chains over a countable state space, the...

Integer lattices play a central role in mathematics and computer science, with applications ranging from number theory and coding theory to combinatorial optimization. Over the past three decades, they have also become a cornerstone of modern...

In this talk, I will talk about applications of the entropy method and a tool that we call the mixture bound. To demonstrate how the mixture bound can be applied, I will show how one can prove Lovász’s version of the Kruskal–Katona theorem. I will...

There is an emerging interest in understanding the behavior of partial differential equations on graphs G=(V,E). The classic approach is to think of a graph as a (discretized) compact manifold without boundary (since there is no `complement', no...

The global population with access to electricity is constantly increasing from 84 to 92 percent. However, as the world continues to advance towards sustainable energy targets, there still exist 900 million people living without access to electricity...

Throughout scientific and commercial domains, we are often interested in separating mixed signals into their component sources. Supervised deep learning is state-of-the-art when large and well-labeled datasets can be used. But in many applications...

We obtain symmetry results of the solution to some overdetermined problems related to the eigenvalue equation on a weakly star shaped annular domain in space forms. If the associated P-function is constant on the boundary, then we get a Serrin type...

Given an abelian variety G defined over a field of characteristic 0, the intersection between a subvariety X of G with another subvariety Y of G for which dim(X) + dim(Y) dim(G) is generally expected to be empty. Rooted in this basic observation...

Last time, we discussed simplicial complexes and homological properties of their face rings. Every simplicial complex defines a toric space called its moment-angle complex. We'll discuss the construction, examples, its cellular structure, and some...

An abstract discrete dynamical system consists of a set X and a self-map f from X to itself. Dynamics studies the orbits of points of X under repeated application of f. When X and f are defined by polynomials, algebraic geometry comes into play, and...