Past Events

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...

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...

Let X be your favorite type of algebraic structure. For example, X could be the class of quadratic forms, algebras or algebraic varieties. To estimate the complexity of X, you might consider the following natural question: how many algebraically...

The microscopic theory of equilibrium phenomena is highly developed and rather exhaustive, while that of non-equilibrium phenomena still faces fundamental challenges and lacks a unitary formulation, although both the equilibrium and the non...

Are there really primitive tribes whose system of counting goes: “One, Two, Many,...” indicating that from three on it’s a blur? It’s surprising how little progress we’ve made in addressing some basic problems in 3D or beyond, or when solving...

Measure zero sets containing intricate structure are foundational in geometric measure theory. These include Besicovitch sets in the plane (also known as Kakeya sets), which are measure zero sets containing a line in every direction. Closely related...

Infectious disease transmission models are used to inform public health policies and gain a better understanding of disease dynamics. For them to accomplish these goals effectively it is important that models accurately represent the mechanisms that...

I will discuss the following question independently posed by Clark and Saltman around 2007: Given a central simple algebra A over a field K, is there a a genus 1 curve X over K such that A is split by the function field K(X)? Federico Scavia and I...

I will use the remarkable Stirling’s formula for N! to introduce the asymptotic analysis of Riemann-Hilbert problems. Then I will describe the kinetic theory of soliton gases. To accomplish this, I will explain by example some integrable nonlinear...

How does one describe the structure of a graph? What is a good way to measure how complicated a given graph is? Tree decompositions are a powerful tool in structural graph theory, designed to address these questions. To obtain a tree decomposition of...