Previous Conferences & Workshops

The circle method has been a versatile tool in the study of rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to information about moduli spaces of rational...

We discuss some questions that arise when studying rational and integral points on curves, especially elliptic curves. For example, for a "random" such curve, how many rational points should it have? This will be a talk suitable for a general math...

The loop equation for circulation PDF as functional of the loop shape is derived from the Hopf equation. This equation is $\textbf{exactly}$ equivalent to the Schrödinger equation in loop space, with viscosity playing the role of Planck's constant...

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions...

We discuss some recent progress on the model-theoretic problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include Castle’s recent solution of the Restricted Trichotomy...

The Bowen-Ruelle conjecture predicts that geodesic flows on negatively curved manifolds are exponentially mixing with respect to all their equilibrium states. In a breakthrough in '98, Dolgopyat pioneered a method rooted in the thermodynamic...

A seminal result in learning theory characterizes the PAC learnability of binary classes through the VC dimension. Extending this characterization to the general multiclass setting has been open since the late 1980s.

We resolve this problem by...

The Markoff equation $x^2+y^2+z^2=3xyz$, which arose in his spectacular thesis (1879), is ubiquitous in a tremendous variety of contexts. After reviewing some of these, we will discuss (briefly) asymptotics of integer points, and (in some detail)...

Our goal is to develop a generic framework for converting modern gradient-descent based optimization algorithms into mechanisms where inputs come from self-interested agents.

We focus on aggregating preferences from n players in a context without...

We review results about random walks on groups, discussing results and conjectures relating critical constant for recurrence/transience, growth and Poisson boundary.

Much less is known about behavior of random walks on Schreier graphs. Since any...