Previous Conferences & Workshops

Machine learning algorithms are ubiquitous in most scientific, industrial and personal domains, with many successful applications. As a scientific field, machine learning has always been characterized by the constant exchanges between theory and...

Given a Shimura variety, we can construct two kinds of automorphic local systems, i.e., local systems attached to algebraic representations of certain associated algebraic group. The first is based on the classical complex analytic construction...

Given $N$ distinct points on the plane, what's the minimal number, $g(N)$, of distinct distances between them? Erdős conjectured in 1946 that $g(N)\geq O(N/(log N)^{1/2})$. In 2010, Guth and Katz showed that $g(N)\geq O(N/log N)$ using the...

This talk discusses three aspects of deep learning from a statistical perspective: interpolation, optimality and sparsity. The first one attempts to interpret the double descent phenomenon by precisely characterizing a U-shaped curve within the...

Linear regression in L_p-norm is a canonical optimization problem that arises in several applications, including sparse recovery, semi-supervised learning, and signal processing. Standard linear regression corresponds to p=2, and p=1 or infinity is...

The path between two measures in the sense of optimal transport yields the notion of *displacement interpolation*. As observed by R. McCann, certain functionals that are not convex in the usual sense are nonetheless *displacement convex*. Following...

I will explain how coisotropic submanifolds of symplectic manifolds can be distinguished among all submanifolds by a criterion ("local rigidity") related to the Hofer energy necessary to disjoin open sets from them. This criterion is invariant under...