Unitary, Symplectic, and Orthogonal Moments of Moments

Emma Bailey
University of Bristol
November 15, 2019

The study of random matrix moments of moments has connections to number theory, combinatorics, and log-correlated fields. Our results give the leading order of these functions for integer moments parameters by exploiting connections with Gelfand-Tsetlin patterns and counts of lattice points in convex sets. This is joint work with Jon Keating and Theo Assiotis. 

Some Statistical Results on Deep Learning: Interpolation, Optimality and Sparsity

Guang Cheng
Purdue University; Member, School of Mathematics
November 13, 2019

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 “over-fitting regime,” while the second one focuses on the statistical optimality of neural network classification in a student-teacher framework. This talk is concluded by proposing sparsity induced training of neural network with statistical guarantee. 

Lie algebras and homotopy theory

Jacob Lurie
Professor, School of Mathematics
November 11, 2019

In this talk, I'll discuss the role that Lie algebras play in algebraic topology and motivate the development of a "homotopy coherent" version of the theory. I'll also explain an "equation-free" formulation of the classical theory of Lie algebras, which emerges as a concrete byproduct.