First IMTech Colloquium on May 13

Shahar Mendelson is a Professor at the Australian National University and a Guest Professor at the University of Vienna. He studies high dimensional phenomena, focusing mainly on the connections between Statistical Learning Theory, Empirical Processes Theory and Asymptotic Geometric Analysis. He is an editor of the journal Mathematical Statistics and Learning.

May 13 at 15:00 in this link: meet.google.com/umd-afzc-jfe

Shahar Mendelson, Australian National University and University of Vienna

The small-ball method and (some of) its applications

Abstract: 

I will present three seemingly unrelated problems - one in Asymptotic Geometric Analysis; one in random matrices theory; and one in statistics - that turn out to be very closely related: the solution to all of them is based on finding a nontrivial lower bound on the infimum of the same nonnegative random process. As it happens, the standard way of controlling that process (and the way all three problems have been studied previously) involves a natural, two-sided concentration argument.
I will explain why, despite its popularity, the two-sided concentration argument is very restrictive and often terribly loose; and I will suggest an alternative - the small-ball method - which leads to sharp estimates and holds under minimal restriction.

The present colloquium is a continuation of the Col·loqui de matemàtiques FME-UPC that took place from 2016 to 2020, featuring distinguished researchers each year including Louis Nirenberg, Andreu Mas-Colell, and Claire Voisin.