Quoc Ho: Factorization homology and the arithmetics and topology of configuration spaces

Abstract

The last decade has witnessed many interesting interplays between homological/representation stability phenomena and questions in arithmetic statistics. In this talk, I will show how the algebro-geometric version of factorization homology provides a unifying framework for studying these phenomena in the case of configuration spaces. In particular, I will explain the relationship between various zeta values coming out of point-counts on configuration spaces and homological stability phenomena exhibited by these spaces, answering questions of Farb--Wolfson--Wood. Time permitting, I will explain how these ideas can be further developed to study representation stability for ordered configuration spaces.

Zoom Notes: The meeting ID is 657 9019 8929 and the passcode is 3517257.