Arithmetic statistics for homotopy theorists

Ishan Levi (UCPH) has agreed to give some lectures about arithmetic statistics and the relationship to homotopy theory. First lecture will be Monday Feb 24 at 13:00 in Aud 7.

Lecture series abstract: Arithmetic statistics aims to understand questions such as the distribution of class groups of a randomly chosen quadratic number field, or counting the asymptotic number of G-Galois extensions of bounded discriminant of the rational numbers. In this lecture series, I will explain how, in the function field setting, questions in arithmetic statistics may be reduced to questions about the homology of Hurwitz spaces, and how tools from homotopy theory can be used to answer those questions.

First lecture description: In the first lecture, I will explain some of the basic questions in arithmetic statistics, such as the Cohen--Lenstra heuristics, Malle's conjecture and the Poonen--Rains heurstics. I will indicate how these problems can be related to problems about Hurwitz spaces in the function field setting. A key tool in this relation is the ability to reduce questions about understanding probability distributions to questions about understanding moments of the distributions, which I will explain in some detail.