Arithmetic statistics via homological stability

Name: Arithmetic statistics via homological stability
Start: 2025-04-23T15:00:00+00:00
End: 2025-04-23T16:00:00+00:00
Location: Science Center 507

SEMINARS: NUMBER THEORY

When: April 23, 2025

3:00 pm - 4:00 pm

Where: Science Center 507

Address: 1 Oxford Street, Cambridge, MA 02138, United States

Speaker: Aaron Landesman (Harvard University)

In my view, the three main conjectures in arithmetic statistics are the Cohen-Lenstra conjectures, Malle’s conjecture, and the Poonen-Rains conjectures. We will explain the statements of these three conjectures and how, in the function field setting, they are related to understanding the homology of certain Hurwitz spaces. This is partially an advertisement for my topics course at Harvard next year and is related to joint work with Ishan Levy and work with Jordan Ellenberg.

Pretalk, 2:00 pm in SC 530:

The relation between counting the finite field points of a variety and its cohomology

The Grothendieck Lefschetz trace formula relates the number of points of a variety over a finite field to its cohomology. We will go through several examples to illustrate this relation, and explain how it can be of use in arithmetic statistics problems.