Number theory seminar: Tuesday Feb 28

[Masahiro Nakahara]

Hi everyone,

Our next NT seminar this quarter will be Yuan Liu from University of Illinois Urbana-Champaign. We will be taking Yuan to lunch afterwards.

Time: Tuesday, Feb 28, 11am 

Location: PDL C-401

Title: Nonabelian Cohen—Lenstra heuristics in the presence of roots of unity

Abstract: The nonabelian Cohen—Lenstra program studies the distribution of the Galois group of maximal unramified extension of $K$ as $K$ varies in a family of global fields. In this talk, we will discuss some new developments for this type of question. We will introduce a cohomological invariant of a Galois extension of $\mathbb{F}_q$. We show that by keeping track of this invariant we can generalize the nonabelian Cohen—Lenstra Heuristics given by Liu, Wood, and Zureick-Brown to cover the case when the base field contains extra roots of unity; moreover, we show that the new conjecture is a nonabelian generalization of the work by Lipnowski, Tsimerman, and Sawin. We will prove the conjecture with a large $q$ limit, and discuss how to make a similar conjecture for number fields.

See you there!

Masahiro

[Masahiro Nakahara]

A friendly reminder about seminar today, see below.