Number theory seminar: Tuesday Feb 28

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Masahiro Nakahara

Feb 24, 2023, 8:05:31 PM2/24/23
to Number Theory at Univ. of Washington
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 Nakahara

Feb 28, 2023, 12:01:25 PM2/28/23
to Number Theory at Univ. of Washington
A friendly reminder about seminar today, see below.
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