# Grayson Plumpton (Queen's University)

Date

Tuesday November 21, 20234:00 pm - 5:00 pm

Location

Jeffery Hall, Room 319## Number Theory Seminar

**Tuesday, November 21st, 2023**

**Time:** 4:00 p.m. **Place:** Jeffery Hall, Room 319

**Speaker:** Grayson Plumpton (Queen's University)

**Title:** Some probability laws concerning the Dedekind zeta functions of $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.

**Abstract:** This talk is a follow up to a talk given at the number theory seminar in winter 2023, in which we introduce the paper “Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions” by Phillipe Biane, Jim Pitman, and Marc Yor. In this talk, we will reframe some ideas from this paper using the language of Tate-Iwasawa theory, and use this to give a probabilistic interpretation of the Dedekind zeta functions of the fields $\mathbb{Q}$, $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-2})$.