## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Plancherel density theorem

**Speaker:** Sug Woo Shin

**Speaker Info:** Chicago

**Brief Description:**

**Special Note**: **Note the unusual location!**

**Abstract:**

Serre asked and answered the following question: Fix a prime p. Consider the eigenvalues of the Hecke
operator T_p on the space of cuspforms of weight k and level N, where (p,N)=1. What is the distribution of the
eigenvalues as k and/or N tend to infinity? The answer turns out to be the Plancherel measure. First I will
review the Plancherel measure in the context of harmonic analysis on p-adic (and real) Lie groups. Next I will
interpret, reformulate and generalize Serre's question to the case of arbitrary reductive groups over Q. (Serre's
situation is concerned with the case G=GL_2. When G is anisotropic over Q, this result is due to Sauvageot.)

**Date:** Monday, November 16, 2009

**Time:** 3:00PM

**Where:** Lunt 105

**Contact Person:** Florian Herzig

**Contact email:** herzig@math

**Contact Phone:** 847-467-1898

Copyright © 1997-2024
Department of Mathematics, Northwestern University.