Title: Plancherel density theorem
Speaker: Sug Woo Shin
Speaker Info: Chicago
Special Note: Note the unusual location!
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