## EVENT DETAILS AND ABSTRACT

**Representation Theory Seminar**
**Title:** On the cohomology of some non-compact Shimura varieties, part 2

**Speaker:** Professor Sophie Morel

**Speaker Info:** IAS

**Brief Description:**

**Special Note**:

**Abstract:**

In this talk, I will explain how the method originally developed by Ihara, Langlands and Kottwitz to compute the cohomology of a Shimura variety (use the Grothendieck-Lefschetz fixed point formula in positive characteristic to calculate the trace on the cohomology of a power of Frobenius at a good place times a Hecke operator trivial at that place, and then compare the result with Arthur's trace formula) applies to intersection cohomology of the Satake-Baily-Borel compactification of the Shimura varieties of unitary groups over Q and of the Siegel moduli varieties. I will also present applications to the calculation of the L-function of the intersection complex (for unitary groups and small-dimensional symplectic groups) and some applications involving base change from quasi-split unitary groups to general linear groups.

**Date:** Tuesday, November 18, 2008

**Time:** 5-6pm

**Where:** Lunt 104

**Contact Person:** Prof. Kari Vilonen

**Contact email:** vilonen@math.northwestern.edu

**Contact Phone:** 847-491-5557

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