## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** Coxeter representations appearing in the cohomology of hyperplane complements

**Speaker:** Joel Specter

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

Given a finite Coxeter group W, there exists a unique irreducible, real representation V of W on which W acts as a reflection group. Let X(W) be the complement of the reflection hyperplanes in the complexification of V. Deligne showed that X(W) is a classifying space for the pure Artin-tits group attached to W. In this talk, I will expand on work of Arnol'd, Brieskorn, Orlick and Solomon, and Lehrer to give an explicit formula for the character of the $W$ on the cohomology of $X(W)$. The proof will use etale cohomology to equate this calculation to a counting problem in elementary number theory over finite fields. This is joint work with Weiyan Chen.

**Date:** Monday, February 08, 2016

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Yifeng Liu

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

**Contact Phone:**

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