#### Reflection Groups & Coxeter Groups

### Welcome

Welcome to the course web page for the Spring 2015 manifestation of MAT 690: Reflection Groups and Coxeter Groups at Northern Arizona University.

### Instructor Information

**Instructor:** Dr. Dana C. Ernst

**Office:** AMB 176

**Office Phone:** 928.523.6852

**Email:** dana.ernst@nau.edu

**Office Hours:** 10:00-11:15AM on Mondays, Wednesdays, or Fridays (or by appointment)

**Webpage:** http://danaernst.com

### What is This Course All About?

This course will develop the theory of Coxeter groups. The beauty of Coxeter groups lies in the rich interplay between geometry, combinatorics, and lattice theory. Most proofs about Coxeter groups exploit a combination of methods. The methods that play a role include the combinatorics of words, the geometry of arrangements of reflecting hyperplanes (or the geometry of root systems), order/lattice theory, and linear algebra. We will begin our study with geometry, closely mixed with order/lattice theory, and progress towards an understanding of the combinatorics of finite Coxeter groups. With the geometric intuition in mind, we will proceed to study the more combinatorial aspects of (not necessarily finite) Coxeter groups.