## Algebra and its Applications Seminar

Title: Coxeter Systems

Speaker: Kyle Armstrong

Abstract:
A Coxeter system is a pair (W,S) consisting of a group W, a set of
generators for that group S satisfying relations of a particular form,
and a representation of the group W as a reflection group.
Given an ordering, the product of the generators is called the
Coxeter element.

What's neat about Coxeter systems is that they can be nicely encoded into a graph, and have representations in GLn(R). By looking only at some properties of the associated Coxeter graph we are able to make some conclusions about the leading eigenvalues of the Coxeter elements.