Coxeter groups and Bruhat order: algebraic and topological structure
Time and place
12 PM on Tuesday, March 24th, 2009; NAC 1/511E
Dr. Bridget Eileen Tenner (DePaul University)
Abstract
Coxeter groups are classical objects of interest to mathematicians in a
variety of disciplines. One aspect of these systems is the study of a
particular partial ordering of their elements, known as the Bruhat order.
In this talk we explore several different structural aspects of Coxeter
groups and of the Bruhat order, from both algebraic and topological
perspectives. The results discussed will involve reduced words,
permutation patterns, zonotopal tilings, order ideals, and the homotopy
type of a particular cell complex. For example, recent work has uncovered
significant links between permutation patterns, the reduced words of a
permutation, and the interval structure of the Bruhat order. Among other
things, this connection implies that a certain class of 2n-gons can be
tiled by convex centrally symmetric 2k-gons iff k is 2 or n.
