Combinatorics of Bruhat order

The so called "Bruhat order" is a partial order structure on Coxeter
groups with remarkable properties. It arises naturally in several contexts
in mathematics, for instance in algebraic geometry (e.g. containment of
Schubert varieties), representation theory (e.g. Kazhdan-Lusztig theory)
and in combinatorics.

This talk will first give an introduction to Bruhat order and then
continue with an account of some recent research (joint work with T.
Ekedahl) on the combinatorial structure of intervals in Bruhat order on
crystallographic Coxeter groups.