The representation theory of monoids associated to Coxeter groups and other combinatorial structures

In the last twenty years it has been noticed that many combinatorial and geometric structures also have the structure of a monoid. These include real and complex hyperplane arrangements, Bruhat order of Coxeter groups, Schubert cells of linear algebraic groups and more.

The representation theory of these monoids can be used to study random walks and give other  information about these structures. Connections between combinatorial and geometric structures and representations of finite monoids has led to important developments in these fields.

In this talk, we look at the monoids associated to the Coxeter complex and to the Bruhat order of a Coxeter group. No previous knowledge required.