# Pipe dreams and Schubert polynomials.

#### by Richard Brak

Institution: University of Melbourne
Date: Tue 30th August 2011
Time: 1:00 PM
Location: Room 215, Richard Berry Building

Abstract: I will give a brief overview of Fomin and Kirillov's
combinatorial construction of Schubert polynomials. The definition
uses combinatorial objects now called "pipe dreams". These diagrams
are canonical representatives of bipartite diagrams representing
elements of the $$A_n$$ Coxeter group. The set of pipe dreams that
occur in Schubert polynomials are those arising from the nil-Coxter
algebra associated with $$A_n$$. I will also discuss the connection with
divided difference operators.