Mathematics

This talk will be a tour through the combinatorics of reduced
decompositions in the symmetric group (and, if time permits, the affine
symmetric and hyperoctahedral groups).  This subject has connections to
many areas of mathematics.  For instance, it is closely tied to the
geometry of the Grassmannian and of the flag variety, through the theory
of Schubert polynomials.  Also there are also some very surprising (and,
apparently, very difficult) analytic and probabilistic questions about
large reduced decompositions.