Title: Affine Mirkovic-Vilonen polytopes.
<br><br>
Abstract:
Kashiwara developed combinatorial objects called crystals to study the
representation theory of complex simple Lie groups and Lie algebras.
The construction is quite involved, but one can often realize the same
combinatorics by more elementary means. I will explain one such
realization based on the Mirkovic-Vilonen polytopes of the title, and
try to convince you it is useful. I will then explain current work
giving an analogous construction for symmetric affine Kac-Moody
algebras. This will be done mainly via examples and pictures, and I
will not assume much familiarity with the representation theory
involved. This includes joint work with Pierre Baumann, Thomas Dunlap
and Joel Kamnitzer.