|Date: Friday, November 14, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Geometric crystals and Whittaker functions
Abstract: Crystal graphs were invented by Kashiwara as a combinatorial model for the highest weight representations of a semisimple complex Lie algebra.
Berenstein and Kazhdan's geometric crystals are birational lifts of crystal graphs: they are algebraic varieties that tropicalize to crystal graphs. I will talk about an integral formula for the "character" of a geometric crystal. This character turns out to be an Archimedean Whittaker function.
The integral formula has applications to mirror symmetry of flag varieties and to the theory of random directed polymers (though I probably won't have time to discuss this).
Speaker: Thomas Lam
Institution: U. Michigan