Thursday, December 9, 2021 - 13:00 to 14:00

### Abstract or Additional Information

A famous foundational problem concerns finding combinatorial

expressions for tensor products of irreducible representations. One

way to solve this problem is to use the combinatorics of

Mirkovic-Vilonen polytopes. These polytopes were originally defined

as moment map images of MV cycles, but they also arise from the study

of submodules of preprojective algebra modules. With Pierre Baumann

and Allen Knutson, we defined measures

supported on these polytopes. These measures allow us to perform

computations which distinguish among different bases for representations.