Speaker: Colin McSwiggen (Brown University)

Title: Horn's problem, polytope volumes and tensor product decompositions

Time/Date: 1:00-2:30pm, January 29 (Wed.), 2020

Room: 002

Abstract: If A and B are Hermitian matrices and we know only their eigenvalues, what are the possible eigenvalues of A+B? This is the classical Horn's problem in linear algebra, which was posed by Weyl in 1912 but not completely solved until 1998. This talk will present some new results on a probabilistic version of Hornfs problem that arises naturally in random matrix theory. In particular, we will discuss how this matrix model encodes various geometric and combinatorial quantities of interest, including volumes of Berenstein-Zelevinsky polytopes and tensor product multiplicities for semisimple Lie algebras. The results presented include joint work with Robert Coquereaux and Jean-Bernard Zuber.