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 Hornfs 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.