Douglas Lectures

Date: November 17, 2016

Time: 4:00PM - 5:00PM

Location: BLOCKER 117

Speaker: Hari Bercovici, Indiana University

Title: Eigenvalues of sums of matrices: Non-random Matrices

Abstract: Suppose that the eigenvalues of two selfadjoint matrices A and B of size N are known. As shown by Klyachko, the possible eigenvalues of A+B are described by a system of inequalities which were later shown by Knutson and Tao to be the same as a system first described by Horn. The Horn inequalities can now be proved in a completely elementary way which allows us to prove similar results in other contexts, for instance in an arbitrary factor. The argument involves an elementary solution to certain intersection problems in Grassmann manifolds.