**Date & Time:** Friday, July 25, 2014, 16:30-17:30.

**Venue:** Ramanujan Hall

**Speaker:** Prakash Belkale, UNC Chapel Hill

**Title:** Eigenvalues of hermitian matrices

**Abstract:** We consider the problem of characterizing the possible
eigenvalues of a sum of hermitian matrices given the eigenvalues of the
summands. Hermitian matrices of a given size can be thought of as elements
in the Lie algebra of a suitable unitary group, and this problem is
therefore one in Lie theory (and admits various natural generalizations).
The modern solution of this problem uses the geometry of some homogeneous
spaces, and will be described in the lecture.