Austin Shapiro

The Horn Conjecture, Part II

The Horn conjecture (now a theorem) addresses the following question: If A and B are Hermitian matrices, how is the spectrum of A+B constrained by the spectra of A and B? This problem has unexpected relations with several areas of mathematics, including representation theory, Schubert calculus, and the theory of endomorphisms of free modules over a ring. I will state results in these areas and sketch some of the connections as time permits. This talk is a continuation of a two-part series, but I will provide a recap for first-time attendees.