Eigenvalue Inequalities and Schubert Calculus

Beginning with Weyl, many mathematicians have been interested in the following question: Given two Hermitian matrices with fixed eigenvalues, what are the possible eigenvalues of the sum? I will survey some results on this topic, including a complete solution, and describe a generalization to unitary matrices. The answers involve the (quantum) cohomology of the Grassmannian.

Refreshments will be served in Math Annex Room 1115, 3:15 p.m.