Theatre B, Richard Berry Building
The University of Melbourne
Department of Mathematics, University of California at Los Angeles
In 1912 Weyl posed the following problem: given the eigenvalues of two n by n Hermitian matrices A and B, what are the possible sets of eigenvalues of A + B? This question has been studied extensively, and is linked with representation theory, symplectic geometry, algebraic geometry, and several other fields. The problem was only completely solved last year. In this talk we discuss the background for this problem and some of the techniques involved in the solution. The arguments revolve around the combinatorics of a beautiful but mysterious geometric object known as a "honeycomb".