Bor Plestenjak: New results on singular two-parameter eigenvalue problems

A two-parameter eigenvalue problem $W$ is related to an associated pair of matrix pencils $\Delta$ built from operator determinants. While we know that in a nonsingular case the eigenvalues of $W$ agree to the eigenvalues of $\Delta$, only partial results are known for the singular two-parameter eigenvalue problem under the assumption that all eigenvalues are algebraically simple. We will generalize some of these results and discuss the remaining open problems.

The seminar will most likely consist of several parts.