Speaker
Description
Symplectic geometry appears in many areas of mathematics, physics, and applications, and naturally gives rise to interesting matrix families and properties. Symplectic eigenvalues extend the classical notion of eigenvalues to the symplectic setting and are guaranteed to exist for positive definite matrices by Williamson's theorem. We introduce the inverse symplectic eigenvalue problem for positive definite matrices whose zero and nonzero pattern is described by a labeled graph (ISEPG). In this talk, we define the ISEPG and present key tools developed to address it. We focus particularly on coupled graph zero forcing, a combinatorial technique used to bound the maximum symplectic eigenvalue multiplicity for a given graph. This is joint work with Leslie Hogben, Bryan Shader, and Tony Wong.