Department Colloquium

Location: RI 209

Speaker: Himanshu Gupta, University of Regina

Title:  The Inverse Symplectic Eigenvalue Problem for Graphs

Abstract:

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 patterns are described by a labeled graph (ISEPG). We define the ISEPG formally and present key tools for addressing it, including the strong symplectic spectral property and coupled graph zero forcing. This is joint work with Leslie Hogben, Bryan Shader, and Tony Wong.