In this talk we will discuss the differences in the methodology of determining time-dependent and time-independent coefficients appearing in a hyperbolic equation in a Riemannian manifold. The talk is based on two recent research projects: 1) We will prove that a local source-to-solution map of a hyperbolic partial differential operator on a complete Riemannian manifold (no…

In this talk, I will explore the relationship between a domain's shape and its first Laplace eigenvalue, with emphasis on the domains which minimize, or are more generally critical points, for this eigenvalue, for their given volume.