Szego Seminar: Heat, Waves and Eigenvalues of the Laplacian

Abstract: The manner in which heat and waves propagate on a surface should (at least intuitively) depend on the geometry of the surface. As a result, any differential equation that governs heat flow/ wave propagation on your surface must reflect some of the geometry of the surface. Since the Laplacian features in both the heat and wave equations, it wouldn’t be unreasonable to expect the Laplacian itself to contain some “geometric information” of the surface. How do we get hold of this “information”? A beautiful result called Weyl’s Law tells us that some of this information can be extracted by studying the spectrum of the Laplacian.

Host: Pooja Joshi