David Sher (DePaul University)
Title: On Pleijel's nodal domain theorem
Abstract:
A classical problem in spectral geometry is to study the number of nodal domains of eigenfunctions of the Laplacian. Courant's nodal domain theorem tells us that the kth eigenfunction of the Dirichlet Laplacian has at most k nodal domains. Pleijel's nodal domain theorem is instead an asymptotic statement, telling us that the ratio of the number of nodal domains to the index of the eigenfunction has limsup bounded above by a fixed constant less than 1. In this talk, we give a survey of recent extensions of and variations on Pleijel's theorem. As an example, we prove that Pleijel's nodal domain theorem holds for the Robin Laplacian on any Lipschitz domain. This is joint work with Katie Gittins (Durham), Asma Hassannezhad (Bristol), and Corentin Lena (Padova).
Meeting ID: 895 2873 0384
Passcode: 077937