Speaker: Jiuyi Zhu (Department of Mathematics, Louisiana State University)
Title: Bounds of nodal sets of eigenfunctions

Abstract: Motivated by Yau’s conjecture, the study of the measure (sizes) of nodal sets (zero-level sets) of  eigenfunctions has been attracting much attention.  We investigate the nodal sets of Steklov eigenfunctions, Neumann eigenfunctions, and Dirichlet eigenfunctions in the domain and on the boundary of the domain. For the analytic domain, we show the sharp upper bounds of  interior nodal sets  for Steklov eigenfunctions, and the sharp upper bounds  of the intersections of nodal sets with the boundary for  Neumann and Dirichlet eigenfunctions. Furthermore, we  will discuss the unified way to obtain the sharp upper bounds of nodal sets for  eigenfunctions of  bi-Laplace equations.