Speaker: Asma HASSANNEZHAD（University of Bristol）

Time： June 8, 16:00-17:00

Place： ZOOM ID: 945 8387 4680 Passcode: 695038

Title： Nodal counts for the Dirichlet-to-Neumann operators with potential

Abstract： The zero set of an eigenfunction is called the nodal set and the connected components of its complement are called the Nodal domains. The well-known Courant nodal domain theorem gives an upper bound for the nodal count of Laplace eigenfunctions on a compact manifold. We consider the harmonic extension of eigenfunctions of the Dirichlet-to-Neumann operators with potential. When the potential is zero, these harmonic extensions are called the Steklov eigenfunctions. It has been known that the Courant nodal domain theorem holds for Steklov eigenfunctions. We discuss how we can get a Courant-type bound for the nodal count of the Dirichlet-to-Neumann operator in the presence of a potential. This is joint work with David Sher.