Nodal counts of the Dirichlet-to Neumann operators

Dr Asma Hassannezhad (University of Bristol) will present her research in Analysis.

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. However, almost nothing is known when we consider Dirichlet-to-Neumann eigenfunctions. We discuss how we can obtain an asymptotic Courant Nodal domain theorem for the Dirichlet to Neumann operators.

This is joint work with David Sher. 


The talks are held using Zoom. Anyone interested in attending (outside the School of Mathematics) should email Ben Sharp at to request zoom coordinates.