A nodal domain refers to a connected region where the eigenfunction is nonzero. The simplest topological invariant of nodal domains is the nodal count. The celebrated Pleijel nodal domain theorem gives an upper bound on the asymptotic behaviour of the nodal count of the Laplace eigenfunctions with Dirichlet boundary condition. There have been advancements in this direction including its extension to the Neumann problem and more generally to the Robin problem with a non-negative parameter as well as improvements of the Pleijel upper bound for the Dirichlet problem. In this talk, we discuss an implication of these results. In particular, we focus on the extension of the Pleijel-type nodal domain theorem to the Robin problem without restriction on the sign of the Robin parameter. This is joint work with David Sher.

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Here you can find more information about our speaker:
https://research-information.bris.ac.uk/en/persons/asma-hassannezhad/publications/