Analysis Seminar

Robin boundary conditions are used in heat conductance theory to interpolate between a perfectly insulating boundary, described by Neumann boundary conditions, and a temperature fixing boundary, described by Dirichlet boundary conditions. The focus of the lecture will be the fluctuations of the gaps between the Robin and Neumann eigenvalues for planar domains. I will present some numerical experimentation which reveals connections with number theory and quantum ergodicity, some new results inspired by these numerical explorations, and several open problems. Joint work with Igor Wigman and Nadav Yesha.
A couple of recent preprints are:
Zeev Rudnick, Igor Wigman, Nadav Yesha. Differences between Robin and Neumann eigenvalues https://arxiv.org/abs/2008.07400
Zeev Rudnick and Igor Wigman On the Robin spectrum for the hemisphere. https://arxiv.org/abs/2008.12964