Peijel's Nodal Domain Theorem in Spaces with Synthetic Ricci Curvature Lower Bounds

Explore the extension of Peijel's Nodal Domain Theorem to metric measure spaces with synthetic Ricci curvature lower bounds in this 59-minute seminar from the Spectral Geometry in the Clouds series. Delve into the challenges of applying classical nodal set and domain concepts to non-locally Riemannian structures. Examine the innovative techniques used to prove the theorem for both Dirichlet and Neumann Laplacians on domains, with special attention to their application in Euclidean space. Gain insights into how this research expands the validity of Pleijel's theorem to a broader class of sets. Based on joint work with Nicoló de Ponti and Ivan Yuri Violo, this talk by Sara Farinelli at the Centre de recherches mathématiques (CRM) offers a deep dive into cutting-edge developments in spectral geometry and analysis on singular spaces.