Spectral Minimal Partitions of Metric Graphs: What and Why

Explore the concept of Spectral Minimal Partitions (SMPs) in metric graphs during this one-hour seminar from the Spectral Geometry in the Clouds series. Delve into the analytical approach of dividing objects like domains, manifolds, or graphs into optimal pieces by minimizing energy functionals. Examine the connections between SMPs and the spectral properties of Laplacians, as well as geometric functionals like Cheeger cuts. Learn about the advantages of studying SMPs in metric graphs as a simplified model with rich connections to higher-dimensional counterparts. Discover new results on partitioning unbounded graphs with potential and the relationship between partition existence and the essential spectrum. Investigate Robin Laplacian-type partitions and their convergence to Cheeger cuts as the Robin parameter approaches zero. Gain insights from multiple research projects involving collaborations with Pavel Kurasov, Corentin Léna, Delio Mugnolo, Matthias Hofmann, Andrea Serio, and João Ribeiro.