Laplacians on Riemann surfaces and Graphs
– Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie
Noema Nicolussi (Potsdam)
There are many interesting parallels between analysis on Riemann surfaces and graphs. Both settings admit a Laplace operator and the Poisson equation reflects crucial geometric information.
Motivated by the question of describing the limit of Green functions on degenerating Riemann surfaces, we introduce new and higher rank versions of metric graphs and their Laplace operators. We discuss how these limit objects describe the asymptotics of solutions to the Poisson equation on metric graphs and Riemann surfaces close to the boundary of their respective moduli spaces.
Based on joint work with Omid Amini (Ecole Polytechnique).