Mathematical Physics and Harmonic Analysis Seminar

Date: October 20, 2021

Time: 10:00AM - 11:00AM

Location: Zoom

Speaker: Noema Nicolussi, Ecole Polytechnique

Title: Asymptotics of Green functions: Riemann surfaces and Graphs

Abstract: There are many interesting parallels between the analysis and geometry of Riemann surfaces and graphs. Both settings admit a canonical measure/metric (the Arakelov--Bergman and Zhang measures) and the associated canonical Green function reflects crucial geometric information.

Motivated by the question of describing the limit of the Green function 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 asymptotic of solutions to the Poisson equation and, in particular, the Green function on metric graphs and Riemann surfaces close to the boundary of their respective moduli spaces.

Based on joint work with Omid Amini (Ecole Polytechnique).