Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

Orateur(s) Omid Amini - École Polytechnique,
Titre Moduli of hybrid curves: hybrid Laplacian and asymptotics of the Arakelov Green function
Horaire14:00 à 15:00
RésumeIn this sequel to our work on moduli space of hybrid curves, we define a hybrid notion of Laplacian, formulate a hybrid Poisson equation, and give a mathematical meaning to the question of the convergence both of the Laplace operator and the solutions to the Poisson equation on Riemann surfaces. As an application, we formulate a hybrid notion of Green function and use this to obtain a layered description of the asymptotics of Arakelov Green functions on Riemann surfaces close to the boundary of their moduli spaces. This solves a well-studied problem arising from the Arakelov geometry of Riemann surfaces. Based on joint works with Noema Nicolussi.