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) Zhe Sun - IHES,
Titre McShane identities and the Goncharov-Shen potential for Higher Teichmuller theory
Horaire14:00 à 15:00
RésumeMcShane established a remarkable identity for the lengths of simple closed geodesics on the hyperbolic surface with cusps. Mirzakhani extended McShane identity to obtain a beautiful recursive formula for the volumes of the moduli spaces of the Riemann surfaces, which again proved the Witten-Kontsevich theorem. On the other hand, Goncharov and Shen formulated an explicit homological mirror symmetry on two variations of moduli spaces of G-local systems using the so-called Goncharov-Shen potential. Using these Goncharov-Shen potentials, we found a collection of new McShane-type identities parametrized by the pairs (cusp/hole, simple positive root), which are the analogs of McShane-Mirzakhani identities with new parameters in the case of higher rank Lie groups, which provided us some expectations to generalize Mirzakhani's recursive formula to the higher rank cases