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) Gérard FREIXAS - IMJ-PRG,
Titre Non-abelian Hodge theory and complex Chern-Simons
Horaire15:45 à 17:00
RésumeIn this talk I will propose a construction of complex Chern-Simons line bundles on moduli spaces of flat vector bundles on families of Riemann surfaces. The approach is based on Deligne’s functorial approach to characteristic classes in Arakelov geometry where we replace hermitian metrics by relative flat connections and Bott-Chern secondary classes by Chern-Simons counterparts. Our construction requires an intermediate result on extensions of relative flat connections to global ones, which can be seen as a geometric avatar of Spinaci’s study of variations of twisted harmonic maps in non-abelian Hodge theory. I will discuss some applications to moduli spaces of curves, projective structures and Deligne pairings of line bundles. This is ongoing work with D. Eriksson (Chalmers University of Technology) and R. Wentworth (University of Maryland)