MS Seminar (Mathematics - String Theory)

Speaker: Georgios Kydonakis (U of Patras, Greece)
Title: Fock bundles and Teichmüller spaces
Date (JST): Mon, Oct 30, 2023, 13:30 - 15:00
Place: Seminar Room A
Abstract: Higher Teichmüller theory is concerned with the study of special connected components of character varieties sharing analogous properties to the classical Teichmüller space. Fixing a complex structure on the underlying topological surface introduces powerful holomorphic techniques through certain holomorphic pairs called Higgs bundles, which correspond to fundamental group representations via the non-abelian Hodge correspondence. Yet, a rather adverse aspect of the correspondence is that it fails to transfer the action of the mapping class group on character varieties to the moduli space of Higgs bundles. We will introduce a similar class of augmented bundles over a topological surface that we call Fock bundles which does not require fixing any complex structure on the underlying surface. We conjecture that there is an alternative passage to the one given by the non-abelian Hodge correspondence from such pairs to certain higher rank Teichmüller spaces that is independent of the complex structure on the surface. This is joint work with Charles Reid (Austin) and Alexander Thomas (Heidelberg).
Remarks: Seminar Room A (No zoom)