Seminario Geometría

Interference phenomena in parabolic character varieties

Ponente:  Ángel González-Prieto (UAM)
Fecha:  miércoles 17 de febrero de 2021 - 15:00
Lugar:  Online -

The algebraic structure of the moduli spaces of representations of surface groups (aka character varieties) has been widely studied in the past decades, partially due to their close relation with the moduli spaces of Higgs bundles and flat connections. Nevertheless, very little is known about the geometry of character varieties when we allow poles in the Higgs field, the so-called parabolic setting. In this framework, new singularities arise in the moduli space that prevent the classical methods to work. In this talk, we will introduce a new hope: Topological Quantum Field Theories (TQFTs). We will construct a TQFT that encodes the Grothendieck motives of parabolic character varieties and we will apply it to obtain explicit expressions of these motives, even with highly non-generic parabolic data. This framework also provides a new interpretation of the singularities: at the side of the TQFT they arise as an interference phenomenon that leads to drastic changes in the geometry.