BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Shapiro (University of Notre Dame) DTSTART:20201009T160000Z DTEND:20201009T170000Z DTSTAMP:20260423T024723Z UID:TQFT/15 DESCRIPTION:Title: Cl uster realization of quantum groups and higher Teichmüller theory\nby Alexander Shapiro (University of Notre Dame) as part of Topological Quant um Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nQuantum higher Teichmü ller theory\, as described by Fock and Goncharov\, endows a quantum charac ter variety on a surface $S$ with a cluster structure. The latter allows o ne to construct a canonical representation of the character variety\, whic h happens to be equivariant with respect to an action of the mapping class group of $S$. It was conjectured by the authors that these representation s behave well with respect to cutting and gluing of surfaces\, which in tu rn yields an analogue of a modular functor. In this talk\, I will show how the quantum group and its positive representations arise in this context. I will also explain how the modular functor conjecture is related to the closedness of positive representations under tensor products as well as to the non-compact analogue of the Peter-Weyl theorem. If time permits\, I w ill say a few words about the proof of the conjecture.\n\nThis talk is bas ed on joint works with Gus Schrader.\n LOCATION:https://researchseminars.org/talk/TQFT/15/ END:VEVENT END:VCALENDAR