BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adrien Brochier (Université Paris Cité) DTSTART:20240417T160000Z DTEND:20240417T170000Z DTSTAMP:20260423T024744Z UID:TQFT/109 DESCRIPTION:Title: A classification of modular functors from generalized skein theory\nby Adrien Brochier (Université Paris Cité) as part of Topological Quantum F ield Theory Club (IST\, Lisbon)\n\n\nAbstract\nModular functors are collec tions of projective representations of mapping class groups of surfaces\, compatible with cutting and gluing operations. They can be thought of as c ategorified\, anomalous 2d topological field theories (TFT) where the "ano maly" is responsible for the projectiveness of the représentations.\n\nA well-known folklore theorem states that ordinary 2d TFT are classified by (commutative) Frobenius algebras. In a similar way\, any modular functor y ields a "categorified Frobenius algebra"\, of which ribbon categories form a large class of examples. In this talk\, we'll explain a necessary and s ufficient condition for such a structure to extend to a modular functor\, formulated in terms of certain generalized skein modules attached to handl ebodies. A key observation is that this is\, indeed\, a condition\, not ex tra structure\, so that such an extension is essentially unique whenever i t exists.\n\nThis construction should be thought of as a far reaching gene ralization of the construction by Masbaum and Roberts of a modular functor from Kauffman skein modules. As a special case it also recovers\, in a pu rely topological way\, the construction of a modular functor from a (not n ecessarily semisimple) modular category by Lyubachenko\, and the uniquenes s result is new even in those cases. This is based on joint work with Luka s Woike.\n LOCATION:https://researchseminars.org/talk/TQFT/109/ END:VEVENT END:VCALENDAR