BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:James Macpherson (Instituto Superior Técnico) DTSTART:20230208T170000Z DTEND:20230208T180000Z DTSTAMP:20260423T024614Z UID:TQFT/74 DESCRIPTION:Title: Lo cally wide quasi-fiat 2-categories and their coalgebra 2-representations\nby James Macpherson (Instituto Superior Técnico) as part of Topologic al Quantum Field Theory Club (IST\, Lisbon)\n\nLecture held in Room 3.10 ( 3rd floor\, Mathematics Department\, Instituto Superior Técnico).\n\nAbst ract\nFinitary 2-representation theory\, pioneered by Mazorchuk and Miemie tz in 2010\, is a categorification of finite dimensional representations o f finite dimensional algebras. It primarily studies the 2-representation t heory of finitary 2-categories\, which are additive\, linear\, Krull-Schmi dt 2-categories with various finiteness conditions. Much progress has been made in the area since\, including various results that fall under the co nceptual banner of 'internal vs. external' - that is\, finding equivalence s between arbitrary 'external' 2-representations and 'internal' 2-represen tations whose data is fully encoded with the finitary 2-category itself.\n \nIn this talk\, I will start by outlining the basic theory of finitary 2- categories and their finitary 2-representations\, and I will discuss two e xamples of 'internal' 2-representations\, namely cell 2-representations an d 2-representations formed of comodule 1-morphisms over a coalgebra 1-morp hism. I will then discuss relaxing the finiteness assumptions of finitary 2-categories\, resulting in a type of 2-category called 'locally wide fini tary 2-categories'. After discussing some of the difficulties this introdu ces\, I will focus on a specific type of locally wide finitary 2-category\ , namely locally wide quasi-fiat 2-categories\, and discuss what we know a bout coalgebra 1-morphisms and their associated 2-representations in this case.\n LOCATION:https://researchseminars.org/talk/TQFT/74/ END:VEVENT END:VCALENDAR