BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Matthew Young (Utah State University) DTSTART:20230202T223000Z DTEND:20230203T000000Z DTSTAMP:20260423T005721Z UID:PIMS_GAP/11 DESCRIPTION:Title: $U_q(\\mathfrak{gl}(1 \\vert 1))$ and $U(1 \\vert 1)$ Chern--Simons theo ry\nby Matthew Young (Utah State University) as part of PIMS Geometry / Algebra / Physics (GAP) Seminar\n\n\nAbstract\nChern--Simons theory\, as introduced by Witten\, is a three dimensional quantum gauge theory associ ated to a compact simple Lie group and a level. The mathematical model of this theory as a topological quantum field theory was introduced by Reshet ikhin and Turaev and is at the core of modern quantum topology. The goal o f this talk is to explain a non-semisimple modification of the constructio n of Reshetikhin and Turaev which realizes Chern--Simons theory with gauge supergroup $U(1 \\vert 1)$\, as studied in the physics literature by Roza nsky--Saleur and Mikhaylov. In particular\, I'll motivate and explain vari ous relative modular structures on the category of representations of the quantum group of $\\mathfrak{gl}(1 \\vert 1)$ which should be seen as non- semisimple analogues of modular tensor categories associated to the quantu m representation theory of a simple Lie algebra at a root of unity. Based on joint work with Nathan Geer.\n LOCATION:https://researchseminars.org/talk/PIMS_GAP/11/ END:VEVENT END:VCALENDAR