BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Patrick Kinnear (University of Edinburgh) DTSTART:20230628T160000Z DTEND:20230628T170000Z DTSTAMP:20260423T021352Z UID:TQFT/91 DESCRIPTION:Title: Va rying the non-semisimple Crane–Yetter theory over the character stack\nby Patrick Kinnear (University of Edinburgh) as part of Topological Qua ntum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nAssociated to a certa in subquotient of the category of representations of the small quantum gro up at a root of unity is an invertible 4d TQFT known as Crane–Yetter: it is the anomaly theory of the 3d theory called Witten–Reshetikhin–Tura ev. In fact\, the non-semisimplified representation category is invertible in the Morita theory of braided tensor categories: under the cobordism hy pothesis this defines a non-semisimple invertible TQFT. Such an invertible theory assigns to a closed 3-manifold a 1-dimensional vector space. In th is talk\, we define a relative TQFT which can be seen as varying non-semis imple Crane-Yetter over the character stack: it assigns to a closed 3-mani fold $M$ a line bundle on its character stack $\\mathrm{Ch}_G(M)$. We cons truct this theory by analysing invertibility of a 1-morphism in the Morita theory of symmetric tensor categories\, coming from representations of Lu sztig's quantum group at a root of unity regarded as a bimodule for $\\mat hrm{Rep}(G)$ using the quantum Frobenius map. In the talk we will describe this 1-morphism and analyse its invertibility and the consequences of thi s in detail.\n LOCATION:https://researchseminars.org/talk/TQFT/91/ END:VEVENT END:VCALENDAR