BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) DTSTART:20220119T170000Z DTEND:20220119T180000Z DTSTAMP:20260423T021410Z UID:TQFT/48 DESCRIPTION:Title: Si mplicial vector bundles and representations up to homotopy\nby Giorgio Trentinaglia (Instituto Superior Técnico\,Lisbon) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\nThe classical Dol d–Kan correspondence for simplicial objects in an abelian category is on e of the cornerstones of homological algebra. When the abelian category is that of vector spaces\, it gives a full identification between simplicial vector spaces and chain complexes of vector spaces vanishing in negative degrees. The Grothendieck construction for fibered categories\, on the oth er hand\, is a cornerstone of category theory. It relates the fibered cate gory point of view with the pseudo-functor point of view and lies at the h eart of the theory of stacks. Our main result can be understood as a far-r eaching simultaneous generalization of both ideas within the contexts of l inear algebra and differential geometry. In our result\, simplicial vector spaces and chain complexes of vector spaces are replaced respectively by vector fibrations over a given (higher) Lie groupoid G and by representati ons up to homotopy of G. (Joint work with Matias del Hoyo.)\n LOCATION:https://researchseminars.org/talk/TQFT/48/ END:VEVENT END:VCALENDAR