BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Ayala (Montana State University) DTSTART:20240807T160000Z DTEND:20240807T170000Z DTSTAMP:20260423T040227Z UID:TQFT/122 DESCRIPTION:Title: F actorization homology of higher categories\nby David Ayala (Montana St ate University) as part of Topological Quantum Field Theory Club (IST\, Li sbon)\n\n\nAbstract\nThe “alpha” version of factorization homology pai rs framed n-manifolds with $E_n$-algebras. This construction generalizes the classical homology of a manifold\, yields novel results concerning con figuration spaces of points in a manifold\, and supplies a sort of state-s um model for sigma-models (i.e.\, mapping spaces) to (n-1)-connected targe ts. This “alpha” version of factorization homology novelly extends Po incaré duality\, shedding light on deformation theory and dualities among field theories. Being defined using homotopical mathematical foundations \, “alpha” factorization homology is manifestly functorial and continu ous in all arguments\, notably in moduli of manifolds and embeddings betwe en them\, and it satisfies a local-to-global expression that is inherently homotopical in nature. \n\nNow\, $E_n$-algebras can be characterized as $(\\infty\,n)$-categories equipped with an (n-1)-connected functor from a point. The (full) “beta” version of factorization homology pairs fram ed n-manifolds with pointed $(\\infty\,n)$-categories with adjoints. Appl ying 0th homology\, or $\\pi_0$\, recovers a version of the string net con struction on surfaces\, as well as skein modules of 3-manifolds. In some sense\, the inherently homotopical nature of (full) “beta” factorizati on homology affords otherwise unforeseen continuity in all arguments\, and local-to-global expressions. \n\nIn this talk\, I will outline a definit ion of “beta” factorization homology\, focusing on low-dimensions and on suitably reduced $(\\infty\,n)$-categories (specifically\, braided mono idal categories). I will outline some examples\, and demonstrate some fea tures of factorization homology. Some of this material is established in the literature\, some a work in progress\, and some conjectural — the st atus of each assertion will be made clear. I will be especially intereste d in targeting this talk to those present\, and so will welcome comments a nd questions.\n LOCATION:https://researchseminars.org/talk/TQFT/122/ END:VEVENT END:VCALENDAR