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Dualizability in the higher Morita category

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HHHW01 - Higher structures in homotopy theory

In this talk I will explain how one can use geometric arguments to obtain results on dualizablity in a ``factorization version’’ of the Morita category. We will relate our results to previous dualizability results (by Douglas-Schommer-Pries-Snyder and Brochier-Jordan-Snyder on Turaev-Viro and Reshetikin-Turaev theories). We will discuss applications of these dualiability results: one is to construct examples of low-dimensional field theories “relative” to their observables. An example will be given by Azumaya algebras, for example polynomial differential operators (Weyl algebra) in positive characteristic and its center. (This is joint work with Owen Gwilliam.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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