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Tasos Moulinos (Paris): Betti realizations of noncommutative motives
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https://youtu.be/ZBPpDtLekmk?si=zdv8b-UMXQAS0a0K This talk was part of the workshop "Motivic and non-commutative aspects of enumerative geometry" held in July 2023 at Radboud University, Nijmegen, The Netherlands. Abstract: In this talk, I will survey some past work of mine on the topological K-theory of dg categories. This is an invariant of complex dg-categories, taking values in the infinity category of KU-module spectra. I will begin the talk with some motivation coming by way of Hodge theoretic mirror symmetry, and will proceed to describe the basic construction, originally due to A. Blanc. I will then describe a variant of this construction from previous work, relative to any base complex scheme, together with applications of such a construction towards computations in twisted K-theory, and towards the theory of variations of Hodge structures. Time permitting, I will describe ongoing work, incorporating Hermitian structures and real topological K-theory into the picture.
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