## Geometric Representation Theory Seminar: Microlocal mirror symmetry and a new coherent theory on open manifolds

Seminar | November 29 | 11 a.m.-12:30 p.m. | 732 Evans Hall

Dmitry Vaintrob, IAS

Department of Mathematics

I will talk about my recent proof of a mirror symmetry statement for microlocal Fukaya categories associated to an $n$-dimensional symplectic cylinder, $T^*(S^1)^n$. Along the way I will define a remarkable new category of coherent sheaves, which I call the log-coherent category (a close cousin of the parabolic coherent category), associated to an open algebraic variety $U$ with choice of compactification $X$, which should be the mirror to microlocal Fukaya categories in a more general SYZ mirror symmetry context. This category in itself is really interesting, and in positive and mixed characteristic its Hochschild theory gives new log invariants of algebraic varieties over local fields which has structures fully analogous to Bhatt, Morrow and Scholze's integral p-adic Hodge theory (originally defined in a very different and much more complicated way).

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