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Introduction to Fukaya categories, Talk 1

Posted in
Jie Min
Mon, 24/01/2022 - 15:00 - 16:00

For zoom details please contact T. Barthel, V. Ozornova, A. Ray, P. Teichner.

Miniseries abstract: The Fukaya category is an invariant of a symplectic manifold governing the intersection theory of its Lagrangian submanifolds, built from the pseudoholomorphic disks which bound these Lagrangians. One particularly important version for non-compact symplectic manifolds is the partially wrapped Fukaya category, which plays a prominent role in homological mirror symmetry. This miniseries will lead up to a toolbox for computing and studying structural properties of partially wrapped Fukaya categories. One of the key tools is a descent formula, i.e. a cosheaf property with respect to Weinstein sectorial coverings. We will emphasize concrete examples, and homological mirror symmetry will be a recurring point of reference.

Abstract of talk: This is meant to be a non-technical introduction to Fukaya categories. Fukaya categories are invariants of symplectic manifolds, containing intersection information of Lagrangian submanifolds, and play a vital role in Kontsevich's homological mirror symmetry conjecture. I will also introduce variants of Fukaya categories for exact symplectic manifolds and present some simple examples.

Datei Miniseries Symplectic topology 1.pdf14.76 MB
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