[geometry-ml:05023] 1/24 GTM seminar

[Hiraku Nakajima]

皆様

直前になってすいません。

1/24 (Tue.) のGTM seminarをご案内申し上げます。

Speaker: Dogancan Karabas
Title: Sheaf-theoretical approach to Fukaya categories of Weinstein
manifolds
Date (JST): Tue, Jan 24, 2023, 15:30 - 17:00
Place: hybrid (対面はIPMUのメンバーに限られます)
Zoom: Meeting ID: 511 392 0663

password: 166602


Abstract: It is shown by Kashiwara and Schapira (1980s) that for every
constructible sheaf on a smooth manifold, one can construct a closed conic
Lagrangian subset of its cotangent bundle, called the microsupport of the
sheaf. This eventually led to the equivalence of the category of
constructible sheaves on a manifold and the (wrapped) Fukaya category of
its cotangent bundle by the work of Nadler and Zaslow (2006), and Ganatra,
Pardon, and Shende (2018). The latter authors also showed that this
equivalence holds for a more general class of symplectic manifolds, called
Weinstein manifolds. Namely, they introduced a way to compute wrapped
Fukaya categories of Weinstein manifolds by taking the homotopy colimit of
wrapped Fukaya categories of their sectorial coverings. I will talk about
the relevant definitions and results, and categorical/computational aspects
of Fukaya categories. In particular, I will explain our formula computing
homotopy colimits of dg categories, and its applications including
expressing wrapped Fukaya categories of plumbing spaces as perfect modules
over Ginzburg dg algebras (work in progress with Sangjin Lee).

中島 啓

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