Fukaya category and sheaf theory over Novikov ring

Speaker: Tatsuki Kuwagaki (Kyoto University)

Time: 2025-11-10 15:00-18:00
Location: 1110, SIMIS
Zoom Meeting ID:822 3076 0473 Passcode:SIMIS

摘要：

The Fukaya category is a powerful invariant in symplectic geometry, defined through highly transcendental nonlinear analysis. Just as Morse cohomology is isomorphic to ordinary cohomology, certain Fukaya categories can be understood via topological methods. In particular, over the last decade, “exact Fukaya categories” have been deeply understood through microlocal sheaf theory. However, the framework of exact Fukaya categories is insufficient for addressing a wider range of Lagrangian submanifolds or for incorporating quantitative information. For the past five years, the speaker has been working on ideas that aim to prove an equivalence between the nonexact Fukaya categories of a class of exact symplectic manifolds and certain categories of sheaves, known as (equivariant) Tamarkin categories. In this talk, I will explain the main ideas and related notions that will eventually lead to the proof of this equivalence.