Stable Weinstein geometry through localizations

Abstract: Much of computational math is formula-driven, while much of categorical math is formalism-driven. Mirror symmetry is rich in part because many of its results are driven by both. With the advent of stable-homotopy-theoretic invariants in symplectic geometry, there has been a real need for better-behaved formalisms in symplectic geometry. In this talk, we will talk about recent success in constructing the formalism, especially in the setting of certain non-compact symplectic manifolds called Weinstein sectors. The results have concrete geometric consequences, like showing that spaces of embeddings of these manifolds map continuously to spaces of maps between certain invariants. (And in particular, leads to higher-homotopy-group generalizations, in the Weinstein setting, of the Seidel homomorphism, similar to works of Savelyev and Oh-Tanaka.) The main result we'll discuss is that the infinity-category of stabilized sectors can be constructed using the categorically formal process of localization. Most of what we discuss is joint with Oleg Lazarev and Zachary Sylvan.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar