Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

A classical construction in topology associates to a space $X$ and prime $p$, a new "localized" space $X_p$ whose homotopy and homology groups are obtained from those of $X$ by inverting $p$. In this talk, I will discuss a symplectic analog of this construction, extending work of Abouzaid-Seidel and Cieliebak-Eliashberg on flexible Weinstein structures. Concretely, I will produce prime-localized Weinstein subdomains of high-dimensional Weinstein domains and also show that any Weinstein subdomain of a cotangent bundle agrees Fukaya-categorically with one of these special subdomains. The key will be to classify which objects of the Fukaya category of $T^{\ast} M$ – twisted complexes of Lagrangians – are quasi-isomorphic to actual Lagrangians. This talk is based on joint work with Z. Sylvan.