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A classical construction in topology associates to a spaceÌýX and primeÌý p, a new "localized" space X_p whose homotopy and homology groups are obtained from those ofÌý 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} MÌý– twisted complexes of Lagrangians – are quasi-isomorphic to actual Lagrangians.

This talk is based on joint work with Z. Sylvan.

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