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There is notion of a smooth categorical compactification of dg/A-infinity categories: for example, a smooth compactification of algebraic varieties induces a smooth categorical compactification of the associated bounded dg categories of coherent sheaves. In symplectic topology, wrapped Fukaya categories of Weinstein manifolds admit smooth compactifications by partially wrapped Fukaya categories. 

The goal of this talk is to explain how to associate an "action filtration" to a smooth categorical compactifications, which is invariant (up to appropriate equivalence) under zig-zags of smooth compactifications. I will then discuss applications to symplectic topology and categorical dynamics. 

This talk reports on joint work with Y. Baris Kartal.