T&G: Yusuf Baris Kartal (Princeton), Categorical action filtrations in symplectic topology

Tue, 09/11/202118:00-19:00
Filtered vector spaces arise naturally in symplectic and algebraic geometry. For instance, given Liouville manifold, one can define its symplectic cohomology-- the cohomology of a chain complex that combines the cohomology of the manifold with the Reeb orbits on its contact boundary-- and it is filtered by the length of the Reeb orbits. Similarly, in algebraic geometry, given a non-proper variety with a chosen compactification, one can filter the ring of functions by the order of pole at infinity. In this talk, we explain how to obtain equivalent filtrations from purely categorical data, using the notion of "smooth categorical compactifications". This allows us to compare the growth of the filtrations in symplectic and algebraic geometry when there is a mirror equivalence, and also to use other homological techniques to deduce results about the growth. This is joint work with Laurent Cote.