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Title:
Categorical action filtrations on wrapped Floer homology
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Abstract:
Filtered vector spaces arise naturally in both symplectic and algebraic geometry: for instance, the symplectic cohomology of a Liouville domain is roughly filtered by the length of the Reeb orbits. Similarly, the cohomology groups of coherent sheaves on a smooth affine variety are filtered by the order of pole at infinity. In this talk, we explain how to categorify these invariants using the notion of ``smooth categorical compactification''. This allows us to relate the growth of filtrations on symplectic and algebraic geometry via mirror symmetry, and also to use homological techniques to deduce results about these growth functions. This is joint work with Laurent Cote.
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