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In this lecture, Filip Zivanovic from the Simons Center for Geometry and Physics explores a curious filtration derived from Floer theory and C*-actions. Discover how Zivanovic and Alexander Ritter constructed a Floer-theory invariant called symplectic cohomology for open symplectic manifolds that admit pseudo-holomorphic C*-actions. Learn about the resulting filtration on ordinary cohomology of these manifolds, which can be explicitly computed using Morse-Bott-Floer spectral sequences. Examine concrete examples of this filtration for ADE resolutions and low-dimensional Higgs bundles, with potential comparisons to other known filtrations for these spaces if time permits.
