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This lecture from the Unni Namboodiri Lectures in Geometry and Topology series features Princeton mathematician Peter Ozsvath discussing the journey from Heegaard diagrams to holomorphic disks. Explore Heegaard Floer homology, a powerful tool for studying three- and four-dimensional manifolds using methods inspired by symplectic geometry. Learn about various manifestations of this theory, including knot Floer homology for studying knots in three-manifolds and bordered Floer homology for examining three-manifolds with parameterized boundary. Discover both the topological applications of this theory and computational advances that connect Floer homology with other algebraic objects in symplectic geometry. The lecture acknowledges that Heegaard Floer homology was originally discovered through joint work with Zoltan Szabo. This one-hour presentation is hosted by the University of Chicago Department of Mathematics as part of the 2025 lecture series.
