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Explore a lecture on "Morse Theory of Loop Spaces and Hecke Algebras" presented by Roman Krutowski from the University of California, Los Angeles as part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar. Delve into the mathematical connections between HDHF (symmetric) wrapped Fukaya categories and Liouville domains through the counting of higher genus curves that are branched covers. Learn about Honda, Tian, and Yuan's demonstration that the A∞-algebra associated with k disjoint cotangent fibers is quasi-equivalent to the HOMFLY-PT braid skein algebra for cotangent bundles of orientable surfaces with genus at least one. Discover the Morse-theoretic model that computes the HDHF A∞-algebra of k fibers of the cotangent bundle of orientable smooth manifolds, with specific application to the two-dimensional sphere case. The presentation covers joint work with Honda, Tian, and Yuan and offers insights into advanced topics in symplectic geometry.
