Seminars & Colloquia Calendar
Hecke algebras via Morse theory of loop spaces
Roman Krutowski (UCLA)
Location: Hill 525
Date & time: Friday, 10 October 2025 at 12:30PM - 1:30PM
Abstract: Higher-dimensional Heegaard Floer homology (HDHF) is defined by extending Lipshitz's cylindrical reformulation of Heegaard Floer homology from surfaces to arbitrary Liouville domains. The HDHF also serves as a model for Lagrangian Floer homology of symmetric products.
In this talk, I will present a Morse-theoretic model allowing for computations of the HDHF A_infty-algebra of k cotangent fibers in the cotangent bundle of a smooth manifold. We apply this model to get an explicit computation of this A_infty-algebra for the cotangent bundle of the 2-dimensional sphere. The result of this computation produces a differential graded algebra which may be regarded as the derived HOMFLYPT skein algebra of the sphere.
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