Speaker: Roman Krutowski (University of California, Los Angeles)   

Title: Hecke algebras via Morse theory of loop spaces.

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_∞ -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_∞-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.

This talk is based on joint work with Ko Honda, Yin Tian, and Tianyu Yuan.