Abstract: Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a special case, it's related to symplectic Khovanov homology. In this talk, we discuss HDHF of contangent fibers of the cotangent bundle of an oriented surface and show that it is isomorphic to various Hecke algebras. This is a joint work with Ko Honda and Tianyu Yuan.
