Roman Krutowski, UCLA

Abstract: Higher-dimensional Heegaard Floer homology (HDHF), and more generally higher-dimensional Heegaard Floer Fukaya category, arises as a generalization of Lipshitz's cylindrical reformulation of Heegaard Floer homology. In this talk, I will introduce the HDHF Fukaya category and speak about the HDHF of the cotangent bundle of surfaces. In particular, I will show the existence of an isomorphism between the HDHF of a tuple of cotangent fibers at distinct points on a surface S and a braid skein algebra BSk(S) of the surface. As a corollary, we will see that HDHF is isomorphic to the double affine Hecke algebra (DAHA) in the case of S=T^2. Time permitting, we will talk about the action of DAHA on the HDHF Fukaya category of the torus.