Abstract: We show how to recover the (finite) Hecke algebra by directly computing the wrapped higher-dimensional Heegaard Floer homology of cotangent fibers of the disk. More generally, the finite, affine, and double affine Hecke algebras correspond to that of the disk, the annulus, and the torus, respectively. We also propose a Morse model of symmetric product spaces, which is expected to recover the (finite) Hecke algebra as well. This is joint work with Yin Tian.
