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Title:
Double Affine Hecke Algebra and Instanton Counting
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Abstract:
I shall discuss how double affine Hecke algebra (DAHA) arises in different physical and mathematical contexts including deformation quantization, enumerative geometry as well as instanton and vortex counting. For spherical DAHA of rank one we study geometrically its category of representations and provide a conjectured relation of this category with Fukaya category of the space whose quantization gives DAHA. We also discuss rank-n DAHAs and their stable limit when n goes to infinity. This leads us to elliptic Hall algebras acting on the moduli spaces of instantons.
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