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Mirror Symmetry Seminar

Cohomological Hall algebra of a curve

Francesco Sala (IPMU)

Location:  Serrin E372
Date & time: Thursday, 21 September 2017 at 1:30PM - 2:30PM

Cohomological Hall algebras associated with preprojective algebras of quivers play a preeminent role in algebraic geometry and representation theory. For example, if the quiver is the 1-loop quiver, the corresponding CoHA is the Maulik-Okounkov affine Yangian of gl(1). It acts on the equivariant cohomology of Hilbert schemes of points on the complex affine place ("extending" previous results of Nakajima, Grojnowski, Vasserot, etc, for action of Heisenberg algebras) and moduli spaces of framed sheaves on the complex projective plane. In the present talk, I will follow the recipe of "replacing quivers with curves" and I will end up by introducing cohomological Hall algebras associated with the stack of Higgs sheaves on a smooth projective complex curve. (This is a joint work with Olivier Schiffmann)

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Department of Mathematics

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