AaDAG seminar

Wednesday, 7 June, 2017, at 15:15-16:15, (1530-326) QGM Lounge

Abstract:

K-theoretic and Cohomological Hall algebras of preprojective algebras play a preeminent role in algebraic geometry, representation theory and mathematical physics.

For example, if the preprojective algebra is the one of the Jordan quiver, the corresponding CoHA contains the Maulik-Okounkov Yangian associated with the Jordan quiver. It acts on the equivariant cohomology of Hilbert schemes of points on the complex affine plane ("extending" the previous results of Nakajima, Grojnowski, Vasserot, etc for actions of Heisenberg algebras) and of moduli spaces of framed sheaves on the complex projective plane. The latter action yields an action of W-algebras and hence provides a proof of the Alday-Gaiotto-Tachikawa conjecture for pure supersymmetric gauge theories on the real four-dimensional space.

In this talk, I will discuss K-HAs/CoHAs associated with the (derived) stack of (nilpotent) Higgs sheaves on a smooth projective complex curve.

For example, if the preprojective algebra is the one of the Jordan quiver, the corresponding CoHA contains the Maulik-Okounkov Yangian associated with the Jordan quiver. It acts on the equivariant cohomology of Hilbert schemes of points on the complex affine plane ("extending" the previous results of Nakajima, Grojnowski, Vasserot, etc for actions of Heisenberg algebras) and of moduli spaces of framed sheaves on the complex projective plane. The latter action yields an action of W-algebras and hence provides a proof of the Alday-Gaiotto-Tachikawa conjecture for pure supersymmetric gauge theories on the real four-dimensional space.

In this talk, I will discuss K-HAs/CoHAs associated with the (derived) stack of (nilpotent) Higgs sheaves on a smooth projective complex curve.

Organised by: QGM

Contact person: Artan Sheshmani