Higgs sheaves on a curve and Cohomological Hall algebras

Francesco Sala
(Kavli IPMU, Japan)
AaDAG seminar
Wednesday, 7 June, 2017, at 15:15-16:15, (1530-326) QGM Lounge
Abstract:
Cohomological Hall algebras associated with preprojective algebras of quivers play a preeminent role in geometric representation theory and mathematical physics. For example, if the preprojective algebra is the one of the Jordan quiver (i.e., the quiver with one vertex and one loop), 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 the present talk, I will introduce and describe CoHAs associated with the stack of Higgs sheaves on a smooth projective curve. Moreover, I will address the connections with representation theory and gauge theory. (This is a joint work with Olivier Schiffmann.)
Organised by: QGM
Contact person: Artan Sheshmani