Abstract: The goal of the present talk is the introduction of two-dimensional cohomological Hall algebras of quivers, curves, and surfaces, and discuss their categorification. In the first part of the talk, I will also provide some motivation to the theory of cohomological Hall algebras arising from the study of Hilbert schemes of points and moduli spaces of stable sheaves on smooth surfaces. In the last part of the talk, I will discuss in detail an ongoing joint work with Diaconescu, Schiffmann, and Vasserot, in which we consider the cohomological Hall algebra of a Kleinian surface singularity.

(Organisator: Professor Dr. Alexander Schmitt)