Title: Moduli spaces and algebras associated to curves
Speaker: Niccolò Giacomini (EPFL)
Abstract: This talk is an accessible introduction to cohomological Hall algebras of smooth complex projective curves. A common theme in representation theory is recovering geometric information about moduli spaces (e.g. Hilbert schemes of points, Quot schemes…) by realizing their cohomology as a representation for big algebras of operators.
In the first part of the talk I am going to explain this concept by means of a toy example, based on the works of Marian and Negut. Moreover, the algebraic structure of such algebras is heavily dependent on the geometry involved. In the second part of the talk I will make this connection precise by defining cohomological Hall algebras. Finally, I will discuss some further applications and future directions.
Some snacks will be provided before and after the talk.