|Speaker:||Sala, Francesco (IPMU)|
|Title:||Categorification of 2d cohomological Hall algebras|
|Date (JST):||Thu, Apr 25, 2019, 15:30 - 16:30|
|Place:||Seminar Room A|
Let M denote the moduli stack of either coherent sheaves on a smooth projective surface or Higgs sheaves on a smooth projective curve X. The convolution algebra structure on the Borel-Moore homology of M is an instance of two-dimensional cohomological Hall algebras.
In the present talk, I will describe a full categorification of the cohomological Hall algebra of M. This is achieved by exhibiting a derived enhancement of M. Furthermore, this method applies also to several other moduli stacks, such as the moduli stack of vector bundles with flat connections on X and the moduli stack of finite-dimensional representations of the fundamental group of X. In the second part of the talk, I will focus on the case of curves and discuss some relations between the Betti, de Rham, and Dolbeaut categorified cohomological Hall algebras. This is based on joint work with Mauro Porta,