# Seminars & Colloquia Calendar

Geometry, Symmetry and Physics Seminar

## Categorification of 2d cohomological Hall algebras

#### Francesco Sala, IPMU

Location:  Serin Lab E372
Date & time: Thursday, 11 April 2019 at 1:00PM - 2:00PM

Abstract: Let $$\mathcal{M}$$ 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 $$\mathcal{M}$$ 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 $$\mathcal{M}$$. This is achieved by exhibiting a derived enhancement of $$\mathcal{M}$$. 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 a paper with Mauro Porta ( arXiv:1903.07253).

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