Abstract: Given any smooth projective curve, one can define a Hall algebra-type structure on the cohomology of a moduli stack of coherent sheaves on the curve, called the cohomological Hall algebra of a curve (CoHA). In this talk, I will explain how CoHA is defined and show that CoHA naturally acts on the virtual homology of the Quot schemes. Virtual homology is a cohomological analog of the numerical invariants associated with the virtual fundamental class. If time permits, I will explain how one can define a double of the subalgebra of torsion sheaves and describe it in terms of generators and relations. This talk is based on joint work with Woonam Lim.