Francesco Sala

Nakajima’s seminal work was followed by a plethora of results about the geometry and topology of Hilbert schemes of points of smooth surfaces, and more generally, of moduli spaces of torsion free sheaves (stable, framed, etc) on smooth surfaces. These results were mainly obtained by means of representation theoretic techniques. Recently, thanks to Schiffmann and Vasserot’s work, a new research direction has emerged: the search of hidden algebraic structures of K-theory, homology, etc, of moduli stack of torsion sheaves on smooth surfaces. 

 

Schiffmann and Vasserot focused on the study of these algebraic structures for the moduli stack of zero-dimensional sheaves on the affine plane. In this talk, I will discuss the case of torsion sheaves on the cotangent bundle of a smooth projective curve. This reduces to the introduction of an associative algebra structure "à la Hall” on the cohomology of the stacks of Higgs bundles and sheaves (semistable or not, nilpotent or not) on a smooth projective complex curve X, and its characterization.