Francesco Sala

Last Update 2024/02/15
My research interests are geometric representation theory, algebraic geometry, and mathematical physics. At the moment I am studying algebraic structures (called Hall algebras structure) on the homology (Gtheory, etc) of moduli stacks parametrizing objects in 2dimensional CY categories. In particular, I have already defined, together with O. Schiffmann, a cohomological Hall algebra for the moduli stack of Higgs sheaves (nilpotent or not, semistable or not) on a smooth projective curve. When the curve is the projective line, such algebras are related to the cohomology of moduli spaces of torsionfree sheaves on resolutions of Atype toric singularities and Nakajima cyclic quiver varieties. This yields to applications in physics, most notably in fourdimensional supersymmetric gauge theories on Atype ALE spaces and the AGT conjecture for these theories.
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