Last Update 2017/09/26 11:12:25
My research interests are algebraic geometry, geometric representation theory, and mathematical physics. At the moment I study different realizations of Hall algebras and their refined versions (K-theoretical/cohomological) by using (Higgs) sheaves on curves. One can construct geometric representations of these algebras by using the K-theory/cohomology of moduli spaces of torsion- free sheaves on resolutions of A-type toric singulaties and Nakajima cyclic quiver varieties. This yields
to applications in physics, most notably in four- dimensional supersymmetric gauge theories on A-type ALE spaces and the AGT conjecture for these theories.
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