Research

Hiraku Nakajima is working on the interplay between geometry and representation theory. More specially he has defined the quiver varieties, as moduli spaces of coherent sheaves on the minimal resolution of simple singularities and constructed integrable representations of affine Kac-Moody algebras and quantum toroidal algebras on their cohomology groups and equivariant K-group respectively. Many representation theoretic results can be deduced from the geometry of quiver varieties. He is also interested in Donaldson type invariants defined by similar moduli spaces, and a mathematical definition of Coulomb branches of supersymmetric gauge theories.