Geometry of quiver varieties and representation theory

考虑复杂代数曲面在某一点上的爆破。与Yoshioka一起，我在凝聚层的派生范畴中引入了一个交换范畴，称为逆凝聚层范畴，并研究了它的模空间。作为应用，我进一步与Gottsche一起证明了Witten猜想等于复杂曲面的Donaldson不变量和Seiberg-Witten不变量。

Consider the blowup of a complex algebraic surface at a point. Together with Yoshioka, I introduced an abelian category in the derived category of coherent sheaves, called the category of perverse coherent sheaves, and study its moduli spaces. As an application, further with Gottsche, I proved Witten's conjecture equating Donaldson invariants and Seiberg-Witten invariants for complex surfaces.