My original research area is algebraic geometry and I have studied quotient singularities and the resolution. When I started to learn algebraic geometry, I came across an amazing problem on singularities from superstring theory. It implies a generalization of two-dimensional McKay correspondence. I studied several ways to construct crepant resolutions of quotient singularities for three-dimensional McKay correspondence. The McKay correspondence is now generalized to a higher dimensional case in terms of derived categories. However, there are two problems: most results hold only for abelian finite subgroups. Moreover, they need a crepant resolution. To show the existence of a crepant resolution is difficult in general, but I believe there is a way, and non-abelian cases may bring us new mathematics. I would like to expand my mathematical world at the Kavli IPMU with many other mathematicians and physicists.