I am mainly interested in algebraic geometry.
More precisely, I am working on the birational
geometry of higher-dimensional algebraic varieties.
In the early 1980s, Shigefumi Mori initiated a new
approach for higher-dimensional birational geometry,
which is now usually called the Minimal Model Program
or Mori theory. Unfortunately, this beautiful approach
has not been completed yet. One of my dreams
is to complete the Minimal Model Program in full
generality. I am also interested in toric geometry,
Hodge theory, complex geometry, and so on.