Research

Takuro Mochizuki is working on complex differential geometry, algebraic geometry, and algebraic analysis. One of his main themes is to pursue correspondences between objects in algebraic geometry and differential geometry. For example, he established an equivalence between semisimple algebraic holonomic D-modules and pure twistor D-modules, which he applied to prove the decomposition theorem for the projective push-forward of semisimple algebraic holonomic D-modules, conjectured by Kashiwara. More recently, he is interested in equivalences between monopoles with periodicity and various types of difference modules. Another central theme is the irregular singularity of D-modules. For example, he recently obtained a characterization for a complex of enhanced ind-sheaves induced by a holonomic D-modules, called the curve test.