Research

Takuro Mochizuki is working on complex differential geometry, algebraic geometry, and algebraic analysis. One of his main themes is pursuing equivalences between objects in algebraic geometry and differential geometry. In particular, he established the Kobayashi-Hitchin correspondence between good filtered flat bundles and good wild harmonic bundles. As an application, he obtained an equivalence between semisimple holonomic D-modules and polarizable pure twistor D-modules to prove the decomposition theorem for semisimple holonomic D-modules via projective morphisms. He also studied correspondences between monopoles with periodicity and difference modules. Relatedly, he has been investigating the existence of harmonic metric on some types of Higgs bundles on non-compact Riemann surfaces, the asymptotic behavior of large-scale solutions of the Hitchin equation, and the asymptotic behavior of the Hitchin metric on the moduli space of Higgs bundles. It is another theme of Mochizuki to develop the theory of twistor D-modules. He obtained the basic functorial properties of mixed twistor D-modules. He applied them to studying the Kontsevich complexes associated with algebraic functions. More recently, he studied some fundamental properties of the irregular Hodge filtrations associated with rescalable mixed twistor D-modules.