Staff -MOCHIZUKI, Takuro-
Name
MOCHIZUKI, Takuro
MOCHIZUKI, Takuro
Position
Professor
Professor
E-Mail
takuro (email address: add @kurims.kyoto-u.ac.jp)
takuro (email address: add @kurims.kyoto-u.ac.jp)
Research
I have been interested in D-modules
on algebraic varieties for many years.
D-module was introduced
for the study on linear differential equations.
Since then, it has been investigated intensively,
and turned out to be related with
various fields of mathematics.
Many Japanese mathematicians,
in particular M. Sato, M. Kashiwara,
T. Kawai and M. Saito,
have played the leading roles
in creation and development of
the theory of D-module.
I proved that the category of semisimple holonomic D-modules is preserved by various procedures. It is a supreme variant of the fundamental theorem due to A. Beilinson, J. Bernstein, P. Deligne and O. Gabber. It was conjectured by Kashiwara, and expected to take a long time for the solution.
I was luckily able to solve this challenging problem with a help of fruit of progress in a different field. Before attacking it, I investigated a generalization of C. Simpson's work on harmonic bundle. Namely, I studied the asymptotic behaviour of a harmonic bundle around singularity. I applied it to the theory of pure twistor D-module, which was introduced by C. Sabbah based on Saito's pure Hodge module, and I established the connection between semisimple holonomic D-modules and polarizable pure twistor D-modules. Then, I arrived at the affirmative solution of Kashiwara's conjecture.
I have also investigated holonomic D-modules with some enriched structures, such as Betti structure and mixed twistor structure. I hope that it will be a part of foundation of an interesting research area. I also want to challenge subjects which are new for me.
I proved that the category of semisimple holonomic D-modules is preserved by various procedures. It is a supreme variant of the fundamental theorem due to A. Beilinson, J. Bernstein, P. Deligne and O. Gabber. It was conjectured by Kashiwara, and expected to take a long time for the solution.
I was luckily able to solve this challenging problem with a help of fruit of progress in a different field. Before attacking it, I investigated a generalization of C. Simpson's work on harmonic bundle. Namely, I studied the asymptotic behaviour of a harmonic bundle around singularity. I applied it to the theory of pure twistor D-module, which was introduced by C. Sabbah based on Saito's pure Hodge module, and I established the connection between semisimple holonomic D-modules and polarizable pure twistor D-modules. Then, I arrived at the affirmative solution of Kashiwara's conjecture.
I have also investigated holonomic D-modules with some enriched structures, such as Betti structure and mixed twistor structure. I hope that it will be a part of foundation of an interesting research area. I also want to challenge subjects which are new for me.