Takurō Mochizuki

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Takurō Mochizuki (2015)

Takurō Mochizuki ( Japanese 望月 拓 郎 Mochizuki Takurō ; born August 26, 1972 ) is a Japanese mathematician who deals with differential geometry and algebraic analysis (theory of D modules based on algebraic varieties).

Life

Mochizuki studied from 1992 at the University of Kyoto and received his doctorate there in 1999. He then went to Osaka City University , became Assistant Professor at Kyoto University in 2004 and Associate Professor at the Research Institute for Mathematical Sciences (RIMS) at Kyoto University in 2008 .

plant

Mochizuki researched the asymptotic behavior of harmonic vector bundles near singularities and came to the proof of a conjecture by Masaki Kashiwara , who suspected the invariance of regular holomorphic semi-simple D-modules on projective varieties under different functors . In particular, the semi-simplicity is retained, which shows the influence of the algebraic nature of the base spaces not only on the geometric, but also on the analytical properties of the solutions of differential equations considered there . At the same time, this also provided a proof of the fundamental theorems (decomposition theorem, Harter Lefschetz theorem, semi-simplicity) of Beilinson , Bernstein , Deligne and Gabber for a more general class of D-modules. While the proof of Beilinson-Bernstein-Deligne-Gabber used algebraic methods, the proof of Mochizuki was additionally based on analytical methods, the investigation of nonlinear partial differential equations. Mochizuki looked at Twistor-D-Modules originally introduced by Claude Sabbah and proved the decomposition theorem, the Harten Lefschetz Theorem and semi-simplicity for Pure Twistor-D-Modules ( Pure Twistor D-Modules ). Then he showed that all semi-simple perverted sheaves had a pure twistor D-module structure. Mochizuki subsequently extended these results to irregular singularities (mixed Twistor-D modules).

Overall, the research area of ​​the D-modules was essentially developed by Japanese mathematicians, such as the introduction of the D-modules by Kashiwara based on an idea by Mikio Satō from the late 1960s and the theory of the Hodge D-modules by Morihiko Saitō . Mochizuki worked eight years to prove the very difficult conjecture of Kashiwara, the publication of which takes up around 1,000 pages.

Prices

In 2010 he received the medal (advancement award for science) of the Japanese Academy of Sciences and a year later the award of the academy. Also in 2010 he received the JSPS (Japan Society for the Promotion of Science) Prize, in 2006 he received the Spring Prize of the Japanese Mathematical Society .

He was selected as plenary speaker at the International Congress of Mathematicians 2014 in Seoul (Wild harmonic bundles and twistor modules).

Fonts

  • Asymptotic behavior of tame harmonic bundles and an application to pure twistor D-modules, 2 volumes, Memoirs AMS 185, 2007
  • Kobayashi-Hitchin-Correspondence for tame harmonic bundles and applications, Astérisque, Volume 309, 2006, Part 2 Geometry & Topology, 13, 2009, pp. 359-455, Part 1 , Part 2
  • Donaldson type invariants for algebraic surfaces: transition of moduli stacks, Lecture Notes in Mathematics 1972, Springer Verlag 2009
  • Wild harmonic bundles and wild pure twistor D-modules, Arxiv, 2008
  • A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric, 2004, Arxiv
  • Mixed Twistor D-modules, Arxiv 2011

literature

  • Claude Sabbah , Théorie de Hodges et correspondance de Hitchin-Kobayashi sauvage, d´après T. Mochizuki , Seminaire Bourbaki No. 1050, January 2012, pdf

Web links

Individual evidence

  1. ↑ Receiving the Japan Academy Award, Kyoto University 2011
  2. ↑ Associate Professor Takuro Mochizuki of the Research Institute for Mathematical Sciences receives the Japan Academy Medal. Kyoto University, March 1, 2010, accessed September 21, 2013 .
  3. ↑ Professor Emeritus Masahiro Shogaito and Associate Professor Takuro Mochizuki of the Research Institute for Mathematical Sciences Receive the Japan Academy Prize. Kyoto University, April 12, 2011, accessed September 21, 2013 .
  4. ↑ To receive the 6th JSPS award
personal data
SURNAME Mochizuki, Takurō
ALTERNATIVE NAMES 望月 拓 郎
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH August 26, 1972