KUIP

講師&講演概要LECTURERS & PRESENTATIONS 

ABSTRACTS OF LECTURER & PRESENTATION

TAKURO MOCHIZUKI
  • Professor, Research Institute for Mathematical Sciences, Kyoto University
Keywords:
  • Differential geometry
  • Algebraic geometry
  • Algebraic analysis
  • Twistor D-module
  • Harmonic bundle

Presentation Abstract

An Invitation to Cohomology Theory

The goal of geometry is to investigate the properties of manifolds (spaces and figures). In geometry up to high school, we focus on quantities (invariants) such as length, area, and angle, but there are other invariants that are suitable for investigating properties. While invariants are quantities that should be observed instead of length and the like, they can also be regarded as instruments like microscopes and telescopes in the sense of their use for investigating the properties of manifolds. In this view, it is also an important goal to raise the performance of observation.

One important invariant is cohomology. Originally found as the dual of homology, which is an invariant for examining topological properties, cohomology also reflects the analytic properties of manifolds. In particular, the cohomology theory has been extended and refined to many varieties in order to capture interesting properties of algebraic varieties. One of the streams of research has led to twistor D-modules through the theory’s extension to D-modules and refinement by Hodge and twistor structures. At the symposium, the lecturer will introduce some aspects of the spread of cohomology theory.

LECTURER’S PROFILE

Biography (As of August 2022)

Mar 1994
Faculty of Science, Kyoto University (Withdrawal)
Mar 1996
Graduate School of Science, Kyoto University
Mar 1999
Ph.D., Graduate School of Science, Kyoto University
Apr 1999
Research Associate, Faculty of Science, Osaka City University
Apr 2004
Associate Professor, Graduate School of Science, Kyoto University
May 2008
Associate Professor, Research Institute for Mathematical Sciences, Kyoto University
Apr 2012 – Present
Professor, Research Institute for Mathematical Sciences, Kyoto University

Awards and Honors

2006
Spring prize, Mathematical Society of Japan
2008
Yukawa-Tomonaga Memorial prize, Kyoto University
2010
Japan Academy Medal, The Japan Academy
2010
JSPS prize, Japan Society for the Promotion of Sciences
2011
Japan Academy Prize, The Japan Academy
2012
Osaka Science Prize, Osaka Science and Technology Center
2021
The Asahi Prize, The Asahi Shimbun Foundation
2022
Breakthrough Prize, Breakthrough Prize Foundation

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