(1) Non compact geometric analysis (2) Non commutative geometry (3) Dynamical scale transform
Overview of the research
Atiyah-Singer index theorem is a monumental theory in differential topology. Later around 2000 year, it has created two main streams where one is non linear moduli theory in topology and the other is the index theorem on non compact spaces. My research objective in (1) (2) is to construct moduli theory over non compact spaces by unifying these two subjects. Tropical geometry is a kind of dynamical scale transform, which is also called ultra-discretization, and the objective in (3) is to apply such scale transform to geometric objects such as automata groups.
Career Paths in Mathematics and Mathematical Sciences
M516, Year-long, Institute for Liberal Arts and Sciences, 1
From 01 Apr. 2024, To 31 Mar. 2025
Career Paths in Mathematics and Mathematical Sciences
0577, Year-long, Graduate School of Science, 1
From 01 Apr. 2024, To 31 Mar. 2025
Special study course (Mathematical Science)
5140, Year-long, Faculty of Science, 12
From 01 Apr. 2024, To 31 Mar. 2025
Topology
4131, Spring, Faculty of Science, 2
From 01 Apr. 2024, To 31 Mar. 2025
Graduate Lecture in Topology
0403, Spring, Graduate School of Science, 2
From 01 Apr. 2024, To 31 Mar. 2025
Exercises in Geometry I
3182, Spring, Faculty of Science, 4
From 01 Apr. 2024, To 31 Mar. 2025
Seminar on Differential Geometry A
0532, Spring, Graduate School of Science, 3
From 01 Apr. 2024, To 31 Mar. 2025
Seminar on Differential Geometry B
0533, Fall, Graduate School of Science, 3
From 01 Apr. 2024, To 31 Mar. 2025
Seminar on Differential Geometry D
0535, Fall, Graduate School of Science, 3
From 01 Apr. 2024, To 31 Mar. 2025
Seminar on Differential Geometry C
0534, Spring, Graduate School of Science, 3
From 01 Apr. 2023, To 31 Mar. 2024
Forefront of Mathematics and Mathematical Science II
4139, Fall, Faculty of Science, 2
From 01 Apr. 2023, To 31 Mar. 2024
Topology
4131, Spring, Faculty of Science, 2
From 01 Apr. 2023, To 31 Mar. 2024
Advanced Geometry I
4102, Fall, Faculty of Science, 2
From 01 Apr. 2023, To 31 Mar. 2024
Seminar on Differential Geometry B
0533, Fall, Graduate School of Science, 3
From 01 Apr. 2023, To 31 Mar. 2024
Seminar on Differential Geometry A
0532, Spring, Graduate School of Science, 3
From 01 Apr. 2023, To 31 Mar. 2024
Topics in Geometry C
0273, Fall, Graduate School of Science, 2
From 01 Apr. 2023, To 31 Mar. 2024
Graduate Lecture in Topology
0403, Spring, Graduate School of Science, 2
From 01 Apr. 2022, To 31 Mar. 2023
Special study course (Mathematical Science)
5140, Year-long, Faculty of Science, 12
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry A
0532, Spring, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Geometry c
0472, Spring, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Exercises in Geometry II
3162, Fall, Faculty of Science, 4
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry a
0434, Spring, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Geometry d
0473, Fall, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry B
0533, Fall, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Geometry b
0471, Fall, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Geometry a
0470, Spring, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry b
0435, Fall, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry d
0437, Fall, Graduate School of Science, 3
From 01 Apr. 2022, To 31 Mar. 2023
Seminar on Differential Geometry c
0436, Spring, Graduate School of Science, 3
From Apr. 2011, To Mar. 2012
数学と自然科学・社会科学Ⅰ
Fall, 理学研究科
From Apr. 2011, To Mar. 2012
数学と自然科学・社会科学Ⅱ
Fall, 理学研究科
From Apr. 2011, To Mar. 2012
数学と自然科学・社会科学Ⅲ
Fall, 理学研究科
From Apr. 2011, To Mar. 2012
数学基盤研究 幾何学A
Spring, 理学研究科
From Apr. 2011, To Mar. 2012
数学基盤研究 幾何学B
Fall, 理学研究科
From Apr. 2011, To Mar. 2012
Advanced Calculus A
Spring, 全学共通科目
From Apr. 2011, To Mar. 2012
幾何学演義II
Fall, 理学部
From Apr. 2012, To Mar. 2013
Geometry II
Fall, 理学部
From Apr. 2012, To Mar. 2013
Mathematics seminary
Year-long, 理学部
From Apr. 2013, To Mar. 2014
Exercises in Geometry I
Spring, 理学部
From Apr. 2013, To Mar. 2014
Calculus A
Spring, 全学共通科目
From Apr. 2014, To Mar. 2015
Set Theory & Topology
Spring, 理学部
From Apr. 2014, To Mar. 2015
Geometry II
Fall, 理学部
From Apr. 2014, To Mar. 2015
Mathematics and Natural Science, Social Science I
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Mathematics and Natural Science, Social Science II
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Mathematics and Natural Science, Social Science III
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Differential Geometry A
Spring, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Differential Geometry B
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Differential Geometry C
Spring, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Differential Geometry D
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Geometry C
Spring, 理学研究科
From Apr. 2014, To Mar. 2015
Seminar on Geometry D
Fall, 理学研究科
From Apr. 2014, To Mar. 2015
Calculus A
Spring, 全学共通科目
From Apr. 2014, To Mar. 2015
Calculus B
Fall, 全学共通科目
From Apr. 2015, To Mar. 2016
Geometry II
Fall, 理学部
From Apr. 2015, To Mar. 2016
Seminar on Differential Geometry A
Spring, 理学研究科
From Apr. 2015, To Mar. 2016
Seminar on Differential Geometry B
Fall, 理学研究科
From Apr. 2015, To Mar. 2016
Seminar on Differential Geometry C
Spring, 理学研究科
From Apr. 2015, To Mar. 2016
Seminar on Differential Geometry D
Fall, 理学研究科
From Apr. 2015, To Mar. 2016
Calculus with Exercises A
Spring, 全学共通科目
From Apr. 2015, To Mar. 2016
Calculus with Exercises B
Fall, 全学共通科目
From Apr. 2015, To Mar. 2016
Seminar on Geometry A
Spring, 理学研究科
From Apr. 2015, To Mar. 2016
Seminar on Geometry B
Fall, 理学研究科
From Apr. 2015, To Mar. 2016
Set Theory & Topology
Spring, 理学部
From Apr. 2016, To Mar. 2017
Introduction to Geometry
Fall, 理学部
From Apr. 2016, To Mar. 2017
Exercises in Basic Geometry
Fall, 理学部
From Apr. 2016, To Mar. 2017
Seminar on Differential Geometry A
Spring, 理学研究科
From Apr. 2016, To Mar. 2017
Seminar on Differential Geometry B
Fall, 理学研究科
From Apr. 2016, To Mar. 2017
Seminar on Differential Geometry C
Spring, 理学研究科
From Apr. 2016, To Mar. 2017
Seminar on Differential Geometry D
Fall, 理学研究科
From Apr. 2016, To Mar. 2017
Seminar on Geometry C
Spring, 理学研究科
From Apr. 2016, To Mar. 2017
Seminar on Geometry D
Fall, 理学研究科
From Apr. 2017, To Mar. 2018
Introduction to Geometry
Fall, 理学部
From Apr. 2017, To Mar. 2018
Exercises in Basic Geometry
Fall, 理学部
From Apr. 2017, To Mar. 2018
Calculus with Exercises A
Spring, 全学共通科目
From Apr. 2017, To Mar. 2018
Seminar on Differential Geometry A
Spring, 理学研究科
From Apr. 2017, To Mar. 2018
Seminar on Differential Geometry B
Fall, 理学研究科
From Apr. 2017, To Mar. 2018
Seminar on Differential Geometry C
Spring, 理学研究科
From Apr. 2017, To Mar. 2018
Seminar on Differential Geometry D
Fall, 理学研究科
From Apr. 2017, To Mar. 2018
Mathematics seminary
Year-long, 理学部
From Apr. 2018, To Mar. 2019
Topology
Spring, 理学部
From Apr. 2018, To Mar. 2019
Graduate Lecture in Topology
Spring, 理学研究科
From Apr. 2018, To Mar. 2019
Seminar on Differential Geometry a
Spring, 理学研究科
From Apr. 2018, To Mar. 2019
Seminar on Differential Geometry b
Fall, 理学研究科
From Apr. 2018, To Mar. 2019
Seminar on Differential Geometry c
Spring, 理学研究科
From Apr. 2018, To Mar. 2019
Seminar on Differential Geometry d
Fall, 理学研究科
From Apr. 2018, To Mar. 2019
Mathematics seminary
Year-long, 理学部
From Apr. 2019, To Mar. 2020
Topology
Spring, 理学部
From Apr. 2019, To Mar. 2020
Graduate Lecture in Topology
Spring, 理学研究科
From Apr. 2019, To Mar. 2020
Seminar on Differential Geometry a
Spring, 理学研究科
From Apr. 2019, To Mar. 2020
Seminar on Differential Geometry b
Fall, 理学研究科
From Apr. 2019, To Mar. 2020
Seminar on Differential Geometry c
Spring, 理学研究科
From Apr. 2019, To Mar. 2020
Seminar on Differential Geometry d
Fall, 理学研究科
From Apr. 2020, To Mar. 2021
Topology
Spring, 理学部
From Apr. 2020, To Mar. 2021
Graduate Lecture in Topology
Spring, 理学研究科
From Apr. 2020, To Mar. 2021
Calculus with Exercises B
Fall, 全学共通科目
From Apr. 2020, To Mar. 2021
Seminar on Differential Geometry a
Spring, 理学研究科
From Apr. 2020, To Mar. 2021
Seminar on Differential Geometry b
Fall, 理学研究科
From Apr. 2020, To Mar. 2021
Seminar on Differential Geometry c
Spring, 理学研究科
From Apr. 2020, To Mar. 2021
Seminar on Differential Geometry d
Fall, 理学研究科
From Apr. 2020, To Mar. 2021
Special study course (Mathematical Science)
Year-long, 理学部
From Apr. 2021, To Mar. 2022
Geometry I
Spring, 理学部
From Apr. 2021, To Mar. 2022
Seminar on Differential Geometry a
Spring, 理学研究科
From Apr. 2021, To Mar. 2022
Seminar on Differential Geometry b
Fall, 理学研究科
From Apr. 2021, To Mar. 2022
Seminar on Differential Geometry c
Spring, 理学研究科
From Apr. 2021, To Mar. 2022
Seminar on Differential Geometry d
Fall, 理学研究科
From Apr. 2021, To Mar. 2022
Seminar on Geometry a
Spring, 理学研究科
From Apr. 2021, To Mar. 2022
Seminar on Geometry b
Fall, 理学研究科
From Apr. 2021, To Mar. 2022
Forefront of Mathematics and Mathematical Science II
Fall, 理学部
From Apr. 2021, To Mar. 2022
Special Lecture on Mathematics 10
Year-long, 理学部
From Apr. 2021, To Mar. 2022
Special Lecture on Mathematics 9
Year-long, 理学部
From Apr. 2021, To Mar. 2022
Linear Algebra with Exercises B
Fall, 全学共通科目
Participation in PhD Defense
Instanton knot invariants with rational holonomy parameters and an application for torus knot groups
IMORI HAYATO, Graduate School of Science, Chief Examiner
25 Mar. 2024
ACTIONS OF AUTOMORPHISM GROUPS OF FREE GROUPS ON SPACES OF JACOBI DIAGRAMS. II
KATADA MAI, Graduate School of Science, Sub-chief Examiner
23 Mar. 2023
Cohomology of the spaces of commuting elements in Lie groups of rank two
TAKEDA MASAHIRO, Graduate School of Science, Chief Examiner
26 Sep. 2022
A topological invariant for continuous fields of Cuntz algebras
SOGABE TARO, Graduate School of Science, Sub-chief Examiner
24 Nov. 2021
list
Last Updated :2025/01/21
Administration
School management (title, position)
From 01 Apr. 2022, To 31 Mar. 2023
京都大学スーパーグローバルコース実施運営協議会 委員
From 20 Sep. 2009, To 31 Mar. 2011
京都大学国際交流センター外国人留学生日本語・日本文化研修委員会 委員
From 01 Apr. 2011, To 31 Mar. 2014
外国人留学生日本語・日本文化研修委員会 委員
From 01 Jul. 2011, To 30 Jun. 2013
国際交流委員会 委員
From 19 Sep. 2013, To 31 Mar. 2014
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From 01 Jul. 2013, To 30 Jun. 2015
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国際交流委員会 委員
From 01 Apr. 2016, To 31 Mar. 2018
国際教育委員会留学生受入専門委員会アジア未来リーダー育成奨学金プログラム小委員会 委員
From 01 Jun. 2016, To 31 Mar. 2018
国際教育委員会国際学生交流委員会アジア未来リーダー育成奨学金プログラム小委員会 委員長
From 01 Apr. 2018, To 31 Mar. 2020
アジア未来リーダー育成奨学金プログラム小委員会 委員
From 01 Apr. 2020, To 31 Mar. 2021
国際高等教育院 企画評価専門委員会 数学部会 委員
From 01 Apr. 2021, To 31 Mar. 2022
国際高等教育院 企画評価専門委員会 数学部会 委員
From 01 Apr. 2021
スーパーグローバルコース企画運営幹事会 委員
From 01 Apr. 2021, To 31 Mar. 2022
スーパーグローバルコース企画運営幹事会 協議員
Faculty management (title, position)
From 01 Apr. 2023, To 31 Mar. 2024
理学研究科将来計画委員会委員
From 01 Apr. 2022, To 31 Mar. 2023
理学研究科将来計画委員会委員
From 01 Apr. 2014, To 31 Mar. 2015
理学研究科自己点検・評価委員会委員
From 01 Apr. 2014, To 31 Mar. 2015
理学研究科大学院教育教務委員会委員
From 01 Apr. 2014, To 31 Mar. 2015
理学研究科国際・社会交流委員会委員長
From 01 Apr. 2014, To 01 May 2015
理学研究科会議構成員
From 01 Apr. 2015, To 31 Mar. 2016
理学研究科自己点検・評価委員会委員
From 01 Apr. 2015, To 31 Mar. 2016
理学部・教育委員会委員
From 01 Apr. 2015, To 31 Mar. 2016
理学研究科大学院教育教務委員会委員
From 01 Apr. 2014, To 31 Mar. 2015
理学研究科会議構成員
From 01 Apr. 2015, To 30 Jun. 2015
理学研究科国際・社会交流委員会委員長
From 01 Jul. 2015, To 31 Mar. 2016
理学研究科国際・社会交流委員会委員長
From 01 Apr. 2015, To 31 Mar. 2016
理学研究科国際・社会交流委員会 国際交流奨学生推薦小委員会委員
From 01 Apr. 2015, To 31 Mar. 2016
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From 01 Apr. 2016, To 31 Mar. 2017
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From 01 Apr. 2016, To 31 Mar. 2017
理学研究科国際・社会交流委員会 国際交流奨学生推薦小委員会委員長
From 01 Apr. 2017, To 31 Mar. 2018
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From 01 Apr. 2017, To 31 Mar. 2018
理学研究科国際・社会交流委員会 国際交流奨学生推薦小委員会委員
From 01 Apr. 2018, To 31 Mar. 2019
理学研究科数学・数理解析専攻副専攻長
From 01 Apr. 2018, To 31 Mar. 2019
理学研究科将来計画委員会委員
From 01 Apr. 2018, To 31 Mar. 2019
理学研究科専攻長会議構成員
From 01 Apr. 2019, To 31 Mar. 2020
From 01 Apr. 2019, To 31 Mar. 2020
From 01 Apr. 2020, To 31 Mar. 2021
理学部・教育委員会委員
From 01 Apr. 2020, To 31 Mar. 2021
理学部・教育委員会 全学共通教育委員会委員
From 01 Apr. 2020, To 31 Mar. 2021
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From 01 Apr. 2019, To 31 Mar. 2020
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From 01 Apr. 2021, To 31 Mar. 2022
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Last Updated :2025/01/21
Academic, Social Contribution
Academic Contribution
KTGU special workshop on algebraic topology
Planning, management, etc.
T.Kato, D.Kishimoto, From 29 Jan. 2025, To 29 Jan. 2025
East Asian Gauge Theory Conference on Gauge Theory and Related Topics 2
Planning, management, etc.
Huijun Fan (Peking University) Fuquan Fang (Beijing Normal University) Tsuyoshi Kato (Kyoto University) (Local Organizer) Jianfeng Lin (Tsinghua University) Nobuhiro Nakamura (Fukushima Medical University) (Local Organizer) Jongil Park (Seoul National University) Hirofumi Sasahira (Kyushu University) (Local Organizer), Nara Prefectural Convention Center, From 17 Dec. 2024, To 20 Dec. 2024
Special workshop in Gauge theory
Planning, management, etc.
T. Kato, N. Nakamura, From 09 Jan. 2024, To 12 Jan. 2024
The Second Australia-China-Japan-Singapore-U.S. Index Theory Conference
Other
Fei Han Tsuyoshi Kato Yasu Kawahigashi Varghese Mathai Hitoshi Moriyoshi Toshikazu Natsume Guoliang Yu Weiping Zhang, From 29 May 2023, To 02 Jun. 2023
Noncommutative Geometry, Index Theory and Representation Theory
Planning, management, etc.
Erik Guentner Erik van Erp Heath Emerson Robert Yuncken Tsuyoshi Kato Yanli Song, Department of Mathematics, Kyoto University, From 03 Jul. 2023, To 07 Jul. 2023
International Workshop on 4-manifold Theory and Gauge Theory
Planning, management, etc.
Jongil Park, Ki-Heon Yun, Tsuyoshi Kato, Nobuhiro Nakamura, Online, From 04 Nov. 2020, To 05 Nov. 2020
Operator K-Theory in Geometry, Topology and Representation Theory
Planning, management, etc.
N. Higson, T. Kato, Department of Mathematics, Kyoto University, From 10 Jun. 2019, To 14 Jun. 2019
Fukaya60, Geometry and Everything
Planning, management, etc.
Manabu Akaho, Koji Fujiwara, Tsuyoshi Kato, Hiroshi Ohta, Kaoru Ono, Department of Mathematics, Kyoto University, From 17 Feb. 2019, To 22 Feb. 2019
East Asian Conference on Gauge Theory and Related Topics
Planning, management, etc.
Tsuyoshi Kato, Nobuhiro Nakamura, Hirofumi Sasahira, Department of Mathematics, Kyoto University, From 11 Sep. 2018, To 15 Sep. 2018
Gauge Theory in Fukuoka
Planning, management, etc.
Mikio Furuta, Tsuyoshi Kato, Nobuhiro Nakamura, Hirofumi Sasahira, Yanagawa and Fukuoka, From 16 Feb. 2018, To 17 Feb. 2018
Gauge theory in Kyoto
Planning, management, etc.
T. Kato, N. Nakamura, From 22 Mar. 2023, To 24 Mar. 2023
Gauge theory seminar
Planning, management, etc.
T. Kato, H. Konno, N. Nakamura
East Asia Core Doctoral Forum in Mathematics
Planning, management, etc.
Global Non Commutative Geometry, Asia-Pasific region