Faculty Profiles - ISHII YUTAKA

Information

写真a

ISHII YUTAKA

Organization

Faculty of Mathematics Division of Analysis Professor
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）
Joint Graduate School of Mathematics for Innovation （Concurrent）

Contact information

Profile

The main theme of my research is a combinatorial study of complex dynamical systems in dimension two, namely the complex Henon maps. I am now working on a criterion of their hyperbolicity, topology and combinatorics of their Julia sets and of their parameter loci, and applications of such complex methods to real dynamics. I gave a series of lectures on the dynamics of complex Henon maps both in Tokyo Institute of Technology and in Hokkaido University, on symbolic dynamics and data storage in Tokushima University. I gave a public lecture under the title "Dimension, Fractals and Dynamical Systems" organized by the Department of Mathematics, Kyushu University.

Homepage

https://sites.google.com/site/webpageyutakaishii/

External link

Degree

Ph D (Mathematical Sciences), University of Tokyo, March 1998

Research Interests・Research Keywords

Research theme： Visualization of 4D spaces with VR

Keyword： higher-dimensional spaces, virtual reality, Julia sets

Research period： 2018.4
Research theme：高次元ラップ数公式とエントロピーの誤差評価付き計算

Keyword：ラップ数公式、エントロピー、区間演算

Research period： 1998.1
Research theme：量子トンネル効果と高次元複素力学系

Keyword：トンネル効果、Julia 集合、Laputa 鎖

Research period： 1998.1
Research theme： Combinatorial study of complex Henon maps

Keyword： Henon maps, complex dynamics, Julia sets, hyperbolicity, parameter loci

Research period： 1997.10
Research theme： Lozi 写像に対する kneading 理論

Keyword： Lozi 写像、二ーディング理論、エントロピー、単調性

Research period： 1992.4

Papers

Polyvision 4D space manipulation through multiple projections International journal

Keigo Matsumoto, Nami Ogawa, Hiroyuki Inou, Shizuo Kaji, Yutaka Ishii, Michitaka Hirose

SIGGRAPH Asia 2019 Emerging Technologies - International Conference on Computer Graphics and Interactive Techniques, SA 2019 SIGGRAPH Asia 2019 Emerging Technologies, SA 2019 36 - 37 2019.11

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Language：English Publishing type：Research paper (international conference proceedings)

Seeing is believing. Our novel virtual reality system, Polyvision, applies this old saying to the fourth dimension. Various shadows of an object in a four-dimensional (4D) space are simultaneously projected onto multiple three-dimensional (3D) screens created in a virtual environment to reveal its intricate shape. The understanding of high-dimensional shapes and data can essentially be enhanced when good visualization is complemented by interactive functionality. However, a method to implement an interface for handling complex 4D transformations in a user-friendly manner must be developed. Using our Polyvision system, the user can manipulate each shadow as if it were a 3D object in their hand. The user’s action on each projection is reflected to the original 4D object, and in turn its projections, in real time. While controlling the object’s orientation minutely on one shadow, the user can grasp its global structure from multiple changing projections. Our system has a wide variety of applications in visualization, education, mathematical research, and entertainment, as we demonstrate with a variety of 4D objects that appear in mathematics and data sciences.

DOI： 10.1145/3355049.3360518
On parameter loci of the H'enon family. Invited Reviewed International journal

Zin ARAI, Yutaka ISHII

Commun. Math. Phys. 2018.12

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Language：English Publishing type：Research paper (scientific journal)

We characterize the hyperbolic horseshoe locus and the maximal entropy locus of the Henon family. The proof employs a combination of complex analytic and complex dynamical methods together with rigorous numerics.

Repository Public URL： http://hdl.handle.net/2324/4123945
Dynamics of polynomial diffeomorphisms of C^2: Combinatorial and topological aspects. Invited Reviewed International journal

Yutaka ISHII

Arnold Math. J. 2017.1

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Language：English Publishing type：Research paper (scientific journal)

The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of C^2 including complex Henon maps with an emphasis on the combinatorial and topological aspects of their Julia sets.

Repository Public URL： http://hdl.handle.net/2324/4123946
Hyperbolic polynomial diffeomorphisms of C^2. III: Iterated monodromy groups. Reviewed International journal

Yutaka ISHII

Advances in Mathematics 255 242 - 304 2014.1

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Language：English Publishing type：Research paper (scientific journal)
Homotopy shadowing. Reviewed International journal

Yutaka Ishii, John Smillie

Amer. J. Math. 132 ( 4 ) 2010.12

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Language：English Publishing type：Research paper (scientific journal)

Michael Shub proved in 1969 that the topological conjugacy class of an expanding endomorphism on a compact manifold is determined by its homotopy type. In this article we generalize this result in two directions. In one direction we consider certain expanding maps on metric spaces. In a second direction we consider maps which are hyperbolic with respect to product cone fields on a product manifold. A key step in the proof is to establish a shadowing theorem for pseudo-orbits with some additional homotopy information.
Symbolic dynamics for Henon maps near the boundary of the horseshoe locus

Hironaka, Y; Ishii, Y

ERGODIC THEORY AND DYNAMICAL SYSTEMS 2024.5 （ ISSN:0143-3857 eISSN:1469-4417 ）

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Publisher：Ergodic Theory and Dynamical Systems

Bedford and Smillie [A symbolic characterization of the horseshoe locus in the Hénon family. Ergod. Th. & Dynam. Sys. 37(5) (2017), 1389-1412] classified the dynamics of the Hénon map <![CDATA[ $f_{a, b}: (x, y)\mapsto (x^2-a-by, x)$ ]]> defined on <![CDATA[ $\mathbb {R}^2$ ]]> in terms of a symbolic dynamics when <![CDATA[ $(a, b)$ ]]> is close to the boundary of the horseshoe locus. The purpose of the current article is to generalize their results for all <![CDATA[ $b\ne 0$ ]]> (including the case <![CDATA[ $b < 0$ ]]> as well). The method of the proof is first to regard <![CDATA[ $f_{a, b}$ ]]> as a complex dynamical system in <![CDATA[ $\mathbb {C}^2$ ]]> and second to introduce the new Markov-like partition in <![CDATA[ $\mathbb {R}^2$ ]]> constructed by us [On parameter loci of the Hénon family. Comm. Math. Phys. 361(2) (2018), 343-414].

DOI： 10.1017/etds.2024.34

Web of Science

Scopus
On the Hausdorff dimension of the recurrent sets induced from endomorphisms of free groups. Reviewed International journal

Yutaka Ishii, Tatsuya Oka

J. Fractal Geom. 9 ( 1 ) 171 - 192 2023.4

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Language：English Publishing type：Research paper (scientific journal)
複素力学系の諸問題 Invited International journal

石井豊

数理解析研究所講究録 2211 2022.4

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Language：Japanese Publishing type：Research paper (scientific journal)
複素力学系の問題 (複素幾何学の諸問題 II)

ISHII YUTAKA

RIMS Kokyuroku 2211 23 - 44 2022.1 （ ISSN:18802818 ）

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Language：Japanese Publisher：京都大学数理解析研究所

CiNii Research
On the Hausdorff dimension of the recurrent sets induced from endomorphisms of free groups

Ishii, Y; Oka, T

JOURNAL OF FRACTAL GEOMETRY 9 ( 1-2 ) 171 - 192 2022 （ ISSN:2308-1309 eISSN:2308-1317 ）

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Publisher：Journal of Fractal Geometry

We show that F. Dekking’s recurrent sets in R2, which correspond to Markov partitions for conformally expanding maps of the 2-torus, have Hausdorff dimension strictly greater than one. This is a counterpart to the classical result of R. Bowen on the non-smoothness of the Markov partitions for Anosov diffeomorphisms of the 3-torus. We also present a non-conformal example where the recurrent set is a parallelogram and hence its Hausdorff dimension is one.

DOI： 10.4171/JFG/120

Web of Science

Scopus
バーチャル・リアリティを用いた4次元可視化プロジェクト

Ishii Yutaka

数学通信 3 49 - 54 2022

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CiNii Research
複素力学系の問題

石井豊

数理解析研究所講究録「複素幾何学の諸問題II」 2211 23 - 44 2022

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CiNii Research
M_4 is regular-closed. Invited Reviewed International journal

Yutaka ISHII, Yutaro HIMEKI

Ergod. Th. & Dynam. Sys. 2020.1

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Language：English Publishing type：Research paper (scientific journal)

Repository Public URL： http://hdl.handle.net/2324/4123944
Boundary of the horseshoe locus for the H'enon family Reviewed International journal

Zin Arai, Yutaka Ishii, Hiroki Takahasi

SIAM J. Appl. Dyn. Syst. 17 ( 3 ) 2234 - 2248 2018.4

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Language：English Publishing type：Research paper (scientific journal)
Corrigendum to ``Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees.'' Reviewed International journal

Yutaka Ishii

Advances in Mathematics 226 ( 4 ) 2011.7

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Language：English Publishing type：Research paper (scientific journal)
Julia sets and chaotic tunneling II. Reviewed International journal

Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda

J. Phys. A: Math. Theor. 42 2009.6

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Language：English Publishing type：Research paper (scientific journal)
Julia sets and chaotic tunneling I. Reviewed International journal

Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda

J. Phys. A: Math. Theor. 42 2009.6

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Language：English Publishing type：Research paper (scientific journal)
Hyperbolic polynomial diffeomorphisms of C^2. II: Hubbard trees. Reviewed International journal

Yutaka Ishii

Advances in Mathematics 220 ( 4 ) 2009.5

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Language：English Publishing type：Research paper (scientific journal)
Hyperbolic polynomial diffeomorphisms of C^2. I: A non-planar map. Reviewed International journal

Yutaka Ishii

Advances in Mathematics 218 ( 2 ) 2008.4

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Language：English Publishing type：Research paper (scientific journal)
Chaos attracts tunneling trajectories: A universal mechanism of chaotic tunneling. Reviewed International journal

Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda

Europhysics Letters 2008.1

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Language：English Publishing type：Research paper (scientific journal)
Lap number entropy formula for piecewise affine and projective maps. Reviewed International journal

Yutaka Ishii, Duncan Sands

Nonlinearity 2007.1

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Language：English Publishing type：Research paper (scientific journal)
Note on a paper by Kawasaki and Sasa on Bernoulli coupled map lattices. Reviewed International journal

Yutaka Ishii

Journal of Physics A: Mathematical and General 2006.1

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Language：English Publishing type：Research paper (scientific journal)
Julia set describes quantum tunnelling in the presence of chaos. Reviewed International journal

Akira Shudo, Yutaka Ishii, Kensuke S. Ikeda

Journal of Physics A: Mathematical and General 35 ( 17 ) L225 - L231 2002.1

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Language：English Publishing type：Research paper (scientific journal)

DOI： 10.1088/0305-4470/35/17/101
Monotonicity of the Lozi family near the tent-maps. Reviewed International journal

Yutaka Ishii, Duncan Sands

Communications in Mathematical Physics 1998.1

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Language：English Publishing type：Research paper (scientific journal)
Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors. Reviewed International journal

Yutaka Ishii

Communications in Mathematical Physics 1997.1

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Towards a kneading theory for Lozi mappings I: A solution of the pruning front conjecture and the first tangency problem. Reviewed International journal

Yutaka Ishii

Nonlinearity 1997.1

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Language：English Publishing type：Research paper (scientific journal)
Ising models, Julia sets, and similarity of the maximal entropy measures. Reviewed International journal

Yutaka Ishii

J.Statist.Phys. 1995.1

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Language：English Publishing type：Research paper (scientific journal)

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Books

カオス力学系入門　第2版

国府　寛司・石井　豊・新居　俊作・木坂　正史（Role：Joint translator）

共立出版 2003.11

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Language：Japanese Book type：Scholarly book

Japanese translation of "An Introduction to Chaotic Dynamical Systems, by Robert L. Devaney"

Repository Public URL： http://hdl.handle.net/2324/1001123577

Presentations

Information theory and symbolic dynamics Invited

Y.Ishii

TIN workshop 2009.7

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Event date： 2009.4

Presentation type：Oral presentation (general)

Country：Japan
Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference

Y.Ishii

Semi-annual conference on dynamical systems 1999.10

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Presentation type：Oral presentation (general)

Venue：Pennsylvania State University, University Park Country：United States
Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference

Y.Ishii

Dynamics and geometry seminar 1999.11

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Presentation type：Oral presentation (general)

Venue：Cornell University, Ithaca Country：United States
Global monotonicity conjecture and renormalization for the skew-Lozi family. Invited International conference

Y.Ishii

Dynamics seminar 2000.4

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Presentation type：Oral presentation (general)

Venue：State University of New York at Stony Brook, New York Country：United States
On the hyperbolicity of some complex H?'enon maps. Invited International conference

Y.Ishii

Hayama Symposium on Several Complex Variables 2000.12

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Presentation type：Oral presentation (general)

Venue：Shonan Village Center, Hayama Country：Japan
Sur l'hyperbolicit?'e de quelques applications de H?'enon complexes. Invited International conference

Y.Ishii

Seminaire de dynamique 2001.3

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Presentation type：Oral presentation (general)

Venue：Universite de Paris-Sud, Orsay Country：France
A lap number formula in higher dimensions and rigorous entropy estimates for Lozi maps. Invited International conference

Y.Ishii

New Directions in Dynamical Systems 2002.8

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Presentation type：Oral presentation (general)

Venue：Kyoto University, Kyoto Country：Japan
A lap number formula in higher dimensions and rigorous entropy estimates for Lozi maps. Invited International conference

Y.Ishii

Ergodic Theory Workshop 2002.12

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Presentation type：Oral presentation (general)

Venue：Nihon University, Tokyo Country：Japan
Hyperbolic polynomial diffeomorphisms of $C^2$. Invited International conference

Y.Ishii

Hayama Symposium on Several Complex Variables 2004.12

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Presentation type：Oral presentation (general)

Venue：Shonann Village Center, Hayama Country：Japan
Hyperbolic polynomial diffeomorphisms of $C^2$. Invited International conference

Y.Ishii

Dynamique conforme, geometrie hyperbolique, et fractions continues 2005.6

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Presentation type：Oral presentation (general)

Venue：Centre International de Rencontres Mathematiques, Luminy Country：France

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MISC

バーチャル・リアリティを用いた 4 次元可視化プロジェクト

石井豊

数学通信 2022.4

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
数学と出会ったころ: 思い出の紙一枚

石井豊

数学セミナー 2004.12

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Language：Japanese
高次元複素力学系と「和田の湖」

石井豊

数学セミナー 2004.11

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
離散可積分系と離散力学系 ---不変量の視点から---

石井豊

数理科学 2003.9

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)
物理現象と複素力学系

石井豊

数理科学 1999.10

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Language：Japanese Publishing type：Article, review, commentary, editorial, etc. (scientific journal)

Professional Memberships

日本数学会

Academic Activities

Screening of academic papers

Role(s)： Peer review

2017

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：4

Number of peer-reviewed articles in Japanese journals：1

Proceedings of International Conference Number of peer-reviewed papers：1

Proceedings of domestic conference Number of peer-reviewed papers：0
organizing committee International contribution

International symposium on complexified dynamics, tunnelling and chaos （ Ritsumeikan University Japan ） 2005.8 - Present

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Type：Competition, symposium, etc.

Number of participants：50

Research Projects

intertwined limits in nearly integrable quantum systems and complex classical dynamics

Grant number：23K22417 2022.4 - 2025.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

首藤啓, 石井豊, 池田研介

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Grant type：Scientific research funding

系が特殊な対称性をもたない限り，運動の自由度を２つ以上もつ系（以下，多自由度系という）の古典力学にはカオスが発生する．多自由度系の量子トンネル効果は古典カオスの影響を受けるのか？量子力学における基本的な問いでありながら，その問題が提起され40年近くが経った現在でも，我々はその答えを知らない．本研究では，複素半古典論など，我々自身が独自に発展させてきた手法，蓄積してきた経験をもとに多自由度トンネル効果に関するこの最も基本的な問題を追求する．特に，複素カオスがトンネル効果に顕在化することを立証し，教科書で学ぶ1自由度のトンネル効果と多自由度のトンネル効果の本質的な違いを明らかにする．

CiNii Research
「かたち」と「うごき」を表す高次元データ記述子の開発

Grant number：22H05107 2022 - 2026

Japan Society for the Promotion of Science・Ministry of Education, Culture, Sports, Science and Technology Grants-in-Aid for Scientific Research Grant-in-Aid for Transformative Research Areas (A)

平岡裕章, 石井豊, 池祐一, 落合啓之

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Authorship：Coinvestigator(s) Grant type：Scientific research funding

現代社会に氾濫する高次元データは，その構造を直接「見る」ことができない．低次元空間への射影や断面を用いる従来法からは，構造の直感的理解を得ることは難しく，さらには幾何・トポロジー構造が潰されたものになる問題点もある．そこで本研究では，高次元データを直感的に知覚できるデータ記述子の開発を目標に据えた，以下の３テーマを実施する．
テーマ１：バーチャルリアリティ（VR）を用いたインタラクティブな高次元可視化の数理
テーマ２：パーシステントホモロジーの代数解析・代数幾何的研究とその応用
テーマ３：マグニチュードホモロジーの自然言語処理・オミックスデータ解析への応用

CiNii Research
Construction of new phase-parameter space correspondence for complex dynamics in dimension two

Grant number：23K20218 2020.4 - 2025.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

石井豊, 小木曽啓示, 上原崇人, 宍倉光広, 荒井迅

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Grant type：Scientific research funding

石井が主に記号力学系的側面と複素力学系的側面を担当し、荒井が主に計算機を用いた数値実験で具体的なモノドロミー作用による記号空間の自己同型群の計算を担当する。以上の計画遂行のため、石井と荒井は数回相互訪問して議論を行ない、各年に1回程度の海外出張で最新の情報を収集する。また、複素局面上の力学系の力学系的じすうの分布について上原が先行的な数値実験を開始した。この点の理解を深めるために、数回相互訪問して議論を行なうための国内旅費が必要となる。

CiNii Research
複素２次元力学系における相空間とパラメータ空間の新たな対応関係の構築

Grant number：20H01809 2020 - 2024

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

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Authorship：Principal investigator Grant type：Scientific research funding
Bifurcation and renormalization of real and complex dynamical systems

Grant number：19H01798 2019.4 - 2024.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

宍倉光広, 奥山裕介, 稲生啓行, 石井豊

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Grant type：Scientific research funding

シンプルで決定論的な力学系はしばしば複雑で予測不可能な挙動（カオス）を示す．カオス的力学系ののパラメータを変化させると，一つのタイプの分岐現象（力学系全体の挙動が変化）が別のタイプの分岐を引き起こし，パラメータ空間の中の分岐パラメータの集合は入り組んだ階層的構造（フラクタルなど）をもつ．この階層的構造は、くりこみと呼ばれる概念により説明されることが多い。
本研究では，カオス的挙動をもつ実および複素の低次元力学系に的を絞って，分岐現象（特に大域的な力学系の構造の分岐）を理解することを目指す．そのためには，トポロジー的方法，実解析的方法，複素解析的方法、数論的方法などを援用する．

CiNii Research
非一様双曲的な実および複素Henon写像の力学系

2019 - 2020

Japan Society for the Promotion of Science Bilateral program

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Authorship：Principal investigator Grant type：Joint research
On the creation of chaos in higher dimensions

Grant number：18H01138 2018.4 - 2023.3

Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

荒井迅, 石井豊, 三波篤郎

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Grant type：Scientific research funding

本研究の目的は，高次元力学系にカオスが発生するメカニズムを解明し，カオス理論の応用範囲を飛躍的に拡大することである．カオスがどのような分岐を経て発生するのか，数学的に完全な理論が存在するのは1次元の最も基本的な場合のみであり，高次元でカオスが発生するメカニズム数学的な説明はいまだ得られていない．これがカオス理論の応用を進める上で大きな障害になっており，本研究はこの困難をトポロジーや計算機科学を応用して突破することを目指している．今年度は，昨年度の研究で得られた，1次元からの摂動論を用いることが出来ない本質的に新しい構造の連結なジュリア集合を持つパラメータを中心に，エノン写像のパラメータ空間の構造を解明するための研究を進めた．これは，ジュリア集合が非連結となるようなパラメータ集合を連結となるパラメータ集合がパラメータ空間のなかで位相的にどのように配位しているかを明らかにしようというもので，1次元を越えた高次元複素力学系を研究する上で基本的な問題であると考える．この目標のためには，パラメータ空間の構造を効率的に探索する数値計算手法を開発し，さらに不動点の不安定多様体の精度保証付き数値計算や，グリーン関数を評価してその特異点の存在を数学的に厳密に証明するためのアルゴリズムなど，計算機援用証明の技法を開発する必要がある．今年度の研究により，これら必要となる技法の本質的な部分は確立された．特にグリーン関数の特異点の存在証明については、局所的な計算を用いる手法だけでなく，グリーン関数の劣調和性を用いた大域的な手法も開発し，今後の研究の幅を拡げることができた．

CiNii Research
Visualization of 4D space by VR and complex dynamics

Grant number：18K18722 2018 - 2020

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Challenging Research(Exploratory)

Ishii Yutaka

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Authorship：Principal investigator Grant type：Scientific research funding

Visualization of higher dimensional objects attracts great interest from mathematics, physics and data science, etc. The purpose of this project is to visualize mathematical objects in 4 dimensional space such as the Julia sets by using virtual reality system. As a consequence, we succeeded a system called Polyvision which is a higher dimensional analogue of CAD (computer aided design) by using the idea of multi-projections. This system has been accepted to SIGGRAPH ASIA, one of the top conferences in computer graphics. We also started psychological test based on this system.

CiNii Research
複素エノン写像の力学系:相空間からパラメータ空間へ

Grant number：25287020 2013 - 2018

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

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Authorship：Principal investigator Grant type：Scientific research funding
複素2変数力学系の実3次元可視化について

Grant number：25610020 2013 - 2016

Grants-in-Aid for Scientific Research Grant-in-Aid for challenging Exploratory Research

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Authorship：Principal investigator Grant type：Scientific research funding
複素Ｈｅｎｏｎ写像族のパラメータ空間の力学系的研究

Grant number：21740125 2009 - 2012

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

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Authorship：Principal investigator Grant type：Scientific research funding
体積保存系としてのＫ３曲面上の複素力学系

Grant number：18740091 2006 - 2008

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

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Authorship：Principal investigator Grant type：Scientific research funding
二次元複素力学系のコンビナトリアルな研究

Grant number：14740120 2002 - 2004

Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

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Authorship：Principal investigator Grant type：Scientific research funding
複素 Henon 写像のコンビナトリアルな研究 International coauthorship

1999.10
Lozi 写像の単調性とラップ数公式 International coauthorship

1995.6

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Educational Activities

I taught calculus and linear algebra to freshmen and introduction to metric space topology to undergraduate students in math department.

Class subject

微分積分学Ⅱ

2023.10 - 2024.3 Second semester
力学系大意

2023.10 - 2024.3 Second semester
微分積分学Ⅰ

2023.4 - 2023.9 First semester
数学概論Ⅱ・演習

2023.4 - 2023.9 First semester
微分積分学Ⅱ

2021.10 - 2022.3 Second semester
微分積分学Ⅰ

2021.4 - 2021.9 First semester
コアセミナーⅠ

2021.4 - 2021.9 First semester
数学概論Ⅱ・演習

2021.4 - 2021.9 First semester
線形代数学・同演習Ｂ

2020.10 - 2021.3 Second semester
微分積分学

2020.10 - 2021.3 Second semester
数学概論Ⅱ・演習

2020.4 - 2020.9 First semester
線形代数学・同演習Ａ

2020.4 - 2020.9 First semester
線形代数

2020.4 - 2020.9 First semester
微分積分学

2019.10 - 2020.3 Second semester
線形代数学・同演習Ｂ

2019.10 - 2020.3 Second semester
線形代数

2019.4 - 2019.9 First semester
線形代数学・同演習Ａ

2019.4 - 2019.9 First semester
数学概論Ⅱ・演習

2019.4 - 2019.9 First semester
線形代数学・同演習Ｂ

2018.10 - 2019.3 Second semester
線形代数学・同演習Ｂ

2018.10 - 2019.3 Second semester
微分積分学

2018.10 - 2019.3 Second semester
線形代数学・同演習Ａ

2018.4 - 2018.9 First semester
線形代数学・同演習Ａ

2018.4 - 2018.9 First semester
線形代数学Ｂ

2017.10 - 2018.3 Second semester
線形代数学Ａ

2017.4 - 2017.9 First semester
線形代数学Ｂ

2016.10 - 2017.3 Second semester
線形代数学Ａ

2016.4 - 2016.9 First semester
線形代数学Ｂ

2015.10 - 2016.3 Second semester
線形代数学Ａ

2015.4 - 2015.9 First semester
微分積分学

2014.4 - 2015.3 Full year
数学演習 I

2014.4 - 2014.9 First semester
複素解析学大意

2014.4 - 2014.9 First semester
数学概論４・演習

2012.10 - 2013.3 Second semester
力学系大意

2012.10 - 2013.3 Second semester
数学概論２・演習

2012.4 - 2012.9 First semester
基礎数学演習

2011.4 - 2012.3 Full year
数学入門演習

2011.4 - 2011.9 First semester
数学概論２

2011.4 - 2011.9 First semester
Google と線形代数

2011.4 - 2011.9 First semester
数学概論１・演習

2008.10 - 2009.3 Second semester
数学概論１・演習

2007.10 - 2008.3 Second semester
数学概論１・演習

2006.10 - 2007.3 Second semester
数学基礎演習Ⅱ

2005.10 - 2006.3 Second semester
複素解析学大意

2004.10 - 2005.3 Second semester
数学特論11,12

2004.10 - 2005.3 Second semester
数学基礎演習Ⅱ

2004.10 - 2005.3 Second semester
解析学B2

2003.4 - 2003.9 First semester
ルベーグ積分論演習・関数論演習

2003.4 - 2003.9 First semester
解析学B1

2003.4 - 2003.9 First semester

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FD Participation

2022.4 Role：Moderator Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2021.7 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2021.3 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2004.4 Role：Participation Title：不明

Organizer：University-wide

Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

2014 名古屋大学多元数理学研究科 Classification:Intensive course Domestic/International Classification:Japan
2008 京都大学情報学研究科 Classification:Intensive course Domestic/International Classification:Japan
2006 Departement de Mathenatiques, Universite de Rennes, France Classification:Affiliate faculty Domestic/International Classification:Overseas

Semester, Day Time or Duration：2006.6
2005 北海道大学理学部 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：2005 年度後期
2005 東京工業大学大学院理工学研究科 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：2005 年度前期
2002 Departement de Mathematiques, Universite de Paris-Sud, France Classification:Affiliate faculty Domestic/International Classification:Overseas

Semester, Day Time or Duration：2002.3 -- 2002.4
2002 徳島大学総合科学部 Classification:Intensive course Domestic/International Classification:Japan

Semester, Day Time or Duration：2002.9

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Outline of Social Contribution and International Cooperation activities

無し

Social Activities

「次元・フラクタル・力学系」一般市民を対象とした講演

九州大学数理学研究院九州大学 2005.8

　More details

Audience：General,　Scientific,　Company,　Civic organization,　Governmental agency

Type：Lecture

Acceptance of Foreign Researchers, etc.

数理学研究院

Acceptance period： 2023.1 - 2026.7 （Period）：1 month or more

Nationality：United Kingdom

Business entity：Japan Society for the Promotion of Science
Centrum voor Wiskunde en Informatica

Acceptance period： 2005.3 （Period）：Less than 2 weeks

Nationality：Netherlands
CNRS, Universite de Paris VII

Acceptance period： 2003.7 （Period）：Less than 2 weeks

Nationality：France
Cornell University & Universite de Provence

Acceptance period： 2001.1 （Period）：Less than 2 weeks

Nationality：United States
Kyoto University

Acceptance period： 1998.1 （Period）：Less than 2 weeks

Nationality：France

Travel Abroad

2010.3 - 2011.3

Staying countory name 1：France Staying institution name 1：Centre de Mathematiques Laurent Schwartz, Ecole Polytechnique
2006.6

Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Rennes
2004.1 - 2004.2

Staying countory name 1：France Staying institution name 1：Institut Henri Poincare
2003.9 - 2003.12

Staying countory name 1：Japan Staying institution name 1：RIMS, Kyoto University
2002.3 - 2002.4

Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud
2001.3 - 2001.4

Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud
1999.10 - 2000.9

Staying countory name 1：United States Staying institution name 1：Department of Mathematics, Cornell University
1997.11 - 1997.12

Staying countory name 1：United States Staying institution name 1：Institute for Mathematical Sciences, State University of New York at Stony Brook
1994.7 - 1996.8

Staying countory name 1：France Staying institution name 1：Departement de Mathematiques, Universite de Paris-Sud

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