SUZUKI Takao

    Department of Science Associate Professor
Last Updated :2024/03/24

Researcher Information

Degree

  • Ph.D(Science)(2004/03 Kobe University)

URL

J-Global ID

Profile

  • I was born in 1974 and received the doctoral degree from Kobe University in 2004.

    My research field is the theory of integrable systems and special functions. Recently, I am investigating higher order generalizations of the Painlev\'e equations from a viewpoint of the affine root system or the monodromy preserving deformation. I am also interested in the hypergeometric functions to which those Painlev\'e systems are closely related.

Research Interests

  • Weyl group   Cluster algebra   Discrete integrable system   Monodromy   Lie algebra   Garnier system   Root system   Hypergeometric function   Special function   Soliton equation   Painlev\'e equation   Integrable system   

Research Areas

  • Natural sciences / Basic analysis
  • Natural sciences / Mathematical analysis

Academic & Professional Experience

  • 2016/04 - Today  Kindai UniversityFaculty of Science and EngineeringAssociate Professor
  • 2012/04 - 2016/03  Kindai UniversityFaculty of Science and EngineeringLecturer
  • 2011/04 - 2012/03  Osaka Prefecture UniversityFaculty of Liberal Arts and SciencesResearch Associate
  • 1998/04 - 2000/09  関西日本電気通信システム株式会社

Education

  • 2001/04 - 2004/03  Kobe University  Graduate School of Science and Technology  Department of Mathematics
  • 1996/04 - 1998/03  Kobe University  Graduate School of Science and Technology  Department of Mathematics
  • 1992/04 - 1996/03  Kobe University  Faculty of Science  Department of Mathematics
  • 1989/04 - 1992/03  大阪府立豊中高等学校

Association Memberships

  • The Mathematical Society of Japan   

Published Papers

Books etc

  • Takao Suzuki (Editor)Research Institute for Mathematical Sciences, Kyoto University 2021/08 163
  • Representation Theory, Special Functions and Painlev\'e Equations — RIMS 2015
    Hitoshi Konno; Hidetaka Sakai; Junichi Shiraishi; Takao Suzuki; Yasuhiko Yamada (Joint editor)Mathematical Society of Japan 2018/06 9784864970501 541

Conference Activities & Talks

MISC

Awards & Honors

  • 2010/10 神戸大学 全学共通教育ベストティーチャー賞
     
    受賞者: 鈴木貴雄

Research Grants & Projects

  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
    Date (from‐to) : 2020/04 -2024/03 
    Author : 鈴木 貴雄
     
    本年度は主に次の二つの成果を得た. (a) 昨年度の研究では,拡大された可約アフィン・ワイル群の双有理表現のラックス形式が得られ,これによりq-ガルニエ系の一般化が系統的に定式化された.本年度はこの結果についての論文をまとめ,Math. Phys. Anal. Geom.誌に投稿し掲載された.また2021年9月の日本数学会や2022年3月のジョージア大学(アメリカ合衆国)での国際会議において,オンライン講演による研究発表を行った. (b) 研究代表者や長尾・山田による先行研究において,q-ガルニエ系はハイネのq-超幾何級数の比によって記述される特殊解を持つことが明らかにされていた.これと上記(a)の結果を組み合わせることで,拡大アフィン・ワイル群のq-超幾何級数への作用を具体的に記述することに成功した.具体的には,まずq-ガルニエ系の由来となる拡大アフィン・ワイル群において,極大な部分群で超幾何関数解の条件と両立するものを求め,その双有理表現の解関数への作用からq-超幾何級数への線形作用を導出し,得られた結果を正方行列を用いて系統的に記述した.これにより,q-超幾何級数の満たす線形差分方程式や昇降演算子の作用などが,すべてワイル群の平行移動変換として理解できるようになった. (b)の成果については,指導院生との共著論文として発表予定であり,現在論文準備中である.
  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research
    Date (from‐to) : 2018/04 -2023/03 
    Author : 青木 貴史; 中村 弥生; 鈴木 貴雄
     
    まず、本年度出版された論文に関して概要を述べる。「研究発表」項目第1番目の論文では、大きなパラメータを持つ超幾何微分方程式に対してヴォロス係数を定義し、一般的な形で明示式を与えた。2番目の論文では、大きなパラメータを持つ超幾何関数・合流型超幾何関数と、これらが満たす微分方程式のWKB解のボレル和との関係を一般的な場合に完全に記述した。応用として、これらの関数のパラメータに関する漸近展開公式を与えた。3番目の論文では、一般化されたq-ガルニエ系に対するLax形式を与えた。本年度実施した研究では、次のような成果が得られた。一般化超幾何関微分方程式に対する原点および無限遠点におけるヴォロス係数を定義し,その具体形を与えた。さらに、一般化超幾何微分方程式の間に成り立つ退化図式と、ヴォロス係数に対する極限操作が整合していることを見出した。多変数の場合への研究にも着手した。その原型として、大きなパラメータを持つエアリーの微分方程式のWKB解をホロノミック系の立場から見直し、接続公式の初等的な別証明を与えた。従来の標準的理論では、超幾何関数の接続公式を用いていた証明に対して、新たに得られた証明は、代数関数の接続のみを用いる。この立場から、多変数の場合の最も基本的なものとして大きなパラメータを持つパーシー積分が満たすホロノミック系(パーシー系と呼ぶ)について研究を行い、エアリーの微分方程式と同様の構造があることを見出した。これにより、パーシー系のWKB解のリサージェンスが証明できた。これらの成果を記載した論文は、現在執筆中である。
  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research (C)
    Date (from‐to) : 2015/04 -2019/03 
    Author : SUZUKI Takao
     
    Recently higher order generalizations of the Painleve equations are proposed both on continuous side and on discrete side. However we haven't clarified yet a classification of equations or a relationship with hypergeometric functions. In this work we have formulated birational representations of a reducible extended affine Weyl group with the aid of cluster mutations. Translations of this group provide the known higher order q-Painleve equations containing the q-hypergeometric functions as particular solutions.
  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research
    Date (from‐to) : 2014/04 -2018/03 
    Author : AOKI TAKASHI; HONDA Naofumi; KAWAI Takahiro; TAKEI Yoshitsugu; YAMAZAKI Susumu; KOIKE Tatsuya; UMETA Yoko
     
    Introducing a large parameter in the 3 parameters contained in the Gauss hypergeometric differential equation, we can construct the WKB solutions which are formal solutions to the equation. The construction is done algebraically and elementarily, however, these formal solutions are divergent in general and do not have analytic sense. We may apply the Borel resummation method to the formal solutions and can construct analytic solutions and bases of the solution space. On the other hand, the Gauss hypergeometric differential equation has standard bases of solutions expressed by the hypergeometric function. In this research, we have obtained linear relations between these two classes of bases. As an application, asymptotic expansion formulas with respect to the large parameter of the Gauss hypergeometric function have been obtained. At the same time, we have some formulas which describe the parametric Stokes phenomena of the WKB solutions.
  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research
    Date (from‐to) : 2013/04 -2016/03 
    Author : Ohyama Yousuke; Watanabe Humihiko; Suzuki Takao
     
    We study a q-analogue of the Painleve equation, which is a difference equation. The main subject is a study of local behavior of generic solutions of q-Painleve equations around a fixed singular point. In case of nonlinear q-difference equation, it is difficult to express local behavior of solutions. We solve a connection problem of some linear q-difference equations with irregular singular points at first. Then we express local behavior of generic solutions of q-Painleve equations around the origin in terms of connection coefficients of the linear q-difference equation. In cases of degenerated q-Painleve equations, the corresponding linear equation has an irregular singular point. Since some local solutions are represented by divergent series, the Stokes phenomenon appears. We decided the Stokes coefficients by means of connection coefficients of q-hypergeometric equations.
  • Japan Society for the Promotion of Science:Grants-in-Aid for Scientific Research
    Date (from‐to) : 2010/04 -2014/03 
    Author : AOKI Takashi; SUZUKI Takao; IZUMI Shuzo; MATSUI Yutaka; NAKAMURA Yayoi; HONDA Naofumi; KAWAI Takahiro; TAKEI Yoshitsugu; KOIKE Tatsuya
     
    In this research, we have investigated the global properties of solutions to differential equations with a large parameter from the view point of the exact WKB analysis. There are three main results. Firstly, we have constructed the exponential-asymptotic (instanton-type) solutions, namely general formal solutions, to the equations which belong to the first Painleve hierarchies. Secondly, we have classified the topological types of the Stokes curves of the Gauss equation in terms of the parameters of the equation. Thirdly we have defined and computed explicit forms of the Voros coefficients of Gauss equation with a large parameter and obtained the Borel sums go them. We have obtained the formulas that describe parametric Stokes phenomena of WKB solutions.

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