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2013 Fiscal Year Annual Research Report

無限群と幾何学の新展開

Research Project

Project/Area Number 24224002
Research InstitutionThe University of Tokyo

Principal Investigator

坪井 俊  東京大学, 数理(科)学研究科(研究院), 教授 (40114566)

Co-Investigator(Kenkyū-buntansha) 小島 定吉  東京工業大学, 情報理工学(系)研究科, 教授 (90117705)
大鹿 健一  大阪大学, 理学(系)研究科(研究院), 教授 (70183225)
小林 俊行  東京大学, 数理(科)学研究科(研究院), 教授 (80201490)
藤原 耕二  京都大学, 理学(系)研究科(研究院), 教授 (60229078)
河澄 響矢  東京大学, 数理(科)学研究科(研究院), 准教授 (30214646)
足助 太郎  東京大学, 数理(科)学研究科(研究院), 准教授 (30294515)
Project Period (FY) 2012-05-31 – 2017-03-31
Keywords無限群 / 幾何学 / 空間形 / 多様体 / 微分同相群 / 力学系 / 写像類群 / 野性的空間
Research Abstract

無限群と幾何学についての広範な研究をおこなった。[空間形と無限群]、[多様体の微分同相群]、[曲面の写像類群]、[無限群の力学系的不変量]、[無限群と野生的空間]のそれぞれのグループで共同研究を継続した。研究支援員を年度前半は3名、年度後半は7名雇用し、研究を推進した。
5月22日~25日に「Geometry and Analysis on Manifolds」国際会議、7月12日~15日に「幾何学とインターネットの数理2013」研究集会、7月25日~28日に「幾何学と変換群の諸相2013」研究集会を開催し、連携研究者と共同研究をおこなうとともに、研究情報の交流に努めた。9月9日~14日に「Geometry and Foliations 2013」国際会議、9月15日~16日に「Geometry and Dynamics 2013」国際研究集会、9月17日~19日に「BGammaSchool」国際ワークショップを共催した。研究代表者、研究分担者、連携研究者は、研究成果の発表を行った。この期間には国外からの多数の参加で多岐にわたる研究交流が行われた。10月11日~14日に「群と幾何学の展望」研究集会、11月30日~12月1日に「Differential Geometry」研究集会を開催した。
トゥールーズ大学に分担者を派遣し、[多様体の微分同相群]について連携研究者と共同研究を行わせた。
研究分担者小島定吉は擬アノソフ写像のエントロピーとその写像トーラスの体積の関係を明らかにした。大鹿健一はクライン群の変形間の新しい完備化を定義した。小林俊行は極小表現について研究を深めた。藤原耕二は区間交換写像群について結果を出版した。河澄響矢は写像類群と関係の深いリー代数について結果を得た。足助太郎は複素力学系と特性類の関係について結果を得た。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

5つのグループによる共同研究は、うまく進行しており、分担者に研究成果が現れている。実際、擬アノソフ写像、クライン群の変形空間、極小表現、写像類群、複素葉層構造についての研究成果などが出ている。新しい研究手法も見つかっているので、今後に期待できる.

Strategy for Future Research Activity

5つのグループの共同研究を全体としてまとめていく研究方法を継続すれば, 十分な研究成果が見込まれる. 無限群と幾何学の合流する点での問題ととらえることを続けていきたい。研究分担者, 連携研究者との共同研究をさらに緊密にし、さらに広い視点を取り込んで研究を継続する予定である.

  • Research Products

    (53 results)

All 2014 2013 Other

All Journal Article (14 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 14 results) Presentation (39 results) (of which Invited: 38 results)

  • [Journal Article] Intertwining operators and the restriction of representations of rank one orthogonal groups2014

    • Author(s)
      T. Kobayashi and B. Speh
    • Journal Title

      C. R. Acad. Sci. Paris, Ser. I

      Volume: 352 Pages: 89-94

    • DOI

      10.1016/j.crma.2013.11.018

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] F-method for symmetry breaking operators2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Differential Geometry and its Applications

      Volume: 33 Pages: 272―289

    • DOI

      10.1016/j.difgeo.2013.10.003

    • Peer Reviewed
  • [Journal Article] Special functions in minimal representations2014

    • Author(s)
      T. Kobayashi
    • Journal Title

      Contemporary Mathematics

      Volume: 610 Pages: 258―266

    • DOI

      10.1090/conm/610/12103

    • Peer Reviewed
  • [Journal Article] Minimal representations via Bessel operators2014

    • Author(s)
      J. Hilgert, T. Kobayashi, and J. Moellers
    • Journal Title

      J. Math. Soc. Japan

      Volume: 66 Pages: 349-414

    • DOI

      10.2969/jmsj/06620349

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behavior2013

    • Author(s)
      E. Kin, S. Kojima and M. Takasawa
    • Journal Title

      Algebr. Geom. Topol.

      Volume: 13 Pages: 3537-3602

    • DOI

      10.2140/agt.2013.13.3537

    • Peer Reviewed
  • [Journal Article] A note on the rigidity of unmeasured lamination spaces2013

    • Author(s)
      Ken’ichi Ohshika
    • Journal Title

      Proc. AMS

      Volume: 141 Pages: 4385--4389

    • DOI

      10.1090/S0002-9939-2013-11670-9

    • Peer Reviewed
  • [Journal Article] F-method for constructing equivariant differential operators2013

    • Author(s)
      T. Kobayashi
    • Journal Title

      Contemporary Mathematics, Amer. Math. Soc.

      Volume: 588 Pages: 141―148

    • DOI

      DOI: 10.1090/conm/598/11998

    • Peer Reviewed
  • [Journal Article] Varna lecture on L^2-analysis of minimal representations2013

    • Author(s)
      T. Kobayashi
    • Journal Title

      Springer Proceedings in Mathematics & StatisticsSpringer

      Volume: 36 Pages: 77―93

    • DOI

      10.1007/978-4-431-54270-4_6. arXiv: 1212.6871

    • Peer Reviewed
  • [Journal Article] Finite multiplicity theorems for induction and restriction2013

    • Author(s)
      T. Kobayashi and T. Oshima
    • Journal Title

      Advances in Mathematics

      Volume: 248 Pages: 921―944

    • DOI

      10.1016/j.aim.2013.07.015

    • Peer Reviewed
  • [Journal Article] Free groups of interval exchange transformations are rare2013

    • Author(s)
      Francois Dahmani, Koji Fujiwara, Vincent Guirardel
    • Journal Title

      Groups, Geometry, and Dynamics

      Volume: 7 Pages: 883-910.

    • Peer Reviewed
  • [Journal Article] Shearing coordinates and convexity of length functions on Teichmueller space.2013

    • Author(s)
      M. Bestvina, K. Bromberg, K. Fujiwara, J. Souto.
    • Journal Title

      Amer. J. Math.

      Volume: 135 Pages: 1449-1476

    • Peer Reviewed
  • [Journal Article] The center of the Goldman Lie algebra of a surface of infinite genus2013

    • Author(s)
      Nariya Kawazumi and Yusuke Kuno
    • Journal Title

      Quarterly J. Math.

      Volume: 64 Pages: 1167-1190

    • DOI

      10.1093/qmath/has017

    • Peer Reviewed
  • [Journal Article] The Lie algebra of rooted planar trees2013

    • Author(s)
      Tomohiko Ishida and Nariya Kawazumi
    • Journal Title

      Hokkaido Math. J.

      Volume: 42 Pages: 397-416

    • Peer Reviewed
  • [Journal Article] On Fatou-Julia decompositions2013

    • Author(s)
      Taro Asuke
    • Journal Title

      Ann. Fac. Sci. Toulouse

      Volume: 22 Pages: 155-195

    • Peer Reviewed
  • [Presentation] Shintani Functions, Real Spherical Manifolds, and Symmetry Breaking Operators2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Conference on the occasion of Professor Matsuki's 60th birthday.
    • Place of Presentation
      Tottori, Japan
    • Year and Date
      20140208-20140209
    • Invited
  • [Presentation] Shintani Functions, Real Spherical Manifolds, and Symmetry Breaking Operators2014

    • Author(s)
      T. Kobayashi
    • Organizer
      Representation Theory and Analysis of Reductive Groups: Spherical Spaces and Hecke Algebras
    • Place of Presentation
      Oberwolfach, Germany
    • Year and Date
      20140119-20140125
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces2013

    • Author(s)
      T. Kobayashi
    • Organizer
      JSPS-DST Asian Academic Seminar 2013: Discrete Mathematics & its Applications
    • Place of Presentation
      Graduate School of Mathematical Sciences, the University of Tokyo, Japan
    • Year and Date
      20131103-20131110
    • Invited
  • [Presentation] Symmetry Breaking for Representations of Rank One Orthogonal Group2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Workshop on Representations of Lie Groups and their Subgroups
    • Place of Presentation
      Chalmers University of Technology, Sweden
    • Year and Date
      20130919-20130920
    • Invited
  • [Presentation] Construction of secondary characteristic classes for foliations using the Chern-Weil theory2013

    • Author(s)
      Taro Asuke
    • Organizer
      BGamma School
    • Place of Presentation
      中央大学理工学部
    • Year and Date
      20130918-20130919
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Japan--Netherlands Seminar
    • Place of Presentation
      Nagoya University, Japan
    • Year and Date
      20130826-20130830
    • Invited
  • [Presentation] Analysis of Minimal Representations (7 lectures)2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Hypergeometric functions and representation theory
    • Place of Presentation
      International summer research school of CIMPA, Mongolia
    • Year and Date
      20130805-20130816
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Hayama Symposium on Complex Analysis in Several Variables XVI.
    • Place of Presentation
      Kanagawa, Japan
    • Year and Date
      20130720-20130723
    • Invited
  • [Presentation] Multiplicities in the Restriction and Real Spherical Varieties2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Representations of Reductive Groups
    • Place of Presentation
      Salt Lake City, USA
    • Year and Date
      20130708-20130712
    • Invited
  • [Presentation] F-method to construct natural operators. X2013

    • Author(s)
      T. Kobayashi
    • Organizer
      International Workshop: Lie Theory and Its Applications in Physics (LT-10)
    • Place of Presentation
      Varna, Bulgaria
    • Year and Date
      20130617-20130623
    • Invited
  • [Presentation] Branching, Multiplicities, and Real Spherical Varieties2013

    • Author(s)
      T. Kobayashi
    • Organizer
      Group Actions with applications in Geometry and Analysis: in honour of Toshiyuki Kobayashi 50th birthday
    • Place of Presentation
      Reims, France
    • Year and Date
      20130603-20130606
    • Invited
  • [Presentation] Several problems on groups of diffeomorphisms

    • Author(s)
      Takashi Tsuboi
    • Organizer
      Geometry and Foliations 2013
    • Place of Presentation
      東京大学(東京都)
    • Invited
  • [Presentation] Normalized entropy versus volume for pseudo-Anosovs

    • Author(s)
      小島定吉
    • Organizer
      Analysis and Geometry of Riemann Surfaces and Related Topics
    • Place of Presentation
      東京工業大学(東京都)
    • Invited
  • [Presentation] Normalized entropy versus volume for pseudo-Anosovs

    • Author(s)
      小島定吉
    • Organizer
      低次元多様体の基本群とその表現に関する様々な構造について
    • Place of Presentation
      国際奈良学セミナーハウス(奈良県)
    • Invited
  • [Presentation] トポロジーと基本群

    • Author(s)
      小島定吉
    • Organizer
      玉城嘉十郎教授記念公開学術講演会
    • Place of Presentation
      京都大学(京都府)
    • Invited
  • [Presentation] Geometric completion for deformation spaces of Kleinian groups

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      Analysis and Geometry of Riemann Surfaces and Related Topics
    • Place of Presentation
      東京工業大学(東京都)
    • Invited
  • [Presentation] Geometric completion for quasi-Fuchsian spaces

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      AMC 2013
    • Place of Presentation
      Pusan BEXCO, Korea
    • Invited
  • [Presentation] Geometric limits and deformation spaces of Kleinian groups

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      KAIST GT Fair
    • Place of Presentation
      Jeonju, Korea
    • Invited
  • [Presentation] Geometric completion for deformation spaces of Kleinian groups

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      Japanese Turkish Joint Geometry Meeting
    • Place of Presentation
      Galatasaray University, Istanbul, Turkey
    • Invited
  • [Presentation] Automorphism groups of Heegaard splittings and their actions

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      離散群と双曲空間の複素解析とトポロジー
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Invited
  • [Presentation] Subgroups of mapping class groups associated to Heegaard splittings and their actions on projective lamination spaces

    • Author(s)
      Ken’ichi Ohshika
    • Organizer
      New Trends in Teichmüller Theory and Mapping Class Groups
    • Place of Presentation
      MFO Oberwolfach, Germany
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally pseudo-Riemannian Symmetric Spaces

    • Author(s)
      T. Kobayashi
    • Organizer
      Sophus Lie Days
    • Place of Presentation
      Cornell, USA
    • Invited
  • [Presentation] Universal sound” of anti-de Sitter manifold

    • Author(s)
      T. Kobayashi
    • Organizer
      Sophus Lie Days
    • Place of Presentation
      Cornell, USA
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces

    • Author(s)
      T. Kobayashi
    • Organizer
      Journée Mathématique de la Fédération de Recherche
    • Place of Presentation
      Amiens, France
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces

    • Author(s)
      T. Kobayashi
    • Organizer
      Colloquium de Mathématiques de Rennes
    • Place of Presentation
      Institut de Recherche mathématique de Rennes, France
    • Invited
  • [Presentation] Global Geometry and Analysis on Locally Pseudo-Riemannian Homogeneous Spaces

    • Author(s)
      T. Kobayashi
    • Organizer
      Colloquium. Chalmers University of Technology and the University of Gothenburg
    • Place of Presentation
      Chalmers University of Technology and the University of Gothenburg, Sweden
    • Invited
  • [Presentation] Branching Laws and F-method for Constructing Natural Differential Operators in Parabolic Geometry

    • Author(s)
      T. Kobayashi
    • Organizer
      Analysis Seminar. Chalmers University of Technology and the University of Gothenburg
    • Place of Presentation
      Chalmers University of Technology and the University of Gothenburg, Sweden
    • Invited
  • [Presentation] Making bridges among long islands.

    • Author(s)
      Koji Fujiwara
    • Organizer
      Geometric Structures in Group Theory
    • Place of Presentation
      Oberwolfach, Germany
    • Invited
  • [Presentation] Group actions on quasi-trees

    • Author(s)
      Koji Fujiwara
    • Organizer
      Differentialgeometrie im Grossen.
    • Place of Presentation
      Oberwolfach, Germany
    • Invited
  • [Presentation] Group actions on quasi-trees and application

    • Author(s)
      Koji Fujiwara
    • Organizer
      The XXIInd Rolf Nevanlinna Colloquim
    • Place of Presentation
      Helsinki
    • Invited
  • [Presentation] Quasi-homomorphisms into non-commutative groups.

    • Author(s)
      Koji Fujiwara
    • Organizer
      New Trends in Teichmüller Theory and Mapping Class
    • Place of Presentation
      Oberwolfach, Germany
    • Invited
  • [Presentation] Group actions on quasi-trees

    • Author(s)
      Koji Fujiwara
    • Organizer
      日本数学会 企画特別講演
    • Place of Presentation
      愛媛大
    • Invited
  • [Presentation] An infinitesimal version of the Dehn-Nielsen theorem

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Teichmuller theory: quantization and relations with physics
    • Place of Presentation
      Erwin Schr\"odingier Institute, Wien.(オーストリア)
    • Invited
  • [Presentation] The Goldman-Turaev Lie bialgebra and the mapping class group

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Caltech Geometry and Topology Seminar
    • Place of Presentation
      California Institute of Technology, Los Angels.(米国)
    • Invited
  • [Presentation] 無限小 Dehn-Nielsen 定理と最大 Torelli 群の埋込み

    • Author(s)
      河澄響矢
    • Organizer
      日本数学会秋季分科会一般講演
    • Place of Presentation
      愛媛大学
  • [Presentation] The Goldman-Turaev Lie bialgebra and the mapping class group

    • Author(s)
      河澄響矢
    • Organizer
      群と幾何学の展望
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Invited
  • [Presentation] The Goldman-Turaev Lie bialgebra and the mapping class group

    • Author(s)
      河澄響矢
    • Organizer
      離散群と双曲空間の複素解析とトポロジー
    • Place of Presentation
      京都大学数理解析研究所
    • Invited
  • [Presentation] The Goldman-Turaev Lie bialgebra and the mapping class group

    • Author(s)
      河澄響矢
    • Organizer
      第 9 回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Invited
  • [Presentation] On Fatou-Julia decompositions of complex dynamical systems

    • Author(s)
      Taro Asuke
    • Organizer
      Geometry and Foliations 2013
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Invited

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Published: 2015-05-28  

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