Updated on 2022/05/30

写真a

 
NAYATANI, Shin
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor

Degree 1

  1. 理学博士 ( 1990.3   大阪大学 ) 

Research Interests 5

  1. buildings

  2. harmonic maps

  3. rigidity of discrete groups

  4. nonpositively curved spaces

  5. conformal geometry

Research Areas 1

  1. Others / Others  / Geometry

Current Research Project and SDGs 2

  1. Geometric approach to rigidity of discrete groups

  2. Riemannian metrics maximizing the first Laplacian eigenvalue on a closed surface

Research History 5

  1. 名古屋大学大学院多元数理科学研究科・教授

    2005.4

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    Country:Japan

  2. 名古屋大学大学院多元数理科学研究科・助教授

    1998.10 - 2005.3

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    Country:Japan

  3. 東北大学理学部・助教授

    1994.10 - 1998.9

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    Country:Japan

  4. 東北大学理学部・助手

    1991.4 - 1994.9

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    Country:Japan

  5. 日本学術振興会特別研究員

    1990.4 - 1991.3

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    Country:Japan

Education 2

  1. Osaka University   Graduate School, Division of Science

    - 1990

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    Country: Japan

  2. The University of Tokyo   Faculty of Science

    - 1985

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    Country: Japan

Professional Memberships 1

  1. 日本数学会   幾何学分科会評議員

    2011.4 - 2013.3

Awards 1

  1. 日本数学会幾何学賞

    2004.9   日本数学会  

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    Country:Japan

 

Papers 25

  1. Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

    Nayatani Shin, Shoda Toshihiro

    COMPTES RENDUS MATHEMATIQUE   Vol. 357 ( 1 ) page: 84-98   2019.1

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

    DOI: 10.1016/j.crma.2018.11.008

    Web of Science

  2. Fixed-point property for affine actions on a Hilbert space Invited Reviewed

    Shin Nayatani

      Vol. B66   page: 115-131   2017

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same random group on a Hilbert space have a fixed point. We discuss some aspects of the proof.

  3. Almost CR structure on the twistor space of a quaternionic CR manifold Invited Reviewed

    Hiroyuki Kamada, Shin Nayatani

    Current developments in differential geomerty and its elated fields     page: 93-114   2016

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    Authorship:Lead author   Language:English  

  4. *Quaternionic CR Geometry Reviewed

    Hiroyuki Kamada, Shin Nayatani

    Hokkaido Mathematical Journal   Vol. 42   page: 1-49   2013

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of the Tanaka-Webster connection in complex CR geometry, we construct a canonical connection associated with a quaternionic pseudohermitian structure, when the underlying quaternionic CR structure satisfies the ultra-pseudoconvexity which is stronger than the strong pseudoconvexity. Comparison to Biquard's quaternionic contact structure is also made.

  5. N-step energy of maps and the fixed-point property of random groups Reviewed

    Shin Nayatani, Hiroyasu Izeki, Takefumi Kondo

    Groups, Geometry, and Dynamics   Vol. 6 ( 4 ) page: 701--736   2012

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    We prove that a random group of the graph model associated with a sequence of
    expanders has the fixed-point property for a certain class of CAT.0/ spaces. We use Gromov's
    criterion for the fixed-point property in terms of the growth of n-step energy of equivariant
    maps from a finitely generated group into a CAT.0/ space, for which we give a detailed proof.
    We estimate a relevant geometric invariant of the tangent cones of the Euclidean buildings
    associated with the groups PGL.m;Qr /, and deduce from the general result above that the
    same random group has the fixed-point property for all of these Euclidean buildings with m
    bounded from above.

    DOI: 10.4171/GGD/171

  6. Fixed-point property of random groups Reviewed

    Shin Nayatani, Hiroyasu Izeki, Takefumi Kondo

    Annals of Global Analysis and Geometry   Vol. 35 ( 4 ) page: 363-379   2009

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  7. A fixed-point theorem for discrete-group actions on Hadamard spaces

      Vol. 1492   page: 56-64   2006

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

  8. 調和写像による超剛性定理および固定点定理へのアプローチ Invited Reviewed

    井関裕靖、納谷信

    数学   Vol. 158   page: 239-262   2006

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    Authorship:Lead author   Language:Japanese  

  9. *Combinatorial harmonic maps and discrete-group actions on Hadamard spaces Reviewed

    Shin Nayatani, Izeki Hiroyasu

    Geometriae Dedicata   Vol. 114   page: 147-188   2005

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  10. 組合せ調和写像と超剛性 --- SINGULAR TARGET の場合

    納谷信、井関裕靖

    数理解析研究所講究録   Vol. 1329   page: 1-7   2003

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

  11. 組合せ調和写像と超剛性

    納谷信、井関裕靖

    数理解析研究所講究録   Vol. 1270   page: 182-194   2002

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    Authorship:Lead author   Language:Japanese   Publishing type:Research paper (scientific journal)  

  12. Quaternionic analogue of CR geometry

    Shin Nayatani, Hiroyuki Kamada

    Séminaire de Théorie Spectrale et Géométrie   Vol. 19   page: 41-52   2001

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  13. *Discrete groups of complex hyperbolic isometries and pseudo-Hermitian structures Invited Reviewed

    Analysis and Geometry in Several Complex Variables, Proceedings of the 40th Taniguchi Symposium, Birkh(]E88D2[)user     page: 209-237   1999

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  14. Canonical metric on the domain of discontinuty of a Kleinian group(共著)

    S(]E85C2[)minaire de Th(]E85C2[)orie Spectrale et G(]E85C2[)om(]E85C2[)trie   Vol. 16   page: 9-32   1998

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    Language:English  

  15. *Patterson-Sullivan measure and conformally flat metrics Reviewed

    Mathematische Zeitschrift   Vol. 225   page: 115-131   1997

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  16. *Self-dual manifolds with positive Ricci curvature(共著) Reviewed

    Mathematische Zeitschrift   Vol. 224   page: 49-63   1997

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  17. Morse indices of Yang-Mills connections over the unit sphere (共著)

    Composition Mathematica   Vol. 98   page: 177-192   1995

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    Language:English  

  18. *Morse index and Gauss maps of complete minimal surfaces in Euclidean 3-space Reviewed

    Commentarii Mathematici Helvetici   ( 68 ) page: 511-537   1993

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  19. Spectrum of the Schr(]E88D8[)dinger operator on a complete manifold (共著)

    Journal of Functional Analysis   ( 112 ) page: 459-479   1993

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    Language:English  

  20. Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold (共著)

    Nagoya Mathematical Journal   ( 132 ) page: 155-173   1993

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    Language:English  

  21. Kleinian groups and conformally flat metrics

    Geometry and Global Analysis, Report of the First MSJ International Research Institute     page: 341-349   1993

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    Language:English  

  22. Morse index of complete minimal surfaces

    THE PROBLEM OF PLATEAU ed. Th. M. Rassias, World Scientific, Singapore     page: 181-189   1992

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    Language:English  

  23. On the Morse index of complete minimal surfaces in Euclidean space

    Osaka Journal of Mathematics   ( 27 ) page: 441-451   1990

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    Language:English  

  24. Lower bounds for the Morse index of complete minimal surfaces in Euclidean 3-space

    Osaka Journal of Mathematics   ( 27 ) page: 453-464   1990

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    Language:English  

  25. On the volume of positively curved Kaehler manifolds Reviewed

    Osaka Journal of Mathematics   ( 25 ) page: 223-231   1988

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

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Books 1

  1. 微分幾何学の最先端----Surveys in Gemometry, special edition

    榎一郎、二木昭人、辻元、小林亮一、深谷賢治、中島啓、藤木明、後藤竜司、納谷信、藤原耕二( Role: Joint author)

    培風館  2005.12 

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    Language:Japanese

    担当部分である第9章「調和写像と剛性」において、調和写像に関する基本事項を紹介した後に、Eells-Sampsonによる調和写像の存在定理とその同変版を解説した。さらに、調和写像の剛性問題への応用について論じた。最後の節では、著者らによる最近の結果を始めとして、研究の現状と展望を述べた。

Presentations 20

  1. Metrics maximizing the first eigenvalue of the Laplacian on a closed surface and extra eigenfunction (Mini-course) Invited International conference

    Shin Nayatani

    UK-Japan Winter School "Variational problems in geometry and mathematical physics"  2019.1 

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    Event date: 2019.1

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Leeds University   Country:United Kingdom  

  2. ラプラシアン第1固有値最大化と埋め込み最適化

    納谷 信

    日本数学会2022年度年会  2022.3  日本数学会

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    Event date: 2022.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  3. First-eigenvalue maximization and embedding optimization Invited International conference

    Shin Nayatani

    2021.12.26 

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    Event date: 2021.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:China  

  4. First-eigenvalue maximization and embedding optimization Invited International conference

    Shin Nayatani

    The 3rd Japan-Taiwan Joint Conference on Differential Geometry  2021.11.3 

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    Event date: 2021.11

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  5. Riemannian metrics maximizing the first eigenvalue of the Laplacian on a closed surface Invited International conference

    Shin Nayatani

    2019.12.6 

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    Event date: 2019.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  6. Riemannian metrics maximizing the first eigenvalue of the Laplacian on a closed surface Invited International conference

    Shin Nayatani

    The first Geometry Conference for Friendship of Japan and Germany  2019.9.22 

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    Event date: 2019.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Chuo University (Korakuen Campus)   Country:Japan  

  7. ラプラシアンの第1固有値を最大化する種数2閉曲面上の計量

    納谷信, 庄田敏宏

    日本数学会2018年度年会 

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    Event date: 2018.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:東京大学   Country:Japan  

  8. Fixed-point property of random groups via energy of maps International conference

    Shin Nayatani

    Geometric Group Theory, Geometric Analysis, and Mapping Class Groups, 

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    Event date: 2008.5

    Language:English   Presentation type:Oral presentation (invited, special)  

  9. Fixed-point property of random groups via harmonic maps

    Shin Nayatani

    International Conference ``Variational Problems in Geometry'' 

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    Event date: 2007.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  10. 群の表示から定まるグラフ達の第1固有値について

    納谷信

    福岡大学微分幾何研究集会 

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    Event date: 2007.2

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  11. ボホナー技法と超剛性・固定点定理

    納谷信

    離散群論と作用素環論 

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    Event date: 2007.1

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  12. Superrigidity and fixed-point property of discrete groups via harmonic maps International conference

    Shin Nayatani

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    Event date: 2006.12

    Language:English   Presentation type:Oral presentation (invited, special)  

  13. 離散群の固定点性質

    金沢大学談話会 

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    Event date: 2006.10

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  14. Fixed-point properties of random groups

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    Event date: 2005.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  15. A fixed-point theorem for discrete-group actions on Hadamard spaces

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    Event date: 2005.10

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  16. On a certain geometric invariant of a CAT($0$) space

    福岡大微分幾何研究集会 

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    Event date: 2005.2

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  17. 離散群に対する固定点定理

    東京工業大学数学教室談話会 

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    Event date: 2005.1

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  18. 離散群作用に対する固定点定理と普遍タイヒミュラー空間

    「リーマン面・不連続群論」研究集会 

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    Event date: 2004.12

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  19. Fixed point theorems for discrete groups

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    Event date: 2004.11

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  20. 組合せ調和写像と CAT($0$) 空間への離散群作用

    日本数学会幾何学分科会特別講演 

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    Event date: 2004.9

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

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Research Project for Joint Research, Competitive Funding, etc. 1

  1. 離散幾何学における非線形問題

    2006

KAKENHI (Grants-in-Aid for Scientific Research) 12

  1. ラプラシアン固有値最大化と極小曲面

    Grant number:22H01122  2022.4 - 2027.3

    科学研究費助成事業  基盤研究(B)

    納谷 信

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    Authorship:Principal investigator 

    Grant amount:\15990000 ( Direct Cost: \12300000 、 Indirect Cost:\3690000 )

  2. 幾何学的剛性理論の深化

    Grant number:20H01802  2020.4 - 2025.3

    科学研究費助成事業  基盤研究(B)

    井関 裕靖, 近藤 剛史, 納谷 信

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    Authorship:Coinvestigator(s) 

    幾何学的対象(以下、空間という)の対称性はその空間に作用する群という代数的対象を用いて記述される。空間の対称性を理解する一つの方法は、どのような群が、どのような空間に、どのように作用するかを明らかにすることである。このような研究は19世紀にまで遡る長い歴史をもつ。本研究が対象とする「群の剛性」とは、その群の適当なクラスの空間への作用がある意味で一意的であることを意味する性質である。この性質は長らく特別なクラスの群が有する非常に特異で神秘的な性質だと考えられてきた。本研究は、この「群の剛性」という現象を、群や空間の無限遠の構造に注目することによって幾何学的な視点から解き明かすことを目指している。

  3. Global analysis of phase transition by using nano-minimal surface theory

    Grant number:17H06466  2017.6 - 2022.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)

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    Authorship:Coinvestigator(s) 

  4. Rigidity of non-isometric actions of discrete groups and non-linear spectral gap

    Grant number:17H02840  2017.4 - 2022.3

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

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    Authorship:Principal investigator 

    Grant amount:\17290000 ( Direct Cost: \13300000 、 Indirect Cost:\3990000 )

  5. Study on geometric structures of singularities of the mean curvature type flow

    Grant number:16H03937  2016.4 - 2021.3

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

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    Authorship:Coinvestigator(s) 

  6. An approach to the superrigidity of infinite discrete groups via random groups

    Grant number:25287013  2013.4 - 2018.3

    IZEKI Hiroyasu

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    The group is an algebraic object which also gives a description of symmetries of spaces. Some important and interesting groups often admits a property called "superrigidity", which we tried to understand as an extremal property among that involving infinite discrete groups. We could show that a fixed-point property, which should be considered to be an important aspect of superrigidity, is shared by finitely presented groups with overwhelming probability.

  7. Geometric and Global Analysis of Scalar Curvature and Einstein Metrics

    Grant number:24340008  2012.4 - 2018.3

    AKUTAGAWA KAZUO

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    On a compact manifold with very general singularities, we have studied the Yamabe problem and have established a generalization of Aubin’s inequality for Yamabe constants. When the inequality is strict, we have proved the existence of singular Yamabe metrics.
    When the equality of the inequality holds, we have constructed an example of singular manifolds which have not singular Yamabe metrics. For an edge-cone Einstein metric on a smooth manifold, we have constructed an appropriate family of smooth metrics with Ricci curvature bounded below by the Einstein constant. As a corollary, we have obtained an estimate of the Yamabe invariant from below by using the existence of edge-cone Einstein metrics.

  8. 非正曲率空間の幾何学と数理計画法

    2010 - 2013.3

    科学研究費補助金  挑戦的萌芽研究,課題番号:22654007

    納谷 信

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    Authorship:Principal investigator 

  9. 離散群に関する諸問題の幾何学的手法による研究

    2009 - 2014.3

    科学研究費補助金  基盤研究(B),課題番号:21340014

    納谷 信

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    Authorship:Principal investigator 

  10. 離散群の剛性の幾何学的手法による研究

    2005

    科学研究費補助金  基盤研究(B),課題番号:17340015

    納谷 信

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    Authorship:Principal investigator 

  11. 単体複体から無限次元非正曲率空間への組合せ調和写像と離散群の剛性の研究

    2002 - 2004

    科学研究費補助金  萌芽研究,課題番号:14654013

    納谷 信

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    Authorship:Principal investigator 

  12. 階数1の単純リー群の離散部分群の幾何学的手法による研究

    2001 - 2004

    科学研究費補助金  基盤研究(B),課題番号:13440019

    納谷 信

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    Authorship:Principal investigator 

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Teaching Experience (On-campus) 2

  1. Calculus II

    2011

  2. Calculus I

    2011