2022/06/27 更新

写真a

コジマ サダヨシ
小島 定吉
所属
理工学術院 国際理工学センター(理工学術院)
職名
教授(任期付)
メールアドレス
メールアドレス

兼担

  • 政治経済学術院   政治経済学部

学内研究所等

  • 2020年
    -
    2022年

    理工学術院総合研究所   兼任研究員

学歴

  • 1979年09月
    -
    1981年05月

    Columbia University  

  • 1976年04月
    -
    1978年03月

    東京大学   理学系研究科   数学  

  • 1972年04月
    -
    1976年03月

    東京大学   理学部   数学科  

学位

  • Columbia University   Ph.D

  • 東京大学   理学修士

経歴

  • 2018年04月
    -
    継続中

    早稲田大学   理工学術院   教授

  • 2016年04月
    -
    2018年03月

    東京工業大学   情報理工学院   教授

  • 1994年06月
    -
    2016年03月

    東京工業大学   大学院情報理工学研究科   教授

  • 1987年08月
    -
    1994年06月

    東京工業大学   理学部   助教授

  • 1985年04月
    -
    1987年07月

    東京都立大学   理学部   助教授

  • 1978年04月
    -
    1985年03月

    東京都立大学   理学部   助手

▼全件表示

所属学協会

  •  
     
     

    American Mathematical Society

  •  
     
     

    日本数学会

  •  
     
     

    日本応用数理学会

 

研究分野

  • 幾何学

論文

  • On the moduli space of equilateral pentagons

    S. Klaus, S. Kojima

    Beitr. Algebra Geom.   60   487 - 497  2019年  [査読有り]

  • Normalize entropy versus volume for pseudo-Anosovs

    S. Kojima, G. McShane

    Geom. & Topol.   22   2403 - 2426  2018年  [査読有り]

  • Minimal dilatations of pseudo-Anosovs generated by the magic 3-manifold and their asymptotic behevior

    E. Kin, S. Kojima, M. Takasawa

    Algebr. Geom. Topol.   13   3537 - 3602  2013年  [査読有り]

  • ENTROPY, WEIL-PETERSSON TRANSLATION DISTANCE AND GROMOV NORM FOR SURFACE AUTOMORPHISMS

    Sadayoshi Kojima

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   140 ( 11 ) 3993 - 4002  2012年11月  [査読有り]

     概要を見る

    Thanks to a theorem of Brock on the comparison of Weil-Petersson translation distances and hyperbolic volumes of mapping tori for pseudo-Anosovs, we prove that the entropy of a surface automorphism in general has linear bounds in terms of a Gromov norm of its mapping torus from below and an inbounded geometry case from above. We also prove that the Weil-Petersson translation distance does the same from both sides in general. The proofs are in fact immediately derived from the theorem of Brock, together with some other strong theorems and small observations.

  • Circle packings on surfaces with projective structures and uniformization

    Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan

    PACIFIC JOURNAL OF MATHEMATICS   225 ( 2 ) 287 - 300  2006年06月  [査読有り]

     概要を見る

    Let Sigma(g) be a closed orientable surface of genus g >= 2 and tau a graph on Sigma(g) with one vertex that lifts to a triangulation of the universal cover. We have shown before that the cross ratio parameter space C-tau associated with tau, which can be identified with the set of all pairs of a projective structure and a circle packing on it with nerve isotopic to tau, is homeomorphic to R6g-6, and moreover that the forgetting map of C-tau to the space of projective structures is injective. Here we show that the composition of the forgetting map with the uniformization from C-tau to the Teichmuller space T-g is proper.

    DOI

  • Circle packings on surfaces with projective structures : A survey

    Sadayoshi Kojima, Shigeru Mizushima, Ser Peow Tan

    LMS Lecture Notes Series   329   337 - 353  2006年  [査読有り]

  • Circle packings on surfaces with projective structures

    S Kojima, S Mizushima, SP Tan

    JOURNAL OF DIFFERENTIAL GEOMETRY   63 ( 3 ) 349 - 397  2003年03月  [査読有り]

     概要を見る

    The Koebe-Andreev-Thurston theorem states that for any triangulation of a closed orientable surface Sigma(g) of genus g which is covered by a simple graph in the universal cover, there exists a unique metric of curvature 1, 0 or -1 on the surface depending on whether g = 0, 1 or greater than or equal to 2 such that the surface with this metric admits a circle packing with combinations given by the,triangulation. Furthermore, the circle packing is essentially rigid, that is, unique up to conformal automorphisms of the surface isotopic to the identity.
    In this paper, we consider projective structures on the surface where circle packings are also defined. We show that the space of projective structures on a surface of genus g greater than or equal to 2 which admits a circle packing contains a neighborhood of the Koebe-Andreev-Thurston structure homeomorphic to R6g-6. We furthermore show that if a circle packing consists of one circle, then the space is globally homeomorphic to R6g-6 and that the circle packing is rigid.

  • Configuration spaces of points on the circle and hyperbolic Dehn fillings, II

    Y Yamashita, H Nishi, S Kojima

    GEOMETRIAE DEDICATA   89 ( 1 ) 143 - 157  2002年02月  [査読有り]

     概要を見る

    In our previous paper (Topology 38 (1999), 497-516), we discussed the hyperbolization of the configuration space of n (greater than or equal to 5) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichmuller space when n = 5 and to the Dehn filling space when n = 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.

  • Complex hyperbolic cone structures on the configuration spaces

    SADAYOSHI KOJIMA

    Rend. Istit. Mat.. Univ. Trieste   32   149 - 163  2001年  [査読有り]

  • Configuration spaces of points on the circle and hyperbolic Dehn fillings

    S Kojima, H Nishi, Y Yamashita

    TOPOLOGY   38 ( 3 ) 497 - 516  1999年05月  [査読有り]

     概要を見る

    A purely combinatorial compactification of the configuration space of n(greater than or equal to 5) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n - 3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of deformations arisen in this manner will be locally described in the existing deformation theory of hyperbolic structures when n - 3 = 2, 3. (C) 1999 Elsevier Science Ltd. All rights reserved.

  • Deformations of hyperbolic 3-cone-manifolds

    S Kojima

    JOURNAL OF DIFFERENTIAL GEOMETRY   49 ( 3 ) 469 - 516  1998年07月  [査読有り]

     概要を見る

    We show that any compact orientable hyperbolic 3-cone-manifoId with cone angles at most pi can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the focal rigidity by Hodgson and Kerckhoff implies the global rigidity for compact orientable hyperbolic 3-cone-manifolds under the same angle assumption.

  • Hyperbolic 3-manifolds singular along knots

    S Kojima

    CHAOS SOLITONS & FRACTALS   9 ( 4-5 ) 765 - 777  1998年04月  [査読有り]

    DOI

  • Flexible boundaries in deformations of hyperbolic 3-manifolds

    M Fujii, S Kojima

    OSAKA JOURNAL OF MATHEMATICS   34 ( 3 ) 541 - 551  1997年09月  [査読有り]

  • Compact hyperbolic universe and singularities

    A Ishibashi, T Koike, M Siino, S Kojima

    PHYSICAL REVIEW D   54 ( 12 ) 7303 - 7310  1996年12月  [査読有り]

     概要を見る

    Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase at an early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time slices. Though the universal covering space of the universe has a past Cauchy horizon and can be extended analytically beyond it, the extended region has densely many points which correspond to singularities of the compact universe. The result is essentially attributed to the ergodicity of the geodesic flow on a compact negatively curved manifold. The relationship with the strong cosmic censorship conjecture also is discussed.

    DOI PubMed CiNii

  • Immersed Geodesic Surfaces in Hyperbolic 3-Manifolds

    SADAYOSHI KOJIMA

    Complex Variables   29   45 - 58  1996年  [査読有り]

  • Geometry of hyperbolic 3-manifolds with boundary

    Sadayoshi Kojima

    Kodai Mathematical Journal   17 ( 3 ) 530 - 537  1994年  [査読有り]

    DOI

  • SHAPES OF STARS

    S KOJIMA, Y YAMASHITA

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   117 ( 3 ) 845 - 851  1993年03月  [査読有り]

     概要を見る

    In this paper we construct a natural geometric structure for the space of shapes of a star-shaped polygon. Roughly speaking we find: The set of similarity classes of marked stars forms a hyperbolic right angle pentagon bundle over the space of external angle sets of inscribed pentagons. The assignment of the shape of its fiber to each angle set forms a hyperbolic plane bundle over the Teichmuller space of hyperbolic right angle pentagons. Any automorphism induced by renumbering is compatible with these geometric structures.

  • HOMOTOPY INVARIANTS OF NONORIENTABLE 4-MANIFOLDS

    MH KIM, S KOJIMA, F RAYMOND

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   333 ( 1 ) 71 - 81  1992年09月  [査読有り]

     概要を見る

    We define a Z4-quadratic function on pi-2 for nonorientable 4-manifolds and show that it is a homotopy invariant. We then use it to distinguish homotopy types of certain manifolds that arose from an analysis of toral action on nonorientable 4-manifolds.

  • APOLLONIAN PACKINGS AND HYPERBOLIC GEOMETRY

    M ISHIDA, S KOJIMA

    GEOMETRIAE DEDICATA   43 ( 3 ) 265 - 283  1992年09月  [査読有り]

     概要を見る

    We review the generalized apollonian packings by Bessis and Demko from 3-dimensional viewpoints and solve their conjectures on the discreteness of the groups they constructed. Moreover, we systematically generalize the construction of packings in terms of the Coxeter group theory, and propose a computational algorithm to draw the pictures efficiently based on the automatic group theory.

  • Polyhedral decomposition of hyperbolic 3-manifolds with totally geodesic boundary

    SADAYOSHI KOJIMA

    Advanced Study in Pure Math.   20   93 - 112  1992年  [査読有り]

  • THE SMALLEST HYPERBOLIC 3-MANIFOLDS WITH TOTALLY GEODESIC BOUNDARY

    S KOJIMA, Y MIYAMOTO

    JOURNAL OF DIFFERENTIAL GEOMETRY   34 ( 1 ) 175 - 192  1991年07月  [査読有り]

  • Polyhedral decomposition of hyperbolic manifolds with boundary

    SADAYOSHI KOJIMA

    Proceedings of workshop in Pure Mathematics, Seoul N. Univ.   10 ( part iii ) 37 - 57  1990年  [査読有り]

  • ISOMETRY TRANSFORMATIONS OF HYPERBOLIC 3-MANIFOLDS

    S KOJIMA

    TOPOLOGY AND ITS APPLICATIONS   29 ( 3 ) 297 - 307  1988年08月  [査読有り]

  • Virtual Betti numbers of some hyperbolic 3-manifolds

    D. D. Long, S. Kojima

    A Fate of Topology, Acadmic Press     417 - 437  1988年  [査読有り]

  • FINITE COVERS OF 3-MANIFOLDS CONTAINING ESSENTIAL SURFACES OF EULER CHARACTERISTIC = 0

    S KOJIMA

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   101 ( 4 ) 743 - 747  1987年12月  [査読有り]

  • BOUNDING FINITE-GROUPS ACTING ON 3-MANIFOLDS

    S KOJIMA

    MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY   96 ( SEP ) 269 - 281  1984年  [査読有り]

  • A CONSTRUCTION OF GEOMETRIC STRUCTURES ON SEIFERT FIBERED-SPACES

    S KOJIMA

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   36 ( 3 ) 483 - 495  1984年  [査読有り]

  • 幾何学

    小島 定吉

    数学   36 ( 1 ) 21 - 22  1984年

    DOI CiNii

  • MILNOR MU-BAR-INVARIANTS, MASSEY PRODUCTS AND WHITNEY TRICK IN 4 DIMENSIONS

    S KOJIMA

    TOPOLOGY AND ITS APPLICATIONS   16 ( 1 ) 43 - 60  1983年  [査読有り]

  • NILPOTENT COMPLETIONS AND LIE-RINGS ASSOCIATED TO LINK GROUPS

    S KOJIMA

    COMMENTARII MATHEMATICI HELVETICI   58 ( 1 ) 115 - 134  1983年  [査読有り]

  • Thurstonの'怪物定理'について

    小島 定吉

    数学   34 ( 4 ) 301 - 316  1982年

    DOI CiNii

  • ALGEBRAIC CLASSIFICATION OF LINKING PAIRINGS ON 3-MANIFOLDS

    A KAWAUCHI, S KOJIMA

    MATHEMATISCHE ANNALEN   253 ( 1 ) 29 - 42  1980年  [査読有り]

  • Some new invariants of links

    S. Kojima, M. Yamasaki

    Inventiones math.   54   213 - 228  1979年  [査読有り]

  • The Matsumoto tripling for compact simply connected 4-manifolds

    M. Kato, S. Kojima, T. Ohkawa, M. Yamasaki

    Tohoku Math. J.   31   525 - 535  1979年  [査読有り]

  • Piecewise linear Dehn's lemma in 4-dimensions

    SADAYOSHI KOJIMA

    Proceedings of Japan Academy   55   65 - 67  1979年  [査読有り]

  • Classification of simple knots by Levine pairings

    SADAYOSHI KOJIMA

    Comment. Math. Helvetici   54   356 - 367  1979年  [査読有り]

  • A classification of some even dimensional fibered knots

    SADAYOSHI KOJIMA

    J. Fac. Sci. Univ. Tokyo   24   671 - 683  1977年  [査読有り]

▼全件表示

書籍等出版物

  • Circle packing and Teichmuller space

    European Mathematical Society Publishing House  2008年 ISBN: 3037190558

  • 3次元の幾何学

    朝倉書店  2002年

  • 多角形の現代幾何学 増補版

    牧野書店  1999年

  • トポロジー入門

    共立出版株式会社  1998年

Misc

受賞

  • 幾何学賞

    2000年  

共同研究・競争的資金等の研究課題

  • Geometric Structures on 3-manifolds

  • Hyperbolic Geometry

  • 3次元多様体の幾何構造

  • 双曲幾何学

講演・口頭発表等

  • A numerical algorithm for block-diagonal decomposition of matrix *-algebra

    HPOPT 2008  

    発表年月: 2008年

  • Entropy vs volume

    KIAS Workshop on Hyperbolic Geometry and Related Topics  

    発表年月: 2008年

  • ポアンカレ予想について

    日本応用数理学会春の研究部会総合発表会  

    発表年月: 2008年

  • A numerical algorithm for block-diagonal decomposition of matrix *-algebra

    HPOPT 2008  

    発表年月: 2008年

  • ポアンカレ予想と幾何化予想

    数理物理2008「リッチフローの微分幾何と位相幾何」  

    発表年月: 2008年

  • ポアンカレ予想について

    静岡大学理学講演会  

    発表年月: 2008年

  • ポアンカレ予想と幾何化予想ートポロジーの100年ー

    奈良女子大学数物情交流シンポジウム  

    発表年月: 2008年

  • Entropy vs volume

    KIAS Workshop on Hyperbolic Geometry and Related Topics  

    発表年月: 2008年

  • Comparison of hyperbolic volume with other invariants

    Workshop on hyperbolic structures on 3-manifolds and large scale geometry of Teichmuller space  

    発表年月: 2007年

  • Packings on surfaces I

    ISM Symposium, Packing and Random Packing  

    発表年月: 2006年

  • Packings on projective Riemann surfaces

    Teichmuller spaces (Classical and Quantum)  

    発表年月: 2006年

  • Quasi-isometry of invariants

    発表年月: 2006年

  • Packings on surfaces I

    ISM Symposium, Packing and Random Packing  

    発表年月: 2006年

  • Packings on projective Riemann surfaces

    Teichmuller spaces (Classical and Quantum)  

    発表年月: 2006年

  • The Dehn filling space of a certain hyperbolic 3-orbifold

    Discrete Geometric Analysis  

    発表年月: 2004年

  • Nonsingular parts of hyperbolic 3-cone-manifolds

    Topology and Teichm\"uller Spaces  

    発表年月: 1996年

  • Determining knots by branched covers

    Low-dimensional Topology and Kleinian Groups  

    発表年月: 1986年

▼全件表示

 

現在担当している科目

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委員歴

  • 2010年04月
    -
    継続中

    日本数学会  監事

  • 2006年08月
    -
    2020年09月

    日本学術会議  連携会員

  • 2016年04月
    -
    2020年03月

    日本学術振興会  学術システム研究センター主任研究員

  • 2005年04月
    -
    2008年04月

    日本数学会  理事

  • 2005年04月
    -
    2006年04月

    日本数学会  理事長