研究者総覧

山下 靖 (ヤマシタ ヤスシ)

  • 研究院自然科学系数学領域 教授
メールアドレス:
yamasitaics.nara-wu.ac.jp
Last Updated :2021/10/27

researchmap

学位

  • 博士(理学), 東京工業大学

研究キーワード

  • 連結和 ヤン・ミルズ方程式 plumbing growth function 橋指数 双曲空間 曲線の頂点 研究支援 極小曲面 ミュ-タント結び目 Zariski対 共形幾何学 アルゴリズム カスプ 実験数学 結び目、絡み目 変分問題 ブレイド Knot スカラ-曲率 Heegaard splitting W-グラフ 山辺計量 結び目理論 グラフィックス 可視化 幾何構造 Mobius幾何 射影幾何 垣水複体 2橋結び目 共形幾何 穴開トーラス Cannon-Thurston map virtual fiber 強可逆結び目 Montesinos knot 穴あきトーラス 錐多様体 Heegaard分解 McShaneの等式 ヘガード分解 ザイフェルト曲面 擬フックス群 トンネル数 結び目 双曲群 低次元トポロジー 射影構造 点配置空間 双曲多様体 タイヒミュラー空間 オートマティック群 配置空間 双曲デーン手術 双曲幾何学 クライン群 双曲構造 三次元多様体 双曲幾何 

研究分野

  • 自然科学一般, 幾何学

経歴

  • 2007年 - 2009年 奈良女子大学 理学部 Faculty of Science 准教授
  • 2005年 - 2007年 奈良女子大学 理学部 Faculty of Science 助教授
  • 1996年 - 2005年 奈良女子大学 理学部 Faculty of Science 講師
  • 1993年 - 1995年 奈良女子大学 理学部 Faculty of Science 助手

論文

  • The diagonal slice of Schottky space

    Caroline Series; Ser Tan; Yasushi Yamashita

    2017年08月03日, Algebraic & Geometric Topology, 17 (4), 2239 - 2282, doi;arxiv;web_of_science;url

    研究論文(学術雑誌)

  • Cosmetic surgery and the link volume of hyperbolic 3–manifolds

    Yo’av Rieck; Yasushi Yamashita

    2016年12月15日, Algebraic & Geometric Topology, 16 (6), 3445 - 3521, doi;web_of_science;url

    研究論文(学術雑誌)

  • Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes

    Yoshiyuki Nakagawa; Makoto Tamura; Yasushi Yamashita

    We discuss a problem posed by Gersten: Is every automatic group which does not contain ℤ × ℤ subgroup, hyperbolic? To study this question, we define the notion of "n-track of length n", which is a structure like ℤ × ℤ, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts freely, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively., 2014年09月, International Journal of Algebra and Computation, 24 (06), 795 - 813, doi;arxiv;web_of_science;url

    研究論文(学術雑誌)

  • The link volume of 3–manifolds

    Yo’av Rieck; Yasushi Yamashita

    2013年04月05日, Algebraic & Geometric Topology, 13 (2), 927 - 958, doi;arxiv;web_of_science;url

    研究論文(学術雑誌)

  • Linear slices of the quasi-Fuchsian space of punctured tori

    Yohei Komori; Yasushi Yamashita

    2012年04月04日, Conformal Geometry and Dynamics of the American Mathematical Society, 16 (5), 89 - 102, doi;arxiv;url

    研究論文(学術雑誌)

  • CREATING SOFTWARE FOR VISUALIZING KLEINIAN GROUPS

    Yasushi Yamashita

    2012年08月, Geometry, Topology and Dynamics of Character Varieties, 159 - 190, doi

    論文集(書籍)内論文

  • Finite planar emulators for K_4,5-4K_2 and K_1,2,2,2 and Fellows' conjecture

    Yo’av Rieck; Yasushi Yamashita

    2010年04月, European Journal of Combinatorics, 31 (3), 903 - 907, doi;arxiv;web_of_science

    研究論文(学術雑誌)

  • Punctured Torus Groups and 2-Bridge Knot Groups (I)

    2007年, Lecture Notes in Mathematics, doi;url;url

  • Computer experiments on the discreteness locus in projective structures

    Yasushi Yamashita

    2006年, Lond. Math. Soc. Lec. Notes, 329, 375 - 390, doi

    研究論文(学術雑誌)

  • Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori

    Yohei Komori; Toshiyuki Sugawa; Masaaki Wada; Yasushi Yamashita

    We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmuller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. For each point in the coordinate plane, we first compute the corresponding monodromy representation by numerical integration along certain loops. Then we decide whether the representation is discrete by applying Jorgensen's theory on the quasi-Fuchsian space of once-punctured tori., 2006年, Experimental Mathematics, 15 (1), 51 - 60, doi;web_of_science

    研究論文(学術雑誌)

  • Jorgensen's picture of punctured torus groups and its refinement

    H. Akiyoshi; M. Sakuma; M. Wada; Y. Yamashita

    2003年, Lond. Math. Soc. Lec. Notes, 299, 247 - 273, doi

    研究論文(学術雑誌)

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

    Yasushi Yamashita; Haruko Nishi; Sadayoshi Kojima

    In our previous paper, we discussed the hyperbolization of the configuration space of n(> 4) 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 Teichm\"uller 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., 1999年07月24日, GEOMETRIAE DEDICATA, 89 (1), 143 - 157, doi;web_of_science;arxiv;url;url

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

    Sadayoshi Kojima; Haruko Nishi; Yasushi Yamashita

    A purely combinatorial compactification of the configuration space of n (>4) 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., 1998年09月25日, TOPOLOGY, 38 (3), 497 - 516, web_of_science;arxiv;url;url

  • An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds

    M Wada; Y Yamashita; H Yoshida

    It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let M be a hyperbolic 3-manifold obtained by identifying the faces of n convex ideal polyhedra P-1, ..., P-n. If the faces of P-1, ..., P-n-1 are glued to P-n, then M can be decomposed into ideal tetrahedra by subdividing the P-i's., 1996年12月, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 124 (12), 3905 - 3911, doi;web_of_science

    研究論文(学術雑誌)

  • 結び目理論研究支援システムの設計

    落合 豊行; 山下 靖; 山田 修司

    We made a new method and a data structure to draw knots and links rapidly. We also developed a computer software which realizes our ideas in order to assist reserchers in knot theory. As an example of using our software in knot theory, we explain computational results of polynomial invariants which can recognize mutant knots of 3-4 braids, Kinoshita-Terasaka knot and Conway knot., 日本応用数理学会, 1994年12月15日, 日本応用数理学会論文誌, 4 (4), 337 - 348, cinii_articles

  • SHAPES OF STARS

    S KOJIMA; Y YAMASHITA

    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., 1993年03月, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 117 (3), 845 - 851, doi;web_of_science

    研究論文(学術雑誌)

  • Random Kleinian Groups, II Two Parabolic Generators

    Gaven Martin; Graeme O’Brien; Yasushi Yamashita

    2020年12月01日, Experimental Mathematics, 29 (4), 443 - 451, doi;arxiv;url

    研究論文(学術雑誌)

  • The realization problem for Jørgensen numbers

    Yasushi Yamashita; Ryosuke Yamazaki

    2019年02月25日, Conformal Geometry and Dynamics of the American Mathematical Society, 23 (2), 17 - 31, doi;arxiv;url

    研究論文(学術雑誌)

MISC

  • 新入生のための数学書ガイド(分担)

    山下靖

    2013年04月, 数学セミナー, 618, 8 - 36, url

    記事・総説・解説・論説等(商業誌、新聞、ウェブメディア)

  • A computer experiment on primitive stable representations (Integrated Research on Complex Dynamics)

    山下 靖

    京都大学, 2012年09月, 数理解析研究所講究録, 1807, 87 - 93, cinii_articles

  • 低次元トポロジーにおける分類

    山下靖

    2011年07月, 数学セミナー, 598, 18 - 22, url

    記事・総説・解説・論説等(商業誌、新聞、ウェブメディア)

  • 対称性と結晶 (特集 現代数学はいかに使われているか(幾何編))

    山下 靖

    サイエンス社, 2009年04月, 数理科学, 47 (4), 19 - 24, cinii_articles

  • OHT : A software for the dynamics of the modular group action on the character variety (Complex Dynamics and Related Topics)

    山下 靖

    京都大学, 2008年04月, 数理解析研究所講究録, 1586, 18 - 25, cinii_articles

  • On Negami's planar cover conjecture

    Yo'av Rieck; Yasushi Yamashita

    Given a finite cover f:tilde{G} \to G and an embedding of tilde{G} in the plane, Negami conjectures that G embeds in P^2. Negami proved this conjecture for regular covers. In this paper we define two properties (Propserties V and E), depending on the cover tilde{G} and its embedding into S^2, and generalize Negami's result by showing: (1) If Properties V and E are fulfilled then G embeds in P^2. (2) Regular covers always fulfill Properties V and E. We give an example of an irregular cover fulfilling Properties V and E. Covers not fulfilling Properties V and E are discussed as well., 2006年12月13日, arxiv;url;url

    機関テクニカルレポート,技術報告書,プレプリント等

  • Searching for $\mathbb{Z+A}$ subgroups in non-hyperbolic automatic groups (Perspectives of Hyperbolic Spaces II)

    中川 義行; 田村 誠; 山下 靖

    京都大学, 2004年07月, 数理解析研究所講究録, 1387, 110 - 117, cinii_articles

  • DRAWING BERS EMBEDDINGS OF THE TEICHMULLER SPACE OF ONCE PUNCTURED TORI (Hyperbolic Spaces and Related Topics II)

    小森 洋平; 須川 敏幸; 和田 昌昭; 山下 靖

    京都大学, 2000年07月, 数理解析研究所講究録, 1163, 9 - 17, cinii_articles

  • FORD DOMAINS OF PUNCTURED TORUS GROUPS AND TWO-BRIDGE KNOT GROUPS (Hyperbolic Spaces and Related Topics II)

    秋吉 宏尚; 作間 誠; 和田 昌昭; 山下 靖

    京都大学, 2000年07月, 数理解析研究所講究録, 1163, 67 - 77, cinii_articles

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

    Sadayoshi Kojima; Haruko Nishi; Yasushi Yamashita

    A purely combinatorial compactification of the configuration space of n( ≥ 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. © 1999 Elsevier Science Ltd. All rights reserved., Elsevier Ltd, 1999年, Topology, 38 (3), 497 - 516, doi;url

    機関テクニカルレポート,技術報告書,プレプリント等

  • Punctured torus groups and two-parabolic groups (Analysis and Geometry of Hyperbolic Spaces)

    秋吉 宏尚; 作間 誠; 和田 昌昭; 山下 靖

    京都大学, 1998年10月, 数理解析研究所講究録, 1065, 61 - 73, cinii_articles

  • ケーリーグラフの組み合せ的性質について

    山下 靖

    京都大学, 1997年12月, 数理解析研究所講究録, 1022, 179 - 184, cinii_articles

  • THE UNIFORMATION THEOREM FOR CIRCLE PACKINGS

    山下 靖

    京都大学, 1995年01月, 数理解析研究所講究録, 893, 36 - 42, cinii_articles

  • Ideal triangulations of noncompact hyperbolic 3-manifolds(Complex Analysis on Hyperbolic 3-Manifolds)

    山下 靖

    京都大学, 1994年08月, 数理解析研究所講究録, 882, 132 - 138, cinii_articles

  • The growth of torus link groups

    Yoshiyuki Nakagawa; Makoto Tamura; Yasushi Yamashita

    Let $G$ be a finitely generated group with a finite generating set $S$. For $g\in G$, let $l_S(g)$ be the length of the shortest word over $S$ representing $g$. The growth series of $G$ with respect to $S$ is the series $A(t) = \sum_{n=0}^\infty a_n t^n$, where $a_n$ is the number of elements of $G$ with $l_S(g)=n$. If $A(t)$ can be expressed as a rational function of $t$, then $G$ is said to have a rational growth function. We calculate explicitly the rational growth functions of $(p,q)$-torus link groups for any $p, q > 1.$ As an application, we show that their growth rates are Perron numbers., 2014年01月15日, arxiv;url;url

  • The Link Volume of Hyperbolic 3-Manifolds

    Yo'av Rieck; Yasushi Yamashita

    We prove that for any V>0, there exist a hyperbolic manifold M_V, so that Vol(M_V) < 2.03 and LinVol(M_V) > V. The proof requires study of cosmetic surgery on links (equivalently, fillings of manifolds with boundary tori). There is no bound on the number of components of the link (or boundary components). For statements, see the second part of the introduction. Here are two examples of the results we obtain: 1) Let K be a component of a link L in S^3. Then "most" slopes on K cannot be completed to a cosmetic surgery on L, unless K becomes a component of a Hopf link. 2) Let X be a manifold and \epsilon>0. Then all but finitely many hyperbolic manifolds obtained by filling X admit a geodesic shorter than \epsilon\ (note that this finite set may correspond to an infinitely many fillings)., 2012年11月08日, doi;arxiv;url;url

  • Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes (Complex Analysis and Topology of Discrete Groups and Hyperbolic Spaces)

    山下 靖

    京都大学, 2015年04月, 数理解析研究所講究録, 1936, 11 - 14, cinii_articles;cinii_books;url;url

  • A VERY BRIEF INTRODUCTION TO VIRTUAL HAKEN CONJECTURE (Representation spaces, twisted topological invariants and geometric structures of 3-manifolds : RIMS合宿型セミナー報告集)

    山下 靖

    京都大学, 2013年05月, 数理解析研究所講究録, 1836, 192 - 199, cinii_articles;cinii_books;url

書籍等出版物

  • Punctured torus groups and 2-bridge knot groups (I)

    秋吉宏尚; 作間誠; 和田昌昭; 山下靖

    Springer, 2007年, cinii_books (ISBN: 9783540718062)

  • 3次元幾何学とトポロジー

    William P. Thurston; Silvio Levy; 小島定吉

    培風館, 1999年, cinii_books (ISBN: 4563002720)

所属学協会

  • 日本数学会

  • 米国数学会



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