Updated on 2024/04/09

写真a

 
YAMASHITA Yasushi
 
Organization
Faculty of Science and Engineering Professor
Other responsible organization
Mathematics Course of Graduate School of Science and Engineering, Master's Program
Mathematics Course of Graduate School of Science and Engineering, Doctoral Program
Contact information
The inquiry by e-mail is 《here
External link

Degree

  • 博士(理学) ( 東京工業大学 )

  • 理学修士 ( 東京工業大学 )

Education

  • 1991.6
     

    Tokyo Institute of Technology   doctor course   withdrawn before completion

  • 1991.3
     

    Tokyo Institute of Technology   master course   completed

  • 1989.3
     

    Tokyo Institute of Technology   graduated

Research History

  • 2022.4 - Now

    Nara Women's University

  • 2012.4 - Now

    Nara Women's University   Faculty Division of Natural Sciences   Professor

  • 2010.1 - 2012.3

    Nara Women's University   Faculty of Science   Professor

  • 2007.4 - 2009.12

    Nara Women's University   Faculty of Science   Associate Professor

  • 2005.8 - 2007.3

    Nara Women's University   Faculty of Science

▼display all

Research Interests

  • knots

  • geometric structure

  • visualization

  • experimental mathematics

  • Kleinian groups

  • hyperbolic geometry

  • 3-manifolds

  • low-dimensional topology

  • Teichmuller theory

  • projective structure

  • configuration space

  • cone manifolds

  • hyperbolic Dehn surgery

  • geometric group theory

  • automatic groups

  • hyperbolic groups

  • growth function

Research Areas

  • Natural Science / Geometry

Papers

  • Random Kleinian Groups, II Two Parabolic Generators Reviewed

    Gaven Martin, Graeme O’Brien, Yasushi Yamashita

    Experimental Mathematics   29 ( 4 )   443 - 451   2020.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Informa UK Limited  

    In earlier work we introduced geometrically natural probability measures on
    the group of all M\"obius transformations in order to study "random" groups of
    M\"obius transformations, random surfaces, and in particular random
    two-generator groups, that is groups where the generators are selected
    randomly, with a view to estimating the likely-hood that such groups are
    discrete and then to make calculations of the expectation of their associated
    parameters, geometry and topology. In this paper we continue that study and
    identify the precise probability that a Fuchsian group generated by two
    parabolic M\"obius transformations is discrete, and give estimates for the case
    of Kleinian groups generated by a pair of random parabolic elements which we
    support with a computational investigation into of the Riley slice as
    identified by Bowditch's condition, and establish rigorous bounds.

    DOI: 10.1080/10586458.2018.1477079

    Web of Science

    arXiv

    researchmap

  • The realization problem for Jørgensen numbers Reviewed

    Yasushi Yamashita, Ryosuke Yamazaki

    Conformal Geometry and Dynamics of the American Mathematical Society   23 ( 2 )   17 - 31   2019.2

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:American Mathematical Society (AMS)  

    Let G be a two generator subgroup of PSL(2,C). The Jorgensen number J(G) of G
    is defined by
    J(G)=inf{ |tr^2 A-4|+|tr[A,B]-2| ; G=<A,B>}.
    If G is a non-elementary Kleinian group, then J(G) >= 1. This inequality is
    called Jorgensen's inequality. In this paper, we show that, for any r >= 1,
    there exists a non-elementary Kleinian group whose Jorgensen number is equal to
    r. This answers a question posed by Oichi and Sato. We also present our
    computer generated picture which estimates Jorgensen numbers from above in the
    diagonal slice of Schottky space.

    DOI: 10.1090/ecgd/331

    Web of Science

    arXiv

    researchmap

  • The diagonal slice of Schottky space Reviewed

    Caroline Series, Ser Tan, Yasushi Yamashita

    Algebraic & Geometric Topology   17 ( 4 )   2239 - 2282   2017.8

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Sciences Publishers  

    An irreducible representation of the free group on two generators X,Y into
    SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study
    the diagonal slice of representations for which X,Y and XY have equal trace.
    Using the three-fold symmetry and Keen-Series pleating rays we locate those
    groups which are free and discrete, in which case the resulting hyperbolic
    manifold is a genus-2 handlebody.
    We also compute the Bowditch set, consisting of those representations for
    which no primitive elements in the group generated by X,Y are parabolic or
    elliptic, and at most finitely many have trace with absolute value at most 2.
    In contrast to the quasifuchsian punctured torus groups originally studied by
    Bowditch, computer graphics show that this set is significantly different from
    the discreteness locus.

    DOI: 10.2140/agt.2017.17.2239

    Web of Science

    arXiv

    researchmap

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

    Yo’av Rieck, Yasushi Yamashita

    Algebraic & Geometric Topology   16 ( 6 )   3445 - 3521   2016.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Sciences Publishers  

    We prove that for any V > 0 there exists a hyperbolic manifold M-V such that Vol(M-V) < 2.03 and LinkVol (M-V) > V. This was conjectured by the authors in [Algebr. Geom. Topol. 13 (2013) 927-958, Conjecture 1.3].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 it is not true that there are only finitely many fillings fulfilling this condition.)

    DOI: 10.2140/agt.2016.16.3445

    Web of Science

    Scopus

    researchmap

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

    Yoshiyuki Nakagawa, Makoto Tamura, Yasushi Yamashita

    International Journal of Algebra and Computation   24 ( 06 )   795 - 813   2014.9

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:World Scientific Pub Co Pte Lt  

    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.

    DOI: 10.1142/s0218196714500349

    Web of Science

    arXiv

    researchmap

▼display all

Books

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

    秋吉宏尚, 作間誠, 和田昌昭, 山下靖( Role: Joint author)

    Springer  2007  ( ISBN:9783540718062

     More details

    Language:English  

    researchmap

  • 3次元幾何学とトポロジー

    William P. Thurston, Silvio Levy, 小島定吉( Role: Joint translator)

    培風館  1999  ( ISBN:4563002720

     More details

    Language:Japanese  

    researchmap

MISC

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

    Yamashita Yasushi

    RIMS Kokyuroku   1936   11 - 14   2015.4

     More details

    Language:English   Publisher:Kyoto University  

    CiNii Books

    researchmap

    Other Link: http://hdl.handle.net/2433/223709

  • The growth of torus link groups

    Yoshiyuki Nakagawa, Makoto Tamura, Yasushi Yamashita

    2014.1

     More details

    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.

    arXiv

    researchmap

    Other Link: http://arxiv.org/pdf/1401.3403v1

  • A VERY BRIEF INTRODUCTION TO VIRTUAL HAKEN CONJECTURE (Representation spaces, twisted topological invariants and geometric structures of 3-manifolds)

    YAMASHITA YASUSHI

    RIMS Kokyuroku   1836   192 - 199   2013.5

     More details

    Language:English   Publisher:Kyoto University  

    CiNii Books

    researchmap

  • 新入生のための数学書ガイド(分担) Invited

    山下靖

    数学セミナー   618   8 - 36   2013.4

     More details

    Language:Japanese   Publishing type:Article, review, commentary, editorial, etc. (trade magazine, newspaper, online media)  

    researchmap

  • The Link Volume of Hyperbolic 3-Manifolds

    Yo'av Rieck, Yasushi Yamashita

    2012.11

     More details

    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).

    DOI: 10.2140/agt.2016.16.3445

    arXiv

    researchmap

    Other Link: http://arxiv.org/pdf/1211.1839v1

▼display all

Presentations

  • Computer experiments on generalized Riley slice Invited

    Yasushi Yamashita

    Topology and geometry seminar at NUS  2024.3 

     More details

    Event date: 2024.3    

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

    researchmap

  • An implementation of the Bestvina-Handel algorithm for surface homeomorphisms in python

    山下靖

    年末セミナー2023〰Topics on Surfaces and Knots  2023.12 

     More details

    Event date: 2023.12    

    Language:Japanese   Presentation type:Oral presentation (general)  

    researchmap

  • Arithmetic Kleinian groups generated by two elliptic elements Invited

    山下靖

    トポロジーとコンピュータ2023  2023.10 

     More details

    Event date: 2023.10    

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

    researchmap

  • Revisiting the moduli space of right-angled hyperbolic pentagon

    Yasushi Yamashita

    Geometry in low-dimensions 2022  2022.12 

     More details

    Event date: 2022.12    

    Language:Japanese   Presentation type:Oral presentation (general)  

    researchmap

  • Riley sliceと仲間たち Invited

    山下靖

    早稲田大学双曲幾何幾何学的群論セミナー  2022.6 

     More details

    Event date: 2022.6    

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

    researchmap

▼display all

Research Projects

  • Invariants of pseudo-Anosov homeomorphisms

    Grant number:21K03259  2021.4 - 2024.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Waseda University

      More details

    Grant amount: \4160000 ( Direct Cost: \3200000 、 Indirect Cost: \960000 )

    researchmap

  • 指標多様体上の幾何と写像類群作用を用いた算術的クライン群の分類

    Grant number:20K03612  2020.4 - 2023.3

    日本学術振興会  科学研究費助成事業 基盤研究(C)  基盤研究(C)  奈良女子大学

    山下 靖

      More details

    Grant amount: \1950000 ( Direct Cost: \1500000 、 Indirect Cost: \450000 )

    曲面Σの基本群πからリー群Gへの表現全体の空間Hom(π,G)には群Gが共役により作用する。この作用による幾何学的不変式論の意味での商空間Xを指標多様体という。この指標多様体を、表現の像が離散群になる部分とそうでない部分に分割すると、前者はΣのG構造の変形の空間とみなすことができる。特にGがSL(2,C)の場合は双曲幾何構造の変形空間であり、重要な研究対象である。特に離散部分群はクライン群とよばれ、重要な研究対象である。また、指標多様体には曲面Σの写像類群が自然に作用し、この作用の複雑さによっても指標多様体は2つに分割される。これら2つの関係は未解明な部分が多い。
    今年度は、SL(2,C)の部分群で楕円型の元2つによって生成されるクライン群で、算術的とよばれる条件をみたすものの分類のための研究を行った。楕円型の元はその位数で特徴づけることができるが、特に位数が6以下の場合において、どのような算術的クライン群が存在しうるかについて、計算機を用いた実験を行った。クライン群は指標多様体のパラメータを用いて記述され、それが算術的になるためにはそのパラメータが代数的整数であって四元数代数等に関する一定の条件をみたす必要があることが知られている。さらに、指標多様体上の写像類群作用に関して、BowditchのQ条件というものをみたさなければならないことが予想されている。そのため、これらに関する計算機実験を進めることで、算術的クライン群の完全分類に向けた候補を与えるための研究を進展させた。

    researchmap

  • Geometry of discrete groups and its applications to 3-dimensional topology

    Grant number:17H02843  2017.4 - 2022.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)  Grant-in-Aid for Scientific Research (B) 

      More details

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

    researchmap

  • 結び目と3次元多様体の量子トポロジー

    Grant number:16H02145  2016.4 - 2021.3

    日本学術振興会  科学研究費助成事業 基盤研究(A)  基盤研究(A)  京都大学

    大槻 知忠, 金信 泰造, 伊藤 哲也, 谷山 公規, 藤原 耕二, 逆井 卓也, 大山 淑之, 山下 靖, 茂手木 公彦, 森藤 孝之, 玉木 大, 志摩 亜希子

      More details

    Grant amount: \33150000 ( Direct Cost: \25500000 、 Indirect Cost: \7650000 )

    結び目のKashaev不変量と双曲体積を関連づける体積予想は、量子トポロジーと双曲幾何を結びつける懸案の予想であり、最近15年間世界的にこの分野の中心的な話題となってきた。本研究の目標は、体積予想を多くの結び目について解決し、Kashaev不変量の漸近展開として得られるべき級数を新しい結び目不変量として研究することである。これにより、量子トポロジーと双曲幾何を融合する新しい研究テーマが創出されることが期待される。また、3次元多様体の量子不変量の漸近展開に双曲体積が現れることを主張する「3次元多様体の体積予想」も近年定式化され、これについての研究もすすめた。とくに、漸近展開の準古典極限の項にはReidemeister torionが現れることが観察され、いくつかの例に対してそれを証明した。
    また、国際会議「East Asian Conference on Geometric Topology」と、研究集会「Intelligence of Low-dimensional Topology」「結び目の数理」「トポロジーシンポジウム」「トポロジー新人セミナー」「Topology and Geometry of Low-dimensional Manifolds」「トポロジーとコンピュータ」「東北結び目セミナー」を開催した。これらの国際会議と研究集会では、国内外の研究者による活発な研究交流が行われ、十分な成果を挙げた。

    researchmap

  • The geometry of character variety given by the dynamics of mapping class group action

    Grant number:17K05250  2017.4 - 2020.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)  Grant-in-Aid for Scientific Research (C)  Nara Women's University

    Yamashita Yasushi

      More details

    Grant amount: \1950000 ( Direct Cost: \1500000 、 Indirect Cost: \450000 )

    Hyperbolic geometry is important in studying two and three-dimensional manifolds. To understand this geometric structure, we studied the character variety of the fundamental group of two-dimensional manifolds.
    In particular, we studied the realization problem of Jorgensen numbers of the Kleinian groups generated by two elements. Also, we performed a computer experiment on the problem of when randomly generated two parabolic elements give a Kleinian group.

    researchmap

▼display all

Teaching Experience

  • Geometric Group Theory

    2019 - Now   Institution:Nara Women's University

  • Special lecture on hyperbolic geometry

    2018 - Now   Institution:Nara Women's University

  • Basic Science 2

    2016 - Now   Institution:Nara Women's University

  • The science you need to know before you enter the workforce

    2016 - Now   Institution:Nara Women's University

  • Basic Science 1

    2016 - Now   Institution:Nara Women's University

▼display all