Researchers Database

MATSUZAWA Jun-ichi

FacultyFaculty Division of Natural Sciences Research Group of Mathematics
PositionProfessor
Last Updated :2022/11/25

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Profile and Settings

  • Name (Japanese)

    Matsuzawa
  • Name (Kana)

    Junichi

Degree

  • Ph.D./Doctor of Science: 1989 The University of Tokyo, The University of Tokyo

Research Interests

  • モジュライ
  • 代数曲面
  • ルート系
  • ワイル群
  • リー環
  • リー群
  • moduli
  • algebraic surface
  • Root system
  • Weyl group
  • Lie Algebra
  • Lie group

Research Areas

  • Natural sciences, Algebra

Research Experience

  • 2000, 2006, :京都大学工学研究科 講師
  • 2000, 2006, :Graduate School of Engineering, Lecturer
  • 2006, -:奈良女子大学理学部 教授
  • 2006, -:Nara Women's University, Faculty of Science, Professor
  • 1989, 1995, :京都大学理学部 助手
  • 1989, 1995, :Faculty of Science, Kyoto University, Instructor

Association Memberships

  • 日本数学会
  • アメリカ数学会
  • American Mathematical Society

Ⅱ.研究活動実績

Published Papers

  • Refereed, Nature Communications, Metallic-mean quasicrystals as aperiodic approximants of periodic crystals, J. Nakakura; P. Ziherl; J. Matsuzawa; T. Dotera, Sep. 2019, 10, Scientific journal
  • Not Refereed, 表面科学, 3 重周期極小曲面上の剛体球, 松澤 淳一; 堂寺知成, 2013, 34, 1, 21, 26
  • Not Refereed, INTERFACE FOCUS, ROYAL SOC, Hard spheres on the gyroid surface, Tomonari Dotera; Masakiyo Kimoto; Junichi Matsuzawa, We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincare disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV., Oct. 2012, 2, 5, 575, 581, Scientific journal
  • Not Refereed, Tukuba Journal of Mathematics, Institute of Mathematics, University of Tsukuba, Representations of the normalizers of maximal tori of simple Lie groups, MATSUZAWA Jun-ichi; Makoto TAKAHASHI, 2009, 33, 2, 189, 237
  • Not Refereed, Kobunshi, Symmetry and Group Theory, Jun’ichi Matsuzawa, The symmetric structures of atoms, molecules and crystals are described in terms of group theory, which gives a method for studying the objects with mathematical structures. This article presents a survey of the applications of group theory in Euclidean geometry, eliiptic geometry and hyperbolic geometry with focusing on discontinuous groups, tessellations, surfaces of constant curvature. © 2008, The Society of Polymer Science, Japan. All rights reserved., 2008, 57, 2, 66, 70, Scientific journal
  • Not Refereed, JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, KINOKUNIYA CO LTD, Blow-ups of P-2 and root systems of type D, J Matsuzawa; A Omura, Dec. 1999, 39, 4, 725, 761, Scientific journal
  • Not Refereed, PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, KYOTO UNIV, ROOT SYSTEMS AND PERIODS ON HIRZEBRUCH SURFACES, J MATSUZAWA, Sep. 1993, 29, 3, 411, 438, Scientific journal
  • Not Refereed, J.Fac.Sci.Univ. Tokyo, Faculty of Science, The University of Tokyo, Monoidal transformations of Hirzebruch surfaces and Weyl groups of type C, MATSUZAWA Jun-ichi, 1988, 35, 2, 425, 429
  • Not Refereed, COMMUNICATIONS IN ALGEBRA, MARCEL DEKKER INC, ON THE GENERALIZED EXPONENTS OF CLASSICAL LIE-GROUPS, J MATSUZAWA, 1988, 16, 12, 2579, 2623, Scientific journal
  • Not Refereed, Proc.Sympos. Pure Math. AMS, On the Generalized Exponents of Classical Lie Groups, MATSUZAWA Jun-ichi, 1987, 47, 463, 471
  • Not Refereed, Algebraic and Topological Thories, Kinokuniya, Representations of Weyl Groups on Zero Weight Spaces of G-modules, MATSUZAWA Jun-ichi; S. Ariki; I. Terada, 1985, 546, 568

MISC

  • Meeting abstracts of the Physical Society of Japan, The Physical Society of Japan (JPS), 25aBF-7 Phase Transition of Hard Spheres on the Gyroid Surface, Dotera T.; Kimoto M.; Matsuzawa J., 05 Mar. 2012, 67, 1, 407, 407
  • Not Refereed, 京都大学数理解析研究所講究録, ポリマーアロイにみられるジャイロイド曲面上の双曲タイリング, 松澤 淳一; 堂寺知成, 2011, 1725, 80, 91
  • Not Refereed, RIMS Kokyuroku, Hyperbolic Tiling on the Gyroid Surface in a Polymeric Alloy, MATSUZAWA Jun-ichi; Tomonari Dotera, 2011, 1725, 80, 91
  • Meeting abstracts of the Physical Society of Japan, The Physical Society of Japan (JPS), 24pTB-4 Hyperbolic Tiling on the Gyroid Membrane in ABC Star Block Copolymers, Hayashida K.; Dotera T.; Matsuzawa J.; Takano A.; Matsushita Y., 18 Aug. 2010, 65, 2, 322, 322
  • Not Refereed, Kobunshi (High Polymers, Japan), Symmetry and Group Theory, MATSUZAWA Jun-ichi, 2008, 57, 2月, 66, 70
  • Not Refereed, 「符合・格子・頂点作用素代数と有限群」報告集, 3次曲面の幾何とルート系, 松澤 淳一, 2001
  • Not Refereed, 「結び目と低次元トポロジー」報告集, Arnold の Strange Duality とCasson-Walker 不変量, 松澤 淳一, 1999
  • Not Refereed, 「等質空間上の非可換解析学」京大数理解析研究所講究録, 京都大学, $E_6$型極大トーラス部分群と3次曲面, 松澤 淳一, 1995, 895, 1, 14
  • Not Refereed, 論集「現代の母関数」, 母関数とトポロジー―moduli・周期写像・モノドロミー, 松澤 淳一, 1991
  • Not Refereed, 京大数理解析研究所講究録, Torelli theorem for certain rational surfaces and root system of type A, 松澤 淳一, 1991, 765
  • Not Refereed, Torelli theorem for certain rational surfaces and root system of type A, MATSUZAWA Jun-ichi, 1991, 765
  • Not Refereed, 京大数理解析研究所講究録, 京都大学, Flag manifold と Robinson-Schensted 対応, 松澤 淳一, 1989, 705, 104, 114
  • Not Refereed, 京大数理解析研究所講究録, Young tableau をめぐって― GLの幾何と表現論, 松澤 淳一, 1988, 670
  • Not Refereed, ユニタリ表現論セミナー報告集VIII, Hirzebruch曲面のブローアップと C型 Weyl群, 松澤 淳一, 1988
  • Not Refereed, 数学, The Mathematical Society of Japan, リー群と表現論, 松澤 淳一; 有木進; 徳山豪, 1987, 39, 1, 60, 63
  • Not Refereed, 京大数理解析研究所講究録, 京都大学, 古典複素リー群のgeneralized exponents―Young図形とuniversal characterとKostant の generalized exponents, 松澤 淳一, 1987, 630, 66, 85
  • Not Refereed, 京大数理解析研究所講究録, Kostant の generalized exponents と Young図形, 松澤 淳一, 1987, 641
  • Not Refereed, トポロジーと代数幾何学, 古典型リー群の generalized exponents, 松澤 淳一, 1985

Books etc

  • 若手女性研究者支援の実践, 日本数学会 数学通信 第22巻 第3号, 2017, Not Refereed
  • 数学セミナー 「数セミ メディアガイド 松澤淳一の書棚探訪」 2017年4月ー2018年3月, 日本評論社, 2017, Not Refereed
  • 書評 A.V.ボロビック、A.ボロビック著「鏡映の数学」、丸善出版, 数学セミナー、日本評論社, 2016, Not Refereed
  • 書評 小林正典著「線形代数と正多面体」朝倉出版, 数学セミナー、日本評論社, 2013, Not Refereed
  • 空間の点群・結晶群と有限性/マッカイ対応とSL_2, SL_3の有限部分群, 数学セミナー、日本評論社, 2012, Not Refereed
  • この数学書がおもしろい 増補新版, 数学書房, 2011, Not Refereed
  • ディンキン図形とルート系, 数学セミナー、日本評論社, 2009, Not Refereed
  • 書評 F. クライン著「20面体と5次方程式」、シュプリンガー, 数学セミナー、日本評論社, 2006, Not Refereed
  • 書評 ティモシー ガウアーズ著「一冊でわかる数学」、岩波書店, 数学セミナー、日本評論社, 2005, Not Refereed
  • 無限遠点と射影幾何, 数学セミナー、日本評論社, 2005, Not Refereed
  • 特異点とは何か/特異点は悪い点か良い点か, 数学セミナー、日本評論社, 2003, Not Refereed
  • 特異点とルート系, 朝倉書店, 2002, Not Refereed

Presentations

  • 松澤 淳一, 非可換代数幾何学の大域的問題とその周辺, ルート系と準結晶タイリングについて, 21 Dec. 2019, 高知大学, False
  • 数理情報科学セミナー, アゲハチョウとエッシャーと保型関数, 2017
  • 非可換代数幾何学の大域的問題とその周辺, 周期的極小曲面とSchwarzの三角群, 2015
  • Phase Transition Dynamics in Soft Matter : Bridging Microscale and Mesoscale, Phase Transition of Hard Spheres on the Gyroid Surface, 2012
  • 日本物理学会年会(関西学院大学), ジャイロイド曲面上の剛体球の相転移, 2012
  • MRS Fall Meeting 2012 (Boston), Hard Spheres on the Gyroid Surface, 2012
  • Phase Transition Dynamics in Soft Matter : Bridging Microscale and Mesoscale, Phase Transition of Hard Spheres on the Gyroid Surface, 2012
  • MRS Fall Meeting 2012 (Boston), Hard Spheres on the Gyroid Surface, 2012
  • The eighth Liquid Matter Conference (Wien), Hard Disks on the minimal Gyroid surface, 2011
  • Geometry of Interfaces (Primosten, Croatia), Hard Spheres on the Gyroid Surface, 2011
  • The eighth Liquid Matter Conference (Wien), Hard Disks on the minimal Gyroid surface, 2011
  • Geometry of Interfaces (Primosten, Croatia), Hard Spheres on the Gyroid Surface, 2011
  • International Soft Matter Conference 2010, Hyperbolic Tiling on the Gyroid Surface in ABC Star Polymers, 2010
  • 日本物理学会秋季大会(大阪府立大中百舌鳥), ABC星型高分子のG曲面上の双曲タイリング相, 2010
  • International Soft Matter Conference 2010, Hyperbolic Tiling on the Gyroid Surface in ABC Star Polymers, 2010

Research Projects

  • Grant-in-Aid for Scientific Research (C), Apr. 2013, Mar. 2018, 25400072, Symmetry of crystals and geometry of minimal surfaces, Matsuzawa Junichi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Nara Women's University, 4940000, 3800000, 1140000, We have studied, from the points of view of mathematics and physics, basic theory of hyperbolic Archimedean tilings on triply periodic minimal surfaces appearing as the interfaces in soft matters or mesoporous materials of nanoscopic size. In particular, we have investigated many tilings on Schwarz minimal surfaces and Schoen’s Gyroid surface. Furthermore we have given concrete expressions of the mappings between these minimal surfaces and the hyperbolic plane., url
  • Grant-in-Aid for Scientific Research (C), 2002, 2005, 14540023, Root system construction of a compactification of the moduli space of rational surfaces, MATSUZAWA Jun-ichi; ISHII Akira; NARUKI Isao, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Kyoto University, 1200000, 1200000, 0, Matsuzawa and Naruki : The aim of our research is to study the geometry of surfaces and its moduli from the point of view of Lie group, root systems and Weyl group. We constructed the universal family of marked cubic surfaces from the maximal torus of adjoint group of simple Lie group of type E6. Also we gave defining equation of a cubic surface in terms of root systems. Furthermore we constructed a smooth compactification of the universal family of marked cubic surfaces and gave a Weyl group equivariant mapping to Naruki's compactification of the moduli space of marked cubic surfaces. These constructions enable us to study the geometry of cubic surfaces from the point of view of root systems and Weyl groups. The family of cubic surfaces can be regarded as the configuration space of seven points of projective plane or mojuli space of algebrac curve of genus 3. We found interesting relationship among the geometry of cubic surface, that of algebraic curve of genus 2 and the structure of root system and Weyl groups of type E7, E6, D4. Ishii : He generalized the Mckay correspondence for simple singularities to general quotient surface singularities via Hilbert scheme of G-orbits. He studied the case for 3-dimensional quotient singularities when the group is abelian and gave a local coordinates of a crepant resolution of the singularity as the representation moduli of the McKay quiver. He also gave explicit description of the groups of self-equivalences of derived category on the minimal resolutions., Competitive research funding
  • Grant-in-Aid for Scientific Research (C), Apr. 2012, Mar. 2017, 24540044, Coinvestigator, global problems on non-commutative algebraic geometry, Tsuchimoto Yoshifumi; Mochizuki Takuro, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Kochi University, 3250000, 2500000, 750000, Regarding non-commutative algebraic geometry, we can apply ordinary algebraic geometry method by understanding through reduction to the positive characteristics. We organized the geometric problems, raised one way of thinking about the definition itself and regularity of non-commutative varieties. I defined the non-commutative projective space and a version of the theory of differential forms on it, and set the pathway of calculating its cohomology., url
  • Grant-in-Aid for Scientific Research (B), Apr. 2011, Mar. 2016, 23340017, Coinvestigator, Analytic torsion and geometry, Yoshikawa Ken-Ichi; MATSUZAWA Junichi; KAWAGUCHI Shu; NAMIKAWA Yoshinori; MUKAI Shigeru; MORIWAKI Atsushi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B), Kyoto University, 13000000, 10000000, 3000000, We studied the holomorphic torsion invariant of 2-elementary K3 surfaces and we determined its explicit formula as a function on the moduli space. It turned out that, for all topological types of involutions, the holomorphic torsion invariant is expressed as the product of an explicit Borcherds product and theta constants. We also studied the BCOV invariant of Calabi-Yau threefolds and we determined its explicit formula as a function on the moduli space for Borcea-Voisin threefolds. We introduced BCOV invariants for Calabi-Yau orbifolds and made comparison of BCOV invariants between Borcea-Voisin orbifolds and their crepant resolution. We studied the Borcherds Phi-function and obtained its algebraic expression. Namely, the value of the Borcherds Phi-function at the period of an Enriques surface is expressed as the product of its period and the resultant of its defining equation. As a by-product, we obtained an infinite product expression of theta constants of genus 2., url
  • Grant-in-Aid for Scientific Research (C), 2008, 2011, 20540046, Coinvestigator, Studies on global problems on non commutative algebraic geometry, YOSHIFUMI Tsuchimoto; JUN' ICHI Matsuzawa; KENTARO Yoshitomi; KATSUHIKO Kikuchi; TAKURO Mochizuki; AKIRA Ishii; HAJIME Kuroiwa, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C), Kochi University, 3510000, 2700000, 810000, For any symplectic polynomial endomorphism of an affine space, the representative defined a sheaf on the affine space. Its triviality is equivalent to the existence of a lift of the map to an Endomorphism of a Weyl algebra. Next we have used the theory of Abe-Yoshinaga on a behavior of reflexive sheaves on the hyperplane at infinity and obtained a result which says that the absence of the singularity on the infinity implies an existence of a` quantization' of a symplectic endomorphism of an affine space. This gives an evidence of effectiveness of ordinary commutative algebraic geometry of' compact' spaces such as projective spaces in dealing with non commutative objects., url;url
  • Grant-in-Aid for Encouragement of Young Scientists (A), 1995, 1995, 07740020, Del pezzo曲面の族とE型リー群, 松澤 淳一, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Kyoto University, 1000000, 1000000, 昨年度より引き続き3次曲面(次数3のDel Pezzo曲面)のモジュライとその上にのるtotal space,およびそれらのコンパクト化の幾何学的構造と群論的な構造の研究を進めてきた。今年度の研究成果は次のようである。 1.3次曲面の族の構成にはE_7型ルート系の構造を使うのであるが、その際にE_7型ルート系のある種の双対性が深くかかわってくることがわかった。それはE_7型ルート系のなかのE6型ルート系とA_4型ルート系の関係から生ずるものであって、3次曲面の族の幾何学的構造と深いところで関係していて、組み合わせ論的な立場からも興味深い現象を示している。またこの双対性からある種の線形符号を構成することができた。 2.3次曲面の族のコンパクト化の構造について、群論的構成とは違った、より一般的な構成のための試みを始めた。その第一歩として今までにところ、性質の良いある直線束をmoduliのコンパクト化の上に構成することができた。この直線束はWely群の作用に関してepuivariantなもので、3次曲面の族の性質およびmoduliの構造を知る上で重要なデータを含んでいるものである。一方、テ-タ関数と深くかかわっている射影空間内の(順序付き)6点および7点の集合のモジュライ空間のコンパクト化として、我々が構成した空間をとらえることができる。そうした立場からは、超幾何方程式との関係も深いのであるが、我々の研究は、これらの問題にリー群の立場から新たなアプローチをしていることになっている。今年度に始めた研究は、これらの問題との関連でも新たな局面をもたらす事ができると期待している。
  • Grant-in-Aid for Scientific Research on Priority Areas, 1992, 1992, 04245225, 無限ルート系と周期積分, 松澤 淳一; 成木 勇夫; 齋藤 恭司, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research on Priority Areas, Kyoto University, 1300000, 1300000, 特異点の普通変形、周期写像、周期領域およびそれらを記述するルート糸,その鏡映群と不変式論などの総合的に研究しようという本研究のために次のようなテーマについての研究会を開いた:原始形式の理論、普遍変形の群論的構成、ミルナーの格子の構造論、ヤコービ形式と母関数ミルナー・ファイバーのコンパクト化、アーベル・ファイブレイションのモルデル-ヴェイユ群の有限性、共形場理論。会議は平成4年7月に開かせれたが参加者は複素解析、群論、リー群リー環論、代数幾何、トポロジーなどの分野にわたり、活発な討論がなされた。その内容は報告集としてまとめられる予定である。個別の研究状況は以下の通りである。 1松澤:単純特異点の普通変形に関して、A型の場合にHirgebruch曲面をブローアップした曲面のmoduliをA型リー群の極大トーラスを用いて記述するという立場から研究を進めており、total spaceの構成、周期写像モノドロミー等を具体的にルート系を使って記述したが、これをD型の場合に試みることが現在進行中である。 2齋藤:Armoldのstrunge dualityと落合のclualityをweight系の概念を用いることにより統一的に証明し、かつ一般化した。これはprimitive fornの群論的構成とは違った、より一般的な構成のための第一歩と思われる。また、teal affine algebraic varietyの連結成分として既に得られていた、Teichmiiller Spaceについて、その定義方程式系をFuchs群から具体的に定めた。 3成木:Arnoldの例外型特異点におけるstrange dualityをK3曲面の幾何学を用いて説明することはPinkhanに始まるが、K3曲面の変形の理論と統分に結びつけるためには、変形のcentral fiberを見いだすこるが不可欠である。このようなcentral fiberの候補として、Picand 数20の特別なK3曲面を個々の場合に構成することを試みている。
  • Grant-in-Aid for Encouragement of Young Scientists (A), 1990, 1990, 02740029, 代数曲面とルート系およびコクスター群, 松澤 淳一, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Encouragement of Young Scientists (A), Kyoto University, 900000, 900000

Ⅲ.社会連携活動実績

1.公的団体の委員等(審議会、国家試験委員、他大学評価委員,科研費審査委員等)

  • Apr. 2010, Mar. 2012, Society
  • Mar. 2010, Feb. 2012, Society
  • Apr. 1995, Mar. 1998, Society


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