Researchers Database
MATSUZAWA Jun-ichi
| ■Faculty | Faculty Division of Natural Sciences Research Group of Mathematics | |||
| ■Position | Professor | |||
Last Updated :2024/05/11
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Profile and Settings
Name (Japanese)
MatsuzawaName (Kana)
Junichi
Degree
Research Interests
Research Areas
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
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, 10.1038/s41467-019-12147-z
- 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, 10.1380/jsssj.34.21
- 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, 10.1098/rsfs.2011.0092
- 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, 10.1295/kobunshi.57.66
- 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, 10.2977/prims/1195167050
- 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, 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;kaken
- 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, kaken
- 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;kaken
- 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;kaken
- 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;kaken
- 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。, kaken
- 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。, kaken
- 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, kaken
- Grant-in-Aid for Scientific Research (B), 2008, 2012, 20340007, A comprehensive research of vertex algebras, especially the W-algebras, ARAKAWA Tomoyuki; MATSUO Atsushi; SUZUKI Takeshi; YAMAUCHI Hiroshi; YAMADA Hiromichi; MIYAMOTO Masahiko; MATUZAWA Jyunichi; KONNO Hitoshi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 17030000, 13100000, 3930000, On admissible representations of affine Kac-Moody algebras, we proved the he conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions, the conjecture of Adamovic and Milas on the corresponding vertex operators algebra, and the conjecture of Feigin and Frenkel on their singular supports. On critical level representations of affine Kac-Moody algebras, we proved the new linkage principal and established a chiral Borel-Weil-Bott theorem. On W-algebras, we prove the C_2-cofinitness of the exceptional W-algebras discovered by Kac and Wakimoto and prove the admissible representations of affine Kac-Moody algebras. We obtained various results on the W-algebras at the critical levels., kaken
- Grant-in-Aid for Scientific Research (B), 2004, 2007, 16340039, Representation Theory and Duality associated with Non-commutative Special Functions, UMEDA Toru; NOUMI Masatoshi; WAKAYAMA Masato; OCHIAI Hiroyuki; MATSUZAWA Jun-ichi; ITOH Minoru, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kyoto University, 8770000, 8200000, 570000, Theory of special functions of non-commutative variables is a framework for us to understand deeply the dual pairs, which is a sort of revival of the classical invariant theory. The aim of the research is to link each other the three theories on special functions, invariants, and representations, to throw a new light to the mathematical world under the non-commutativity. In the center of our study, we have the Capelli identities, the equalities of the invariant differential operators, which arise from the representations of the centers of the universal enveloping algebras. Around the Capelli identities, we found many interesting phenomena caused from the transition from commutative theories to non-commutativeones. And even behind the usual commutative theories, we often found the dominating non-commutative variables. For the goal to obtain the ultimate Capelli type identities, we made a big progress through the new ideas which combine the non-commutative matrix elements, the generalization of the notion of transfer, symbolic method, and the method of generating functions. Though the program has not been accomplished, the results we had will be very useful for the understanding of the ultimate Capelli identities. An important example is in the treatment of Euler's pentagonal number theorem, which we understand a trace identity of matrices of infinite size. In there, we discover the fact that some identities generalizing the pentagonal number theorem are indeed sort of summation formula for q-hypergeometric series. This point of view will lead us to a new link between the representation theory and invariant theory through the infinite-dimensional spaces. Another important discovery is the algebra, which is a very useful toolfor the higher Capelli identities as the non-commutative formal variables. This is done by M. Itoh, an investigator of this research., kaken
- Grant-in-Aid for Scientific Research (B), 1999, 2001, 11440043, Study of special functions based on representation and invariant theories, UMEDA Toru; NOUMI Masatoshi; MATSUZAWA Junichi; NOMURA Takaaki; OEHIAI Hiroyuki; WAKAYAMA Masato, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, KYOTO UNIVERSITY, 9600000, 9600000, The main object of the research is to find the group theoretical background behind the world of special functions and to utilize the symonetious for the special functions. Among them the theory of "dual pairs" is the key to our study, which explains many phenomina from the view-point of representation theory and the theory of invariants. We have Capilli type identities, now commtative harnomic oscillatws as the typical investizations where and pains work very well as the griding principle. On the other hand, for the hyprogeinctic from Rons and Pain lene transcendents, we have claified the grop gymmetric behind them. The helps a lot for deeper investigations of these fnctions. As for the Capelli type identities, we got many interesting formlas including permanets and Pfuffians, not only for the determinants, Furthermore we found some Capelli type identity corresponding to the "group determinant". The invariant theoretic backgroud conneits these identities to some sphenicel functions. There are sort of unification of various objects., kaken
- Grant-in-Aid for Scientific Research (C), 1997, 2000, 09640104, RESEARCH ON HIGHER SIGNATURES, ISHII Akira; MATSUZAWA Jun-ichi; FUKAYA Kenji; KONO Akira; HARADA Masana, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, KYOTO UNIVERSITY, 3100000, 3100000, In this project, we developed so-called Novikov Conjecture, a conjecture in differential topology. First, we treated combing groups, as a class of discrete groups. This class, being a big class, includes cases where a segment may be far from being a geodesic. Therefore, we introduced the geometric notion of properness and its class turned out to be very easy to treat. Secondly, as a Fredholm representation corresponding to the E-theory introduced by Connes and Higson, we introduced the notion of asymptotic Lipschitz maps of spaces. Under these preparations, we proved the Novikov Conjecture for torsion-free, proper combing groups. For a map of discrete metric spaces, we can consider conditions on the metric, such as the Lipschitz condition Putting such conditions on the metric, we defined a map being a fiber structure. By studying fiber structures in the cases of discrete groups, we obtained the following : Let Γ be a fundamental group of almost non positively curved manifold. Then any class in H^* (Γ ; R) is a proper Lipschitz class. In particular, Γ satisfies Novikov conjecture. We studied versal deformations of reflexive modules on rational double points. We constructed a natural stratification of the deformation space and a desingularization of the closure of a stratum as a moduli space, representing a functor defined over the deformation space as a base. In particular, the closure relation of the classes of reflexive modules coincides with the usual order of dominant weights of the corresponding root system. Moreover, we described the singularities arising from adjacent strata. Finally, we generalized Ito-Nakamura type results on McKay correspondence to the cases of general quotient surface singularities, as conjectured by Riemenschneider., kaken
- Grant-in-Aid for General Scientific Research (A), 1993, 1995, 05402001, Structure and symmetries of integrable systems, JIMBO Michio; KONO Akira; UENO Kenji; UMEDA Toru; TAKEI Yoshitsugu; SHIOTA Takahiro, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, KYOTO UNIVERSITY, 12700000, 12700000, The major outcome of the present research project is as follows. 1.Jimbo pushed forward the study of space of states of lattice models. Ising and RSOS type models were formulated in much the same way as for the vertex type models, and difference equations for correlations were derived. The theory was extended to spin chains with a boundary, and physical quantities were derived including vacuum states, energy and magnetization. For critical systems an integral formula for correlations was found. In representation theory, a new level 0 action was constructed on a level one module over the quantum affine algebra. 2.Shiota constructed a notrivial solution to [P,Q] =P using a matrix integral similar to Kontsevich's. Takei showed, usuing the exact WKB analysis, that the Painleve I equation can be taken as a standard form near a simple turning point. He also constructed a general solution using the multiple scale anaysis. 3.Umeda studied a new construction of a q-analog of differential operators, which appear in the Capelli identity for GLq (n) , in terms of classical q-difference operators. This opened up a connection with Gelfand-type hypergeometric equations. 4.Ueno gave a concrete construction of projective flat connections on the vector bundles of conformal blocks over the moduli space of curves. Kono studied the free loop group of a compact simple Lie group, and found a connection between the mod p cohomology of the adjoint action of G on the closed loop group, and the integral cohomology of G., kaken
- Grant-in-Aid for General Scientific Research (C), 1991, 1993, 03640045, Study of Noetherian Local Rings in Commutative Algebra, NISHIMURA Jun-ichi; MATSUZAWA Jun-ichi; YOSHIDA Hiroyuki; HIJIKATA Hiroaki; MARUYAMA Masaki; UENO Kenji, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, 1800000, 1800000, Construction of Counter-Examples of Noetherian Rings Through famous examples due to Akizuki and to Nagata, in commutative Noetherian ring theory, it is well-known that constructing counter-examples is no less important than showing positive results. However, thier methods of construction were complicated and hard to get a general principle. For these twenty years, the new construction method, originated by Rotthaus, have been and developed and simplified by Ogoma and by Heitmann. This new construction enables us not only to reconstruct easily known examples but to obtain new unknown examples, which give answers to a number of open problems. Here, we improve this new tool, combining ideas of Nagata, and get the following examples : 1)3-dimensional factorial local domain which is not universally catenaty. 2)2-dimensional normal local domain of characteristic 0 which is not analytically unramified. 3)3-dimensional local domain of characteristic 0 whose derived normal ring is not NOetherian. Chain Conditions on Ideal-adically Complete Nagata Rings Greco has constructed the following surprising example : Example. There exists a semi-local domain (A,m_1, m_2) with an ideal I=P_1 * P_2 (= the intersection of two prime ideals) such that 1) A is complete in I-adic topology, and 2) A/I is excellent, hence universally catenary. But A itself is not universally catenary. On the other hand, we get the following : Theorem 1. Let (A,m) be a local ring with an ideal I.Suppose that 1) A is complete in I-adictopology, and 2) A/I is a universally catenary Nagata ring. Then, A itself is universally catenary. Theorem 2. Let A be a Noetherian domain with a prime ideal P.Suppose that 1) A is complete in P-adic topology, and 2) A/P is a universally catenary Nagata ring. Then, A itself is universally catenary., kaken
- 一般研究(C), 1992, 1992, 04640053, 開多様体の上の概複素構造, 足立 正久; 松澤 淳一; 谷口 雅彦; 岩崎 敷久; 西田 吾郎, 日本学術振興会, 科学研究費助成事業, 京都大学, 1100000, 1100000, 幾何学的、位相的研究 代表者 足立、分担者 上野、松澤、西田、原田を中心に、CR構造との関連や、超多様体の手法との関連で、一般偶数次元多様体とくに開多様体上の概複素構造の可積分性を研究し、また数理物理学ホモトピー論との関連も研究した。 代数的研究 分担者土方、丸山、吉田、神保を中心にして、整数論、代数幾何学、代数解析学の手法を用いて、代数ベクトル束のモジュライ空間等との関連を研究し、また量子群等との関連についても研究した。また開多様体の概複素構造とそのコンパクト化上の概複素構造についても研究した。 解析的研究 分担者 池部、岩崎を中心にスペクトル論、線型微分方程式論の手法を用いて概複素構造の可積分性の問題を研究し、また分担者 平井を中心にして函数解析学、群の表現論との関連する問題が研究された。また分担者 渡辺、重川を中心として確率論との関連する問題が研究された。分担者 上野、谷口を中心として複素解析学の手法を用いて、タイヒミューラー空間との関連する分野の研究が行なわれた。, kaken
- 一般研究(C), 1991, 1991, 03640211, 可解格子模型の代数的構造, 神保 道夫; 松澤 淳一, 日本学術振興会, 科学研究費助成事業, 京都大学, 研究代表者(神保)の実績 (i)量子群Uq(ojln)のq^N=1における極小巡回表現から、順に基本表現とのテンリル積をとって既約分解することにより生ずる表現の系列を調べ,それがUq(ojlnー1)の表現の分解則と並行した記述をもつことを示した。 (ii)可解格子模型の自発偏極は、一般的計算法が知られていない。6ーVertex modelに対しBethe仮設法からこれを求めたBaxterの手法を用いて,その高スピン類似について平均自発偏極を計算した。 (iii)FrenkelーReshetikhinによって研究されたqー頂点作用素と,柏原による結晶基の整合性を調べ、前者が結晶格子を保存することを示した。この応用として、柏原らが頂点模型(三角函数解)の1点函数とアフィン・リ-環の指標を関係づけた議論を適用することにより、面模型(楕円函数解)について類似の事実を一般の枠組で示した。 (iv)q頂点作用素と結晶基理論を道具として、XXZ模型のハミルトニアンの固有状態全体がアフィンの量子群の表現空間として定式化できることを見出した。(準備中) 分担者(松澤)の実績 Hirzebruch曲面のblow upのモジュライ空間上に曲面族を構成し,そのモジュライ,ホモロジ-,周期写像等がA型ル-ト系の言葉で具体的に記述できることを示した。(準備中), kaken
- Grant-in-Aid for Scientific Research (C), 01 Apr. 2013, 31 Mar. 2016, 25400431, Theoretical Studies on the Structures and the Physical Properties of Triply Periodic Minimal Surfaces, DOTERA Tomonari; MATSUZAWA Junichi, Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Kinki University, 5070000, 3900000, 1170000, On a flat surface the hexagonal arrangement is a ubiquitous regular arrangement arising from dense packing, space division, or interactions between particles. What is regular arrangement when a surface is curved? On a sphere, this question was firstly raised by J. J. Thomson for electrons constituting atoms, Goldberg elucidated regular polyhedra, and for biological icosahedral viruses Caspar and Klug found a construction principle of regular arrangements on a sphere. In contrast, regular arrangements of particles on saddle-shaped periodic surfaces with negative curvatures have not been pursued. In this project, we have shown numerous regular arrangements of spheres on the Schwarz P- and D-surfaces obtained through the Alder transition, where magic numbers have been obtained in analogy with icosahedral viruses. These unprecedented arrangements are analyzed in terms of space groups, and polygonal & hyperbolic tilings., kaken