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Structural Stability and Morphogenesis of Differentiable Maps

Research Project

Project/Area Number 23654028
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

SAEKI OSAMU  九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)

Co-Investigator(Kenkyū-buntansha) OHMOTO Toru  北海道大学, 大学院・理学研究院, 教授 (20264400)
YAMAMOTO Takahiro  九州産業大学, 工学部, 講師 (60435972)
Co-Investigator(Renkei-kenkyūsha) TAKASE Masamichi  成蹊大学, 理工学部, 准教授 (30447718)
YAMAMOTO Minoru  弘前大学, 教育学部, 准教授 (40435475)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords写像空間 / Vassiliev型不変量 / 映像理論 / 多値関数 / データ可視化 / 特異ファイバー / 国際研究者交流(フランス)
Research Abstract

The purpose of this research project was to formulate invariants of manifolds and maps from a new viepoint using a universal framework. For this, we considered Vassiliev complex for each classification of singularities or singular fibers and studied their invariants. Furthermore, we completely classified singular fibers of stable maps of 3-manifolds with boundary into the plane. We then calculated the cohomology groups of the associated Vassiliev complex and discovered new cobordism invariants. Moreover, we applied this kind of study to the visualization of multivariate data, and we showed that this kind of techniques can be very useful for clarifying differential topological features of a given set of big data.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (118 results)

All 2014 2013 2012 2011 Other

All Journal Article (30 results) (of which Peer Reviewed: 30 results) Presentation (81 results) (of which Invited: 56 results) Book (2 results) Remarks (4 results) Patent(Industrial Property Rights) (1 results)

  • [Journal Article] Visualizing multivariate data using singularity theory, The Impact of Applications on Mathematics2014

    • Author(s)
      O. Saeki, S. Takahashi, D. Sakurai, Hsiang-Yun Wu, K. Kikuchi, H. Carr, D. Duke, and T. Yamamoto
    • Journal Title

      Proceedings of Forum "Math-for-Industry"2013

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Visual data mining based on differential topology : a survey2014

    • Author(s)
      O. Saeki and S. Takahashi
    • Journal Title

      Pacific Journal of Mathematics for Industry

      Volume: (印刷中)

    • NAID

      40020377786

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of plane-to-plane mapgerms of corank two2014

    • Author(s)
      T. Yoshida, Y. Kabata and T. Ohmoto
    • Journal Title

      Quarterly Jour. Mathematics

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of Maps and Characteristic Classes2014

    • Author(s)
      T. Ohmoto
    • Journal Title

      Advanced Studies in Pure Mathematics(Proc. Real and Complex Singularities)

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Survey of apparent contours of stable maps between surfaces2014

    • Author(s)
      T. Yamamoto
    • Journal Title

      Advanced Studies in Pure Mathematics (Proc. Real and Complex Singularities)

      Volume: (印刷中)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Connected components of regular fibers of differentiable maps, Topics on Real and Complex Singularities2014

    • Author(s)
      J.T. Hiratuka and O. Saeki
    • Journal Title

      World Scientific

      Pages: 61-73

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Connected components of regular fibers of differentiable maps2014

    • Author(s)
      J. T. Hiratuka and O. Saeki
    • Journal Title

      Topics on Real and Complex Singularities, Proceedings of the 4th Japanese-Australian Workshop (JARCS4), Kobe 2011, World Scientific

      Volume: なし Pages: 61-73

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Visualizing multivariate data using singularity theory2014

    • Author(s)
      O. Saeki, S. Takahashi, D. Sakurai, Hsiang-Yun Wu, K. Kikuchi, H. Carr, D. Duke, and T. Yamamoto
    • Journal Title

      The Impact of Applications on Mathematics, Proceedings of Forum “Math-for-Industry” 2013, Springer

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Visual data mining based on differential topology: a survey2014

    • Author(s)
      O. Saeki and S. Takahashi
    • Journal Title

      Pacific Journal of Mathematics for Industry

      Volume: 印刷中

    • NAID

      40020377786

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of plane-to-plane map-germs of corank two2014

    • Author(s)
      T. Yoshida, Y. Kabata and T. Ohmoto
    • Journal Title

      Quarterly Jour. Mathematics

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Singularities of Maps and Characteristic Classes2014

    • Author(s)
      T. Ohmoto
    • Journal Title

      Advanced Studies in Pure Mathematics (Proc. Real and Complex Singularities, Sao Carlos, 2012)

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Survey of apparent contours of stable maps between surfaces2014

    • Author(s)
      Takahiro Yamamoto
    • Journal Title

      Advanced Studies in Pure Mathematics (Proc. Real and Complex Singularities, Sao Carlos, 2012)

      Volume: 印刷中

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki and M. Takase
    • Journal Title

      Journal of Gökova Geometry Topology

      Volume: 7巻 Pages: 1-24

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Triangulating Stein factorizations of generic maps and Euler characteristic formulas2013

    • Author(s)
      J.T. Hiratuka and O. Saeki
    • Journal Title

      RIMS Kôkyûroku Bessatsu

      Volume: B38巻 Pages: 61-89

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characteristic classes of Hilbert schemes of points via symmetric products2013

    • Author(s)
      L. Maxim, S. Cappell, T. Ohmoto, J. Schürmann, and S. Yokura
    • Journal Title

      Geometry & Topology

      Volume: 17巻 Pages: 1165-1198

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki and M. Takase
    • Journal Title

      Journal of Goekova Geometry Topology

      Volume: 7 Pages: 1-24

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Triangulating Stein factorizations of generic maps and Euler characteristic formulas2013

    • Author(s)
      J. T. Hiratuka and O. Saeki
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characteristic classes of Hilbert schemes of points via symmetric products2013

    • Author(s)
      L. Maxim, S. Cappell, T. Ohmoto, J. Schuermann, and S. Yokura
    • Journal Title

      Geometry and Topology

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cobordism of exact links2012

    • Author(s)
      V. Blanloeil and O. Saeki
    • Journal Title

      Algebraic and Geometric Topology

      Volume: 12巻 Pages: 1443-1455

    • Related Report
      2013 Final Research Report 2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Vassiliev type invariants for generic maps, revisited2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      Contemporary Math., Amer. Math. Soc

      Volume: 569巻 Pages: 143-160

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on Chern-Schwartz-MacPherson class, IRMA Lectures in Mathematics and Theoretical Physics2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      European Math.Soc

      Volume: 20巻 Pages: 117-132

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Vassiliev type invariants for generic maps, revisited2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      Contemporary Math., Amer. Math. Soc.

      Volume: 569 Pages: 143-160

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on Chern-Schwartz-MacPherson class2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      IRMA Lectures in Mathematics and Theoretical Physics, European Math. Soc.

      Volume: 20 Pages: 117-132

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Vassiliev type invariants for generic mappings, revisited2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      Contemporary Math. AMS

      Volume: 掲載予定

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on Chern-Schwartz-MacPherson class2012

    • Author(s)
      T. Ohmoto
    • Journal Title

      IRMA Lectures in Mathematics and Theoretical Physics

      Volume: 掲載予定

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cobordism of algebraic knots defined by Brieskorn polynomials2011

    • Author(s)
      V. Blanloeil and O. Saeki
    • Journal Title

      Tokyo J. Math

      Volume: 34巻 Pages: 429-443

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fox property for codimension one embeddings of product of three spheres into spheres2011

    • Author(s)
      L.A. Lucas and O. Saeki
    • Journal Title

      Algebraic and Geometric Topology

      Volume: 11巻 Pages: 3034-3064

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Apparent contours of stable maps into the sphere2011

    • Author(s)
      T. Fukuda and T. Yamamoto
    • Journal Title

      Journal of Singularities

      Volume: 3巻 Pages: 113-125

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cobordism of algebraic knots defined by Brieskorn polynomials2011

    • Author(s)
      V.Blanloeil, et al
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 34 Issue: 2 Pages: 429-443

    • DOI

      10.3836/tjm/1327931395

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Fox property for codimension one embeddings of products of three spheres into spheres2011

    • Author(s)
      Laercio A.Lucas, et al
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 11 Issue: 5 Pages: 3043-3064

    • DOI

      10.2140/agt.2011.11.3043

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Singular fibers of differentiable maps and low dimensional topology II2014

    • Author(s)
      O. Saeki
    • Organizer
      Visiting Lecture at Center for Advanced Studies
    • Place of Presentation
      Warsaw University of Technology, Poland
    • Year and Date
      2014-03-25
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2014

    • Author(s)
      O. Saeki
    • Organizer
      Visiting Lecture at Institute of Mathematics
    • Place of Presentation
      Polish Academy of Science, Poland
    • Year and Date
      2014-03-20
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Singular fibers of differentiable maps and low dimensional topology I2014

    • Author(s)
      O. Saeki
    • Organizer
      Visiting Lecture at Center for Advanced Studies
    • Place of Presentation
      Warsaw University of Technology, Poland
    • Year and Date
      2014-03-18
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Chern Classes of Image and Discriminant of Stable Maps2014

    • Author(s)
      T. Ohmoto
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2014
    • Place of Presentation
      広島大学理学部
    • Year and Date
      2014-03-09
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] 境界付き多様体上の安定写像芽について2014

    • Author(s)
      山本卓宏
    • Organizer
      第130回日本数学会九州支部会
    • Place of Presentation
      琉球大学
    • Year and Date
      2014-02-15
    • Related Report
      2013 Final Research Report
  • [Presentation] Topology of manifolds and global theory of singularities2014

    • Author(s)
      O. Saeki
    • Organizer
      One day workshop on hypersurface singularity and its link manifolds
    • Place of Presentation
      東京理科大学
    • Year and Date
      2014-01-23
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] 境界付き多様体上の安定写像とその特異ファイバー2014

    • Author(s)
      山本卓宏
    • Organizer
      接触構造, 特異点, 微分方程式及びその周辺
    • Place of Presentation
      高知市文化プラザかるぽーと
    • Year and Date
      2014-01-09
    • Related Report
      2013 Final Research Report
  • [Presentation] 境界付き多様体上の安定写像とその特異ファイバー2014

    • Author(s)
      山本卓宏
    • Organizer
      接触構造,特異点,微分方程式及びその周辺
    • Place of Presentation
      高知市文化プラザかるぽーと
    • Related Report
      2013 Annual Research Report
  • [Presentation] 境界付き多様体上の安定写像芽について2014

    • Author(s)
      山本卓宏
    • Organizer
      第130回 日本数学会九州支部会
    • Place of Presentation
      琉球大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] 現代のトップテクノロジー, トポロジーを使ったデータ構造の解析~トポロジー技術を用いた分子構造解析とデータ可視化~2013

    • Author(s)
      佐伯修
    • Organizer
      数学メガネからみたイノベーション
    • Place of Presentation
      稲盛財団記念館(九州大学伊都キャンパス)
    • Year and Date
      2013-12-12
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of manifolds and global theory of singularities2013

    • Author(s)
      O. Saeki
    • Organizer
      可微分写像の特異点論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-11-25
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Image and Discriminant Chern Classes of Stable Maps2013

    • Author(s)
      大本亨
    • Organizer
      筑波大学大学院数理物質科学研究科数学教室談話会
    • Place of Presentation
      筑波大学
    • Year and Date
      2013-11-07
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Visualizing multivariate data using singularity theory2013

    • Author(s)
      O. Saeki
    • Organizer
      Forum "Math-for-Industry" 2013 -The Impact of Applications on Mathematics-
    • Place of Presentation
      Nishijin Plaza, Kyushu University
    • Year and Date
      2013-11-04
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 境界付き3次元多様体から平面への安定写像の特異ファイバーとその応用2013

    • Author(s)
      山本卓宏
    • Organizer
      第129回日本数学会九州支部会
    • Place of Presentation
      宮崎大学
    • Year and Date
      2013-10-26
    • Related Report
      2013 Final Research Report
  • [Presentation] Image and Discriminant Chern Classes of Stable Maps2013

    • Author(s)
      大本亨
    • Organizer
      埼玉大学大学院理学研究科数学教室談話会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2013-10-17
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki
    • Organizer
      The 1st Franco-Japanese- Vietnamese Symposium on Singularities (and The 7th Franco-Japanese Symposium on Singularities)
    • Place of Presentation
      Université de Nice Sophia Antipolis, France
    • Year and Date
      2013-09-20
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Shoji Yokura's works and Kagoshima2013

    • Author(s)
      T. Ohmoto
    • Organizer
      1st Franco-Japanese- Vietnamese Symposium on Singularities of the CNRS-VAST-JSPS
    • Place of Presentation
      ニース大学デュドンネ数学研究所(ニース, フランス)
    • Year and Date
      2013-09-17
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] On study group activities2013

    • Author(s)
      O. Saeki
    • Organizer
      Seminarios do LMACC
    • Place of Presentation
      ICMC-USP, Brazil
    • Year and Date
      2013-08-14
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Topology of quasihomogeneous isolated hypersurface singularities2013

    • Author(s)
      O. Saeki
    • Organizer
      Seminarios de Singularidades
    • Place of Presentation
      ICMC-USP, Brazil
    • Year and Date
      2013-08-13
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Image and Discriminant Chern Classes of Stable Maps2013

    • Author(s)
      T. Ohmoto
    • Organizer
      Mini workshop on singularities 2013
    • Place of Presentation
      東京理科大学(東京都新宿区)
    • Year and Date
      2013-07-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] マス・フォア・インダストリ活動について2013

    • Author(s)
      佐伯修
    • Organizer
      Kobe Studio Seminar for Mathematics
    • Place of Presentation
      神戸大学発達科学部
    • Year and Date
      2013-07-10
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] モース関数とそのレーブグラフ入門2013

    • Author(s)
      佐伯修
    • Organizer
      Kobe Studio Seminar for Mathematics
    • Place of Presentation
      神戸大学発達科学部
    • Year and Date
      2013-07-10
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Broken Lefschetz fibrations and their moves, Special Session "Singularities in Geometry and Topology"2013

    • Author(s)
      O. Saeki
    • Organizer
      The Second Pacific Rim Mathematical Association Congress (PRIMA2013)
    • Place of Presentation
      Shanghai Jiao Tong Univ., China
    • Year and Date
      2013-06-27
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki
    • Organizer
      Topology Seminar
    • Place of Presentation
      Fudan University, Shanghai, China
    • Year and Date
      2013-06-27
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Broken Lefschetz fibrations and their moves2013

    • Author(s)
      O. Saeki
    • Organizer
      Geometry and topology of smooth 4-manifolds
    • Place of Presentation
      Max Planck Institute for Mathematics, Germany
    • Year and Date
      2013-06-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Broken Lefschetz fibrations and their moves2013

    • Author(s)
      O. Saeki
    • Organizer
      Geometry and topology of smooth 4-manifolds
    • Place of Presentation
      Max Planck Institute, Germany
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki
    • Organizer
      Topology Seminar, Fudan University
    • Place of Presentation
      Fudan University, Shanghai, China
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Broken Lefschetz fibrations and their moves2013

    • Author(s)
      O. Saeki
    • Organizer
      Special Session “Singularities in Geometry and Topology”, The Second Pacific Rim Mathematical Association Congress (PRIMA2013)
    • Place of Presentation
      Shanghai Jiao Tong Univ., China
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Topology of quasi-homogeneous isolated hypersurface singularities2013

    • Author(s)
      O. Saeki
    • Organizer
      Seminarios de Singularidades
    • Place of Presentation
      ICMC-USP, Brazil
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2013

    • Author(s)
      O. Saeki
    • Organizer
      The 1st Franco-Japanese-Vietnamese Symposium on Singularities (and The 7th Franco-Japanese Symposium on Singularities)
    • Place of Presentation
      Laboratoire J. A. Dieudonne, Universite de Nice Sophia Antipolis, France
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Visualizing multivariate data using singularity theory2013

    • Author(s)
      O. Saeki
    • Organizer
      Forum “Math-for-Industry” 2013 -The Impact of Applications on Mathematics-
    • Place of Presentation
      Nishijin Plaza, Kyushu University
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Topology of manifolds and global theory of singularities2013

    • Author(s)
      O. Saeki
    • Organizer
      「可微分写像の特異点論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 現代のトップテクノロジー,トポロジーを使ったデータ構造の解析 ~トポロジー技術を用いた分子構造解析とデータ可視化~2013

    • Author(s)
      佐伯修
    • Organizer
      「数学メガネからみたイノベーション」
    • Place of Presentation
      稲盛財団記念館(九州大学伊都キャンパス)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Image and Discriminant Chern Classes of Stable Maps2013

    • Author(s)
      T. Ohmoto
    • Organizer
      Mini-workshop on singularities 2013
    • Place of Presentation
      東京理科大学(東京都新宿区)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Shoji Yokura's works and Kagoshima2013

    • Author(s)
      T. Ohmoto
    • Organizer
      1st Franco-Japanese-Vietnamese Symposium on Singularities of the CNRS-VAST-JSPS
    • Place of Presentation
      ニース大学デュドンネ数学研究所(ニース,フランス)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 境界付き3次元多様体から平面への安定写像の特異ファイバーとその応用2013

    • Author(s)
      山本卓宏
    • Organizer
      第129回 日本数学会九州支部会
    • Place of Presentation
      宮崎大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] Geometry of plane-to-plane map-germs2012

    • Author(s)
      大本 亨
    • Organizer
      可微分写像の特異点論とその応用
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2012-12-12
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Invited
  • [Presentation] Geography of the singularities of stable maps of closed surfaces2012

    • Author(s)
      山本卓宏
    • Organizer
      可微分写像の特異点論とその応用
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2012-12-11
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Topology of quasi-homogeneous isolated hypersurface singularities2012

    • Author(s)
      佐伯修
    • Organizer
      可微分写像の特異点論とその応用
    • Place of Presentation
      日本大学文理学部
    • Year and Date
      2012-12-10
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Invited
  • [Presentation] Novas aplicacões das matemáticas na indústria, Palestra2012

    • Author(s)
      O. Saeki
    • Organizer
      ICMC-USP
    • Place of Presentation
      ICMC-USP, Brazil
    • Year and Date
      2012-11-28
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Desingularizar aplicacões genéricas especiais2012

    • Author(s)
      O. Saeki
    • Organizer
      Seminário de Singularidades
    • Place of Presentation
      ICMC-USP, Brazil
    • Year and Date
      2012-11-27
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2012

    • Author(s)
      佐伯修
    • Organizer
      東京工業大学 大岡山談話会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2012-11-07
    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Invited
  • [Presentation] Geography of the singularities of stable maps of closed surfaces into the plane2012

    • Author(s)
      山本卓宏
    • Organizer
      第127回日本数学会九州支部会
    • Place of Presentation
      大分大学
    • Year and Date
      2012-10-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Broken Lefschetz fibrations and their moves2012

    • Author(s)
      佐伯修
    • Organizer
      第59回トポロジーシンポジウム
    • Place of Presentation
      佐賀大学
    • Year and Date
      2012-08-13
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of the set of singular values of stable maps2012

    • Author(s)
      T. Yamamoto
    • Organizer
      The 12th International Workshop on Real and Complex Singularities
    • Place of Presentation
      ICMC-USP, Brazil
    • Year and Date
      2012-07-24
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Broken Lefschetz fibrations with embedded fold image2012

    • Author(s)
      佐伯修
    • Organizer
      特異点論と幾何構造
    • Place of Presentation
      長野市生涯学習センター
    • Year and Date
      2012-05-30
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] Cobordism of knots associated with complex hypersurface singularities2012

    • Author(s)
      佐伯修
    • Organizer
      トポロジー金曜セミナー
    • Place of Presentation
      九州大学伊都キャンパス
    • Year and Date
      2012-04-13
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      O. Saeki
    • Organizer
      Geometric Topology Seminar
    • Place of Presentation
      Max Planck Institute for Mathematics, Bonn, Germany
    • Year and Date
      2012-03-26
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      O. Saeki
    • Organizer
      Seminaire GT3
    • Place of Presentation
      University of Strasbourg, France
    • Year and Date
      2012-03-13
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      O. Saeki
    • Organizer
      Topology Seminar
    • Place of Presentation
      University of Cambridge, Great Britain
    • Year and Date
      2012-03-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Desingularizing special generic maps2012

    • Author(s)
      O. Saeki
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2012-02-17
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Singular Chern class and degree formula2012

    • Author(s)
      T. Ohmoto
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2012-02-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Topology of the singular value sets of stable maps2012

    • Author(s)
      山本卓宏
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2012-02-14
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Singularities and Characteristic Classes for Differentiable MapsI,II,III(course lecture)2012

    • Author(s)
      T. Ohmoto
    • Organizer
      The 12th International Workshop on Real and Complex Singularities
    • Place of Presentation
      ICMC-USP, Brazil
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Cobordism of knots associated with complex hypersurface singularities2012

    • Author(s)
      佐伯修
    • Organizer
      トポロジー金曜セミナー,九州大学
    • Place of Presentation
      九州大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Broken Lefschetz fibrations and their moves2012

    • Author(s)
      佐伯修
    • Organizer
      第59回トポロジーシンポジウム
    • Place of Presentation
      佐賀大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Desingularizar aplicacoes genericas especiais2012

    • Author(s)
      Osamu Saeki
    • Organizer
      Seminario de Singularidades
    • Place of Presentation
      ICMC-USP, Brazil
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Novas aplicacoes das matematicas na industria2012

    • Author(s)
      Osamu Saeki
    • Organizer
      Palestra, ICMC-USP
    • Place of Presentation
      ICMC-USP, Brazil
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Singularities and Characteristic Classes for Differentiable Maps I, II, III (course lecture)2012

    • Author(s)
      T. Ohmoto
    • Organizer
      The 12th International Workshop on Real and Complex Singularities
    • Place of Presentation
      ICMC-USP, Brazil
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Geography of the singularities of stable maps of closed surfaces into the plane2012

    • Author(s)
      山本卓宏
    • Organizer
      第127回 日本数学会九州支部会
    • Place of Presentation
      大分大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Singular Chern class and degree formula2012

    • Author(s)
      T. Ohmoto
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar(招待講演)
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] Desingularizing special generic maps2012

    • Author(s)
      Osamu Saeki
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar(招待講演)
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      Osamu Saeki
    • Organizer
      Topology Seminar(招待講演)
    • Place of Presentation
      University of Cambridge, Great Britain
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      Osamu Saeki
    • Organizer
      Seminaire GT3(招待講演)
    • Place of Presentation
      University of Strasbourg, France
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of definite fold singularities2012

    • Author(s)
      Osamu Saeki
    • Organizer
      Geometric Topology Seminar(招待講演)
    • Place of Presentation
      Max Planck Institute for Mathematics, Bonn, Germany
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of the singular value sets of stable maps2012

    • Author(s)
      山本卓宏
    • Organizer
      The 7th Kagoshima Algebra-Analysis-Geometry Seminar(招待講演)
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of definite fold singularities2011

    • Author(s)
      O. Saeki
    • Organizer
      The 4th Japanese- Australian Workshop on Real and Complex Singularities
    • Place of Presentation
      Kobe Satellite of Hyogo University of Teacher Education
    • Year and Date
      2011-11-24
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Cobordism of knots defined by Brieskorn polynomials2011

    • Author(s)
      O. Saeki
    • Organizer
      The 19th TAPU Seminar on Knots and Related Topics
    • Place of Presentation
      Seacloud Hotel, Haeundae, Busan, Korea
    • Year and Date
      2011-09-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Survey on knots associated with complex hypersurface singularities2011

    • Author(s)
      Osamu Saeki
    • Organizer
      The 19th TAPU Seminar on Knots and Related Topics
    • Place of Presentation
      Seacloud Hotel, Haeundae, Busan, Korea
    • Year and Date
      2011-09-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 安定な可微分写像の特異点と特異値集合について2011

    • Author(s)
      山本卓宏
    • Organizer
      トポロジーシンポジウム
    • Place of Presentation
      筑波大学
    • Year and Date
      2011-08-10
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 定値折り目特異点の消去と特異レフシェッツ束2011

    • Author(s)
      佐伯修
    • Organizer
      近畿大学数学教室講演会
    • Place of Presentation
      近畿大学理工学部
    • Year and Date
      2011-07-08
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 定値折り目特異点の消去と特異レフシェッツ束2011

    • Author(s)
      佐伯修
    • Organizer
      大阪大学数学教室談話会
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2011-06-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Lifting special generic maps2011

    • Author(s)
      佐伯修
    • Organizer
      特異点論とその応用
    • Place of Presentation
      大分工業高等専門学校
    • Year and Date
      2011-05-31
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Thom polynomial associated to the Milnor number of isolated complete intersections2011

    • Author(s)
      T. Ohmoto
    • Organizer
      Banach Center Conference : Workshop on Singularities in Geometry and Application
    • Place of Presentation
      Banach center, Bendlewo, Poland
    • Year and Date
      2011-05-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Thom polynomial associated to the Milnor number of isolated complete intersections2011

    • Author(s)
      T. Ohmoto
    • Organizer
      Banach Center Conference: Workshop on Singularities in Geometry and Application(招待講演)
    • Place of Presentation
      Banach center, Bendlewo, Poland
    • Related Report
      2011 Research-status Report
  • [Presentation] Survey on knots associated with complex hypersurface singularities2011

    • Author(s)
      Osamu Saeki
    • Organizer
      The 19th TAPU Seminar on Knots and Related Topics(招待講演)
    • Place of Presentation
      Seacloud Hotel, Haeundae, Busan, Korea
    • Related Report
      2011 Research-status Report
  • [Presentation] Cobordism of knots defined by Brieskorn polynomials2011

    • Author(s)
      Osamu Saeki
    • Organizer
      The 19th TAPU Seminar on Knots and Related Topics(招待講演)
    • Place of Presentation
      Seacloud Hotel, Haeundae, Busan, Korea
    • Related Report
      2011 Research-status Report
  • [Presentation] Topology of definite fold singularities2011

    • Author(s)
      Osamu Saeki
    • Organizer
      The 4th Japanese-Australian Workshop on Real and Complex Singularities(招待講演)
    • Place of Presentation
      Kobe Satellite of Hyogo University of Teacher Education
    • Related Report
      2011 Research-status Report
  • [Presentation] 安定な可微分写像の特異点と特異値集合について2011

    • Author(s)
      山本卓宏
    • Organizer
      トポロジーシンポジウム(招待講演)
    • Place of Presentation
      筑波大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 定値折り目特異点の消去と特異レフシェッツ束

    • Author(s)
      佐伯修
    • Organizer
      大阪大学数学教室談話会(招待講演)
    • Place of Presentation
      大阪大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] 定値折り目特異点の消去と特異レフシェッツ束

    • Author(s)
      佐伯修
    • Organizer
      近畿大学数学教室講演会(招待講演)
    • Place of Presentation
      近畿大学理工学部
    • Related Report
      2011 Research-status Report
  • [Book] European Math. Soc., Singularities in Geometry and Topology - Strausbourg 2009, IRMA Lectures in Mathematics and Theoretical Physics2012

    • Author(s)
      V. Blanloeil, T. Ohmoto (eds.)
    • Total Pages
      362
    • Related Report
      2013 Final Research Report
  • [Book] Singularities in Geometry and Topology - Strausbourg 2009, IRMA Lectures in Mathematics and Theoretical Physics, Vol. 202012

    • Author(s)
      V. Blanloeil, T. Ohmoto (eds.)
    • Total Pages
      362
    • Publisher
      European Math. Soc.
    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/index-j.html

    • Related Report
      2013 Final Research Report
  • [Remarks] 佐伯修のホームページ

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/index-j.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] 佐伯修のホームページ

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/index-j.html

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://imi.kyushu-u.ac.jp/~saeki/index-j.html

    • Related Report
      2011 Research-status Report
  • [Patent(Industrial Property Rights)] 材料組織の幾何学形状の特徴量抽出方法、評価方法、抽出装置及びプログラム2012

    • Inventor(s)
      中川淳一、佐伯修、他、計8名
    • Industrial Property Rights Holder
      新日鐵住金株式会社、国立大学法人九州大学
    • Industrial Property Rights Type
      特許
    • Filing Date
      2012-11-28
    • Related Report
      2012 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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