KOBAYASHI Mahito

写真a

Affiliation

Graduate School of Engineering Science  Department of Mathematical Science and Electrical-Electronic-Computer Engineering  Mathematical Science Course 

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Research Interests 【 display / non-display 】

  • 写像による多様体の研究

  • 位相幾何学,　特異点論

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Graduating School 【 display / non-display 】

  • 　
    -
    1987.03

    The University of Tokyo   Faculty of Science   Graduated

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Graduate School 【 display / non-display 】

  • 　
    -
    1984.03

    Tokyo Institute of Technology  Graduate School, Division of Natural Science  Doctor's Course  Completed

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Campus Career 【 display / non-display 】

  • 2016.04
    -
    Now

    Akita University   Graduate School of Engineering Science   Department of Mathematical Science and Electrical-Electronic-Computer Engineering   Mathematical Science Course   Associate Professor  

  • 2010.04
    -
    2016.03

    Akita University   Graduate School of Engineering and Resource Science   Department of Computer Science and Engineering   Associate Professor  

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Research Areas 【 display / non-display 】

  • Natural Science / Geometry

  • Humanities & Social Sciences / Science education

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Research Career 【 display / non-display 】

  • panorama views for closed piecewise linear plane curves

    Basic Science Research Program  

    Periods of research：

    2017.03
    -
    Now

    Classification of research form：Collaboration within Japan

  • shape analysis by Panorama view

    Basic Science Research Program  

    Periods of research：

    2006.06
    -
    Now

    Classification of research form：Collaboration within Japan

  • Study on manifolds with polygonal portraits

    Basic Science Research Program  

    Periods of research：

    1997.04
    -
    Now

    Classification of research form：Individual

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Thesis for a degree 【 display / non-display 】

  • Torus Type Stable Fibrations of Smooth 4-manifolds

    Mahito Kobayashi 

      1994.01

    Single author

    滑らかな写像を用いて多様体の位相的構造を探ることは，Morse理論に代表されるように，幾何学の自然な試みである。本論文では，滑らかな4次元多様体から平面または2-球面への安定写像に着目し，その特異値が作る曲線をもとに多様体の位相構造を探る試みを行った。
    第1部で概要を述べたのち，第2部では，単連結4次元多様体から平面への安定写像に対して，複数の写像改変手術を導入し，微分位相構造を損なうことなく，写像を，より簡単な特異値集合を持つものに取り替えることを試みた。第3部では，4次元閉多様体から2-球面への, torus と2-球面を正則ファイバーとして持つ安定写像を研究対象として導入し torus type stable fibration と呼んだ。正則ファイバーが自明な monodromy を持つとき，2本の torus fibre に対して，小平の log-transformation を行なっても，多様体の微分位相形は限られたクラスの中にあり，exotic smooth structure が発生しないことを示した。この結果は，elliptic fibration に対する log-transformation が Dolgachev の複素曲面を生成し，従って無数の exotic structure を発生させることと好対照をなす。この微分構造の安定性は，1-球面上の3-球面束の，分割貼り合わせに対する安定性に起因することを，平面への安定写像の構成を通して確認した。

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Research Achievements 【 display / non-display 】

    ◆Original paper【 display / non-display 】

  • On planar portraits of manifolds associated with graphs of block decompositions of manifolds

    Mahito Kobayashi

    数理解析研究所講究録 ( 京都大学数理解析研究所 )  2085   126 - 132   2018.08

    Research paper (journal)   Single author

    安定写像による滑らかな閉多様体の平面像が，多様体をブロックに分解した時の接続関係を示すグラフと密接な関係を持つことを示す例を与えた

  • Educational effects and problems of a special class to the SSH designated school by a university teacher

    Sho Suzuki, Mahito Kobayashi

    Bulletin of the Japan society for senior high school education   24   78 - 87   2017.07  [Refereed]

    Research paper (journal)   Domestic Co-author

  • Views of Real Projective 3-space by Stable Maps into the Plane

    Mahito Kobayashi, Minoru Yamamoto

    Experimental Mathematics ( Experimental Mathematics )  26 ( 2 ) 138 - 152   2016.08  [Refereed]

    Research paper (journal)   Domestic Co-author

    DOI

  • On the cusped fan in a planar portrait of a manifold

    Mahito Kobayashi

    Geometriae Dedicata   162   25 - 43   2013.04  [Refereed]

    Research paper (journal)   Single author

    DOI

  • A survey on polygonal portraits of manifolds

    Mahito Kobayashi

    Demonstratio Mathematica   XLIII ( 2 ) 433 - 445   2010.06  [Refereed]

    Research paper (journal)   Single author

    • display all >>

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    ◆University bulletin, Research institution【 display / non-display 】

  • A Study for Assesment of Math-literacies Required in Science-Technology Universities

    Mahito Kobayashi, Yayoi Kobayashi

        2023.03

    Research paper (university bulletin, research institution)   Domestic Co-author

  • Development of Interactive E-learning Contents for Understanding of Mathematical Concepts

    KOBAYASHI Yayoi, YAMAMOTO Minoru, YOKOYAMA Hiroshi, KOBAYASHI Mahito

    Bulletin of Seirei Women's Junior College ( Seirei Women's Junior College )  50 ( 0 ) 102 - 108   2022.03

    Research paper (university bulletin, research institution)   Domestic Co-author

    DOI CiNii Research

  • 4-manifolds restored over the 2-disc by stable maps withthe critical value set D_5

    Mahito Kobayashi

    秋田大学教育学部紀要     1997.03

    Research paper (university bulletin, research institution)   Single author

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    ◆Research society, Symposium materials, etc.【 display / non-display 】

  • Bridge Lectures at High Schools for Theorem Re-finding in Geometry

    KOBAYASHI Mahito, KOBAYASHI Yayoi

    JSSE Research Report ( Japan Society for Science Education )  38 ( 2 ) 257 - 262   2023.12

    Research paper (research society, symposium materials, etc.)   Domestic Co-author

    DOI CiNii Research

  • Evaluation of Students' Understanding of Basic Concepts in the First Year Calculus by Web Tests

    KOBAYASHI Mahito, KOBAYASHI Yayoi

    JSSE Research Report ( Japan Society for Science Education )  37 ( 2 ) 45 - 48   2022.12

    Research paper (research society, symposium materials, etc.)   Domestic Co-author

    DOI CiNii Research

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Books 【 display / non-display 】

  • Basic Training in Linear Algebta, 2021edition

    Mahito Kobayashi, Masaya Ouch and others

    2020.03

    An introductory textbook of Linear Algebra in university students, advanced high school students and for general people. Solid understanding of basic concepts are scoped so that the learners can apply them in various branches of Sciences and Technologies, Data Science to the problems they face in future.

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Grant-in-Aid for Scientific Research 【 display / non-display 】

  • Grant-in-Aid for Scientific Research(C)

    Project Year： 2020.04  -  2022.03  Investigator(s): Mahito Kobayashi

  • Grant-in-Aid for Scientific Research(S)

    Project Year： 2019.04  -  2020.03 

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Joint Research activities 【 display / non-display 】

  • Shape detection by Panorama Views

    Offer organization: Hokkai-Gakuen University   Private Enterprise  Collaboration in Japan  

    Project Year： 2010.04  -  Now 

    Member：Takashi Sano

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Presentations 【 display / non-display 】

  • A trial of theorem-re-discoveing type lectures for highschool students

    Mahito Kobayashi, Yayoi Kobayashi

    2023.12  -  2023.12 

    We reported the responses of the high school students to the special lectures by a university teacher aimed at re-discovering theorems on modern Geometry.

  • An elementary reproof of Fabricius Bjerre theorem for polygons

    Mahito Kobayashi

    Extension of the Singularity theory  (京都大学数理解析研究所)  2023.11  -  2023.11 

    閉じた平面曲線の形状に関して，Fabricius Bjerre による特徴量（交点，双接線，変曲点）の間の関係式が知られている。閉PL曲線（閉折線）に対しても同じ関係式が成立することをT Banchoffが示している。本発表では，閉折線の高さ関数に対してB特性数と呼ばれる数値を導入し，投影方向の変化に対する高さ関数の変化とB特性数の変化を極めて初等的に観察し，Banchoffの結果に別証明を与えた。本研究は，佐野貴志（北海学園大），山本稔（弘前大）と共に閉折線に対して導入したパノラマビュウという道具の利用に関する共同研究の成果である。

  • Generic foling of R^a times R^b into R^2 by two quadratic forms

    Mahito Kobayashi

    可微分写像の特異点論とその応用  (日本大学文理学部)  2023.02  -  2023.02 

  • 2次形式の組から得られる平面への generic folding について

    小林真人, 山本稔

    日本数学会東北支部会  (秋田大学（遠隔方式）)  2022.02  -  2022.02  日本数学会東北支部会

    2次形式を並べて得られるEuclid空間積からの平面への写像は，幾何学的に有用であるが，残念なことに退化特異点を持ち，非安定写像である。この写像を，2次元投影による高次元多様体の可視化と探索に用いるために安定摂動し，安定性の確認，特異値集合の形状を解析するという研究の概略を報告した。

  • Planar portraits of manifolds associated with the cones and the I-products of the nets of handle decompositions

    Mahito Kobayashi

    Local and global study of singularity theory of differentiable maps  (RIMS, Kyoto)  2017.11  -  2017.12 

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Academic Activity 【 display / non-display 】

  • 2021.03
    -
    2022.02

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