KOBAYASHI Mahito

写真a

Affiliation

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

Graduating School 【 display / non-display

  •  
    -
    1987.03

    The University of Tokyo   Faculty of Science   Graduated

Graduate School 【 display / non-display

  •  
    -
    1984.03

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

Campus Career 【 display / non-display

  • 2010.04
    -
    Now

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

Research Field (grants-in-aid-for-scientific-research classification) 【 display / non-display

  • Geometry

  • Science education

 

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

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。

Published Papers 【 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

    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]

    Domestic Co-author

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

    Mahito Kobayashi, Minoru Yamamoto

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

    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]

    Single author

    DOI

  • A survey on polygonal portraits of manifolds

    Mahito Kobayashi

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

    Single author

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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.

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 

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

Presentations 【 display / non-display

  • 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