Updated on 2023/09/28

写真b

 
NISHINO Takeo
 
*Items subject to periodic update by Rikkyo University (The rest are reprinted from information registered on researchmap.)
Affiliation*
College of Science Department of Mathematics
Graduate School of Science Doctoral Program in Mathematics
Graduate School of Science Master's Program in Mathematics
Title*
Associate Professor
Degree
博士(理学) （ 京都大学 ）
Research Theme*

  • 数理物理に由来する幾何学的な問題を、シンプレクティック幾何や代数幾何からのアプローチで研究している。最近はそれらの研究から得られた考え方を用いて、古典的な幾何学の問題に対して組み合わせ論的な新しい視点から考えることによって、これまでと異なる切り口を見いだすことを模索している。

    • Campus Career*
    • 4 2014 - Present 
      College of Science   Department of Mathematics   Associate Professor
    • 4 2014 - Present 
      Graduate School of Science   Master's Program in Mathematics   Associate Professor
    • 4 2014 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Associate Professor
     

    Research Areas

    • Natural Science / Geometry

    Research History

    • 4 2014 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Associate Professor

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    • 4 2014 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Associate Professor

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    • 4 2014 - Present 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Associate Professor

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    Education

    • - 3 2002 
      Kyoto University   Graduate School, Division of Natural Science

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      Country： Japan

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    • - 3 2002 
      Kyoto University   Graduate School, Division of Natural Science

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      Country： Japan

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    • - 3 1997 
      Kyoto University   Faculty of Science

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      Country： Japan

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    Papers

    • Integration of vector fields on cell complexes and Morse theory Peer-reviewed

      Takeo Nishinou

      Journal of Mathematical Analysis and Applications522 ( 1 ) 126982 - 126982   6 2023

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      Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

      DOI： 10.1016/j.jmaa.2022.126982

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    • Obstructions to deforming maps from curves to surfaces Peer-reviewed

      Takeo NISHINOU

      Journal of the Mathematical Society of Japan-1 ( -1 )   9 2 2023

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      Publishing type：Research paper (scientific journal)   Publisher：Mathematical Society of Japan (Project Euclid)  

      DOI： 10.2969/jmsj/86878687

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    • Convergence of Hermitian–Yang–Mills connections on two-dimensional Kähler tori and mirror symmetry Peer-reviewed

      Takeo Nishinou

      Letters in Mathematical Physics111 ( 2 )   26 4 2021

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      Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

      DOI： 10.1007/s11005-021-01405-1

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      Other Link： https://link.springer.com/article/10.1007/s11005-021-01405-1/fulltext.html

    • Toric Degenerations, Tropical Curve, and Gromov-Witten Invariants of Fano Manifolds Peer-reviewed

      Takeo Nishinou

      CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES67 ( 3 ) 667 - 695   6 2015

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：CANADIAN MATHEMATICAL SOC  

      In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds that admit toric degenerations to toric Fano varieties with singularities allowing small resolutions. Examples include (generalized) flag manifolds of type A and some moduli space of rank two bundles on a genus two curve.

      DOI： 10.4153/CJM-2014-006-3

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    • DISK COUNTING ON TORIC VARIETIES VIA TROPICAL CURVES Peer-reviewed

      Takeo Nishinou

      AMERICAN JOURNAL OF MATHEMATICS134 ( 6 ) 1423 - 1472   12 2012

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：JOHNS HOPKINS UNIV PRESS  

      In this paper, we define two numbers. One is defined by counting tropical curves with a stop, and the other is the number of holomorphic disks in toric varieties with Lagrangian boundary condition. Both of these curves should satisfy some incidence conditions. We show that these numbers coincide. These numbers can be considered as Gromov-Witten type invariants for holomorphic disks, and they have similarities as well as differences to the counting numbers of closed holomorphic curves. We study several aspects of them.

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    • Potential functions via toric degenerations Peer-reviewed

      Takeo Nishinou, Yuichi Nohara, Kazushi Ueda

      PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES88 ( 2 ) 31 - 33   2 2012

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：JAPAN ACAD  

      We construct an integrable system on an open subset of a Fano manifold equipped with a toric degeneration, and compute the potential function for its Lagrangian torus fiber if the central fiber is a tone Fano variety admitting a small resolution.

      DOI： 10.3792/pjaa.88.31

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    • Toric degenerations of Gelfand-Cetlin systems and potential functions Peer-reviewed

      Takeo Nishinou, Yuichi Nohara, Kazushi Ueda

      ADVANCES IN MATHEMATICS224 ( 2 ) 648 - 706   6 2010

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

      We define a tonic degeneration of an integrable system on a projective manifold, and prove the existence of a tonic degeneration of the Gelfand-Cetlin system on the flag manifold of type A, As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system. (C) 2009 Elsevier Inc. All rights reserved.

      DOI： 10.1016/j.aim.2009.12.012

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    • Convergence of adiabatic family of anti-self-dual connections on products of Riemann surfaces Peer-reviewed

      Takeo Nishinou

      JOURNAL OF MATHEMATICAL PHYSICS51 ( 2 )   2 2010

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER INST PHYSICS  

      We prove a convergence theorem for a sequence of anti-self-dual connections on a family of products of two Riemann surfaces, where the metric of one factor shrinks, establishing the conjecture of Bershadsky et al. [Topological reduction of 4D SYM to 2D sigma-models," Nucl. Phys. B 448, 166 (1995)]. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3318164]

      DOI： 10.1063/1.3318164

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    • Global gauge fixing for connections with small curvature on T-2 Peer-reviewed

      Takeo Nishinou

      INTERNATIONAL JOURNAL OF MATHEMATICS18 ( 2 ) 165 - 177   2 2007

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

      In this paper, we will construct a global gauge for connections with small curvature on the trivial complex rank 2 bundle on T-2. In this gauge the connection matrix A satisfies parallel to A parallel to (Cr+1) <= const. parallel to FA parallel to(1/2)(Cr).

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    • Toric degenerations of toric varieties and tropical curves Peer-reviewed

      Takeo Nishinou, Bernd Siebert

      DUKE MATHEMATICAL JOURNAL135 ( 1 ) 1 - 51   10 2006

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：DUKE UNIV PRESS  

      We show that the counting of rational curves on a complete toric variety which are in general position relative to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on degeneration techniques and log deformation theory.

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    • ymplectic embedding of thin discs into a ball Peer-reviewed

      T. Nishinou

      Math. Bohem.   2004

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      Language：English   Publishing type：Research paper (scientific journal)  

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    • Some nontrivial homology classes on the space of symplectic forms Peer-reviewed

      T Nishinou

      JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY42 ( 3 ) 599 - 606   12 2002

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：KINOKUNIYA CO LTD  

      We construct a family of examples of non-zero relative homolgy classes on some infinite dimensional spaces of symplectic forms.

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    Research Projects

    • 多様体の退化と関連分野

      基礎科学研究 

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      4 2005 - Present

      Grant type：Competitive

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