Updated on 2024/05/23

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*
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 2024 - Present 
      College of Science   Department of Mathematics   Professor
    • 4 2024 - Present 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2024 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Professor
    • 4 2014 - 3 2024 
      College of Science   Department of Mathematics   Associate Professor
    • 4 2014 - 3 2024 
      Graduate School of Science   Master's Program in Mathematics   Associate Professor
    • 4 2014 - 3 2024 
      Graduate School of Science   Doctoral Program in Mathematics   Associate Professor

    ▼display all

     

    Research Areas

    • Natural Science / Geometry

    Research History

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

      More details

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

      More details

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

      More details

    Education

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

      More details

      Country: Japan

      researchmap

    • - 3 1997 
      Kyoto University   Faculty of Science

      More details

      Country: Japan

      researchmap

    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

      More details

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

      DOI: 10.1016/j.jmaa.2022.126982

      researchmap

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

      Takeo NISHINOU

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

      More details

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

      DOI: 10.2969/jmsj/86878687

      researchmap

    • 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

      More details

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

      DOI: 10.1007/s11005-021-01405-1

      researchmap

      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

      More details

      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

      researchmap

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

      Takeo Nishinou

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

      More details

      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.

      researchmap

    • 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

      More details

      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

      researchmap

    • 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

      More details

      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

      researchmap

    • 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

      More details

      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

      researchmap

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

      Takeo Nishinou

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

      More details

      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).

      researchmap

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

      Takeo Nishinou, Bernd Siebert

      DUKE MATHEMATICAL JOURNAL135 ( 1 ) 1 - 51   10 2006

      More details

      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.

      researchmap

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

      T. Nishinou

      Math. Bohem.   2004

      More details

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

      researchmap

    • 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

      More details

      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.

      researchmap

    ▼display all

    Research Projects

    • 多様体の退化と関連分野

      基礎科学研究 

      More details

      4 2005 - Present

      Grant type:Competitive

      researchmap

    • 正則曲線を通じた幾何構造の研究

      日本学術振興会  科学研究費助成事業 

      西納 武男

      More details

      4 2018 - 3 2023

      Grant number:18K03313

      Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

      退化した多様体上の正則曲線の研究においては, 一般に特異な多様体またはトロピカル多様体と呼ばれる組み合わせ的な対象上のグラフを用いた手法が有効な場合がある。その一例として, 1990年代後半のFukaya-Ohや2000年前後のFukayaによる研究においては, 正則ディスクを適当なモース関数に関する勾配軌道と関係させる試みが提案された。一方, 同時期にFormanにより(多様体と限らない)CW複体上の離散モース理論が考案され, 純粋数学および応用分野において広く用いられている。Formanの理論においては勾配流は胞体の集合上の写像として定義され, 実際にベクトル場の勾配流をとるわけではない。今年度の研究においては, 離散モース理論と上記のグラフによる正則曲線の研究の双方を念頭に置き, CW複体上の一定の条件を満たす関数に対して勾配ベクトル場と勾配流を定義し, その積分曲線を用いることでモース理論を構築できることを示した。これは多様体とは限らないCW複体にも適用できるようになっており, それを反映して通常のベクトル場とは全く異なる性質を持ち, 特に勾配流が(無限に)分岐する場合もある。これは, 区分線形多様体上の区分線形なベクトル場に対する積分曲線の良い定義を与えたとも解釈できる。
      もう一つの研究として, 一般型の複素曲面上の特異曲線の変形を考察し, 曲線がsemiregularityという条件を満たす場合, 種数を変えない変形に関してほぼ最良の性質を持つことを見出した。

      researchmap

    • Study of Riemannian surfaces from novel point of view

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      NISHINOU Takeo

      More details

      4 2014 - 3 2018

      Grant number:26400061

      Grant amount:\4680000 ( Direct Cost: \3600000 、 Indirect Cost:\1080000 )

      Our main work concerns construction of holomorphic curves on various types of varieties, amplifying ideas from tropical geometry. Most of the construction is based on a newly developed theory of deformations which allows us to deal with those cases which are beyond the reach of existing methods of tropical geometry. To overcome this point, we calculated the cohomology groups to which obstructions to deform degenerate curves belong, and also revealed what causes actual obstructions. As a result, we are now able to explicitly calculate obstructions in variety of cases, and then construct and classify holomorphic curves. As applications, we gave a precise relationship between periodic plane tropical curves and holomorphic curves on complex two dimensional tori, and also constructed vast number of rational curves on K3 surfaces.

      researchmap

    • Development of Integrable Geometry

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      Miyaoka Reiko, KOTANI Motoko, NISHINOU Takeo, UEHARA Taketo, MATSUURA Nozomu, IWASAKI Katsunori, IRITANI Hiroshi, KAJIWARA Kenji, NAGATOMO Yasuyuki, NOMURA Takaaki, YAMADA Kotaro, ISHIKAWA Goo, UMEHARA Masaaki, GUEST Martin, SHODA Toshihiro, FUTAKI Akito, FUJIOKA Atsushi, RASSMAN Wayne, TAMARU Hiroshi

      More details

      4 2011 - 3 2015

      Grant number:23340012

      Grant amount:\13780000 ( Direct Cost: \10600000 、 Indirect Cost:\3180000 )

      Isoparametric hypersurfaces with 6 principal curvatures with multiplicity 2 are shown to be homogeneous, which solves one of Yau's problems. As for 4 principal curvature case, we gave a description by using the moment map of spin actions. Transnormal systems are investigated in details.
      We show the non-existence of L2 harmonic 1-form on a complete non-compact stable minimal Lagrangian submanifolds in a Kaheler manifold with positive Ricci curvature. Then the number of non-parabolic ends is less than two, and in the surface case, the genus should vanish. The Floer theory on the intersection of a Lagrangian submanifold with its Hamiltonian deformation is investigated. The Gauss images of isoparametric hypersurfaces in the sphere are Lagrangian submanifolds of complex hyperquadric, and in this case, we show that if the multiplicities of the principal curvatures are bigger than 1, then they are Hamiltonian non-displaceable,

      researchmap

    • Study of mirror symmetry and integrable systems via degeneration of varieties

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      NISHINOU TAKEO

      More details

      4 2010 - 3 2014

      Grant number:22740031

      Grant amount:\4030000 ( Direct Cost: \3100000 、 Indirect Cost:\930000 )

      We studied aspects of mirror symmetry, which implies deep relationship between complex geometry and symplectic geometry, the geometries whose definitions are completely different. We made use of tropical geometry, a rather new field of research in geometry. With this new idea, we were able to describe several complicated geometric constructions in a simpler, combinatorial manner, and applied these results to mirror symmetry. Moreover, we applied our method to the study of important geometric objects such as flag manifolds or moduli space of vector bundles on Riemann surfaces.

      researchmap

    • Fusion of geometry and the theory of integrable systems

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      MIYAOKA Reiko, OHNITA Yoshihiro, MOTOKO Kotani, SASAKI Takeshi, IWASAKI Katsunori, OYSU Yukio, KAJIWARA Kenji, NAGATOMO Yasuyuki, NAKAYAAHIKI Atsushi, YAMADA Kotaro, FUTAKI Akito, MARTIN Guest, WAYNE Rossman, SHODA Toshihiro, IRITANI Hiroshi, ISHIKAWA Goo, UMEHARA Masaaki, KAWAKUBO Satoshi, TAMARU Hiroshi, FUJIOKA Atsushi, MATSUURA Nozomu, NISHINOU Takeo

      More details

      2007 - 2010

      Grant number:19204006

      Grant amount:\27560000 ( Direct Cost: \21200000 、 Indirect Cost:\6360000 )

      We classified almost all isoparametric hypersurface, and characterize them in terms of the moment map, which proves the evidence of a relation with integrable systems. A basic theory of surfaces with singularities, and a new method using the Legendre map have been established. Via the Riemann-Hilbert correspondence, the dynamical system of Painleve equations is investigated, and the view point of the chaos has been developed. The modularity of higher genus Gromov-Witten and the mirror symmetry are discussed. A surface with potential appeared in quantum cohomology is constructed, which contributes to the tt* geometry.

      researchmap

    • Geometry related to mirror symmetry and degenerations of manifolds

      Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research 

      NISHINOU Takeo

      More details

      2007 - 2009

      Grant number:19740034

      Grant amount:\2720000 ( Direct Cost: \2300000 、 Indirect Cost:\420000 )

      The purpose of our study is, to reveal symmetries and structures which are ingeniously hidden in seemingly complicated geometric objects. We mainly developed two devises: One is the degeneration of manifolds, which decomposes complex objects into simpler parts, and the other is the mirror symmetry, which is a kind of duality transformation between geometric objects. As a result, we could define several invariants of manifolds, and calculate them.

      researchmap

    ▼display all