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Matsushita Daisuke

Faculty of Science　Mathematics　MathematicsAssociate Professor

Researcher basic information

■ Degree
  • 博士(数理科学), 東京大学
■ URL
researchmap URLホームページURL■ Various IDs
J-Global ID■ Research Keywords and Fields
Research Keyword
  • Dynamical system
  • シンプレクティック幾何学
  • 代数幾何学
  • Symplectic Geometry
  • Algebraig Geometry
Research Field
  • Natural Science, Algebra
■ Educational Organization

Career

■ Career
Educational Background
  • 1997, The University of Tokyo, 数理科学研究科, 数理科学専攻, Japan
  • 1997, The University of Tokyo, Graduate School, Division of Mathematical Sciences
  • 1994, The University of Tokyo, 数理科学研究科, 数理科学専攻, Japan
  • 1994, The University of Tokyo, Graduate School, Division of Mathematical Sciences
  • 1992, The University of Tokyo, Faculty of Science, Department of Mathematics, Japan
  • 1992, The University of Tokyo, Faculty of Science

Research activity information

■ Papers
■ Syllabus
  • 代数学演習, 2024年, 学士課程, 理学部
  • 代数学演習Ａ, 2024年, 学士課程, 理学部
  • 基礎数学演習Ａ１, 2024年, 学士課程, 理学部
  • 基礎数学Ａ１, 2024年, 学士課程, 理学部
  • 線形代数学Ⅰ, 2024年, 学士課程, 全学教育
  • 線形代数学Ⅱ, 2024年, 学士課程, 全学教育
  • 基礎数学演習Ａ, 2024年, 学士課程, 理学部
  • 基礎数学Ａ, 2024年, 学士課程, 理学部
■ Affiliated academic society
  • 日本数学会
■ Research Themes
  • 既約シンプレクティック多様体のファイバー構造
    科学研究費助成事業
    01 Apr. 2024 - 31 Mar. 2029
    松下 大介
    日本学術振興会, 基盤研究(C), 北海道大学, 24K06640
  • Theory of holomorphic curves, the development of Floer theory and studies on contact and symplectic structures
    Grants-in-Aid for Scientific Research
    01 Apr. 2024 - 31 Mar. 2029
    小野 薫; 入江 慶; 枡田 幹也; 三松 佳彦; 赤穂 まなぶ; 秦泉寺 雅夫; 大場 貴裕; 吉安 徹; 松下 大介
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Kyoto University, 24H00182
  • Symplectic algebraic geometry and moduli spaces
    Grants-in-Aid for Scientific Research
    05 Apr. 2021 - 31 Mar. 2026
    並河 良典; 望月 拓郎; 吉川 謙一; 尾高 悠志; 吉岡 康太; 森脇 淳; 疋田 辰之; 松下 大介
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Kyoto University, 21H04429
  • Studies on Floer theory and symplectic, contact structures
    Grants-in-Aid for Scientific Research
    01 Apr. 2019 - 31 Mar. 2024
    小野 薫; 石川 剛郎; 枡田 幹也; 三松 佳彦; 赤穂 まなぶ; 入江 慶; 秦泉寺 雅夫; 松下 大介; 石川 卓; 泉屋 周一
    倉西構造による仮想的基本類・基本鎖の理論の一般論をまとめ、2020 年に書籍として出版した。擬正則曲線の moduli 空間や、それを用いた代数構造の構成をこの一般論の枠組みで実現することについては、以下の成果がある。moduli 空間の倉西構造の滑らかさを示した論文も出版決定となった。それを基礎にして、周期的ハミルトン系の場合の linear K-system の構成、周期的ハミルトン系の Floer (co)homology の新しい方法を論文にまとめた。Lagrange 部分多様体に付随する tree-like K system の構成などについての論文を投稿に向けて再点検した。(以上は、深谷氏、Oh 氏、太田氏との共同研究である)
    symplectic orbifold の Lagrangian に対する Floer 理論については、clean intersection となる Lagrangians の対の twisted sector の概念を得た。それを用いてLagrangian intersection の Floer 理論の枠組みができる。(Chen 氏、Wang 氏との共同研究)
    また、研究員として吉安徹氏を雇用し、h-原理 特に loose Legendre 部分多様体などについての継続的議論を通してシンプレクティック構造、接触構造の柔な側面について理解を深めた。
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Kyoto University, 19H00636
  • On Global Torelli type theorem of compact Kaehler manifolds with trivial first Chern class
    Grants-in-Aid for Scientific Research
    01 Apr. 2018 - 31 Mar. 2023
    松下 大介
    いわゆる Galois 理論とは体 k の有限次拡大体 K があった時, K と k の間の部分体 H の集合と K の k を固定する自己同型群 Gal(K/k) の部分群 G の集合の間に対応がある, という理論を指す. この対応を代数多様体の定義体と有理関数体に対して以下のように拡張することを試みている.


    作業仮説 : k 上定義された代数多様体 X に対し, X の自己同型群を Aut(X) とする. X の有理関数体 k(X) の k 上超越次数が 1 以上で k(X) よりも超越次数が小さい部分体と Aut(X) の almost abelian という可換な群に極めて近い性質を持つ無限位数の部分群の間に対応がある.


    2021 年度は上記の仮説を X が既約シンプレクティック多様体である時, SYZ 予想と呼ばれる予想が正しい ( これは 2021 年度知られている既約シンプレクティック多様体の全ての具体例で成立することが既に示されている ) と仮定した時に考察し, Aut(X) の almost abelian な無限位数の部分群の k(X) の固定体の超越次数は必ず X の次元の半分となり, 逆に k(X) の超越次数が 1 より大きい部分体 H に対して, Aut(X) の H を固定する部分群は almost abelian となることを示した また SYZ 予想を仮定しない証明を見出す準備として twisted homogeneous coordinate ring と呼ばれる対象について調べた. これは X の自己同型に応じて定まる非可換な字数付き環で, その交換子イデアルが自己同型の固定点集合の定義イデアルとなる, ということを示した.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 18K03231
  • Development of Floer theory and study on symplectic structures
    Grants-in-Aid for Scientific Research
    01 Apr. 2014 - 31 Mar. 2019
    ONO Kaoru; Ogawa Noboru
    Floer theory and the theory of pseudo-holomorphic curves have provided powerful tools in the study of symplectic geometry and brought many important results. During the academic years 2014-2018, the following achievements on Floer theory and its applications were made public:Lagrangian Floer theory and mirror symmetry on compact toric manifolds (joint paper, Asterisque 376, 2016), Anti-symplectic involution and Floer cohomology (joint paper, Geometry and Topology, 2016).
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), Kyoto University, 26247006
  • Construction of Lagrangian fibrations
    Grants-in-Aid for Scientific Research
    01 Apr. 2014 - 31 Mar. 2018
    MATSUSHITA Daisuke
    We investigated the linear system associated to ample divisors and an automorphism group of an irreducible symplectic manifold using deformation of complex structure. Regarding the former, we obtain the following
    result. Let X be the set of the complex structures which defining the mapping and Y the set of the complex structures which defining the embedding in the projective space. Both X and Y are open in the space of deformation of the complex structures of irreducible symplectic manifolds. With respect to the latter, by appropriately deforming the complex structure, we prove that an automorphism group of irreducible symplectic manifold contain an infinite cyclic group whose rank equals to the second Betti number minus two.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), Hokkaido University, 26400032
  • Developments in Interactions between Algebraic Geometry and Integrable Systems
    Grants-in-Aid for Scientific Research
    31 May 2012 - 31 Mar. 2017
    Saito Masa-Hiko; NORO Masayuki; KOIKE Tatsuya; INABA Michi-aki; MORI Shigefumi; MUKAI Shigeru; IWASAKI Katsunori; KANEKO Masanobu; HARAOKA Yoshishige; NAMIKAWA Yoshinori; ISHII Akira; FUJINO Osamu; HOSONO Shinobu; MATSUSHITA Daisuke; ABE Takeshi; IRITANI Hiroshi; TODA Yukinobu; NAKAJIMA Hiraku; NAKAMURA Iku; TANIGUCHI Takashi; ONO Kaoru; ROSSMAN Wayne; MITSUI Kentaro; SANO Taro
    We established the geometric Painleve property of nonlinear differential equations for isomonodromic deformations of connections with generic unramified irregular singularities and regular singularities with fixed spectral types. We also established theory of Mixed twister D-modules and developed several geometric theories for integrable systems. As for higher dimensional algebraic geometry, certain types of extremal contractions of 3-dimensinal terminal varieties were classified in detail. Fujino proved that canonical rings of compact Kahler manifolds are finitely generated. Several results for symplectic varieties, moduli theory were obtained in our research projects.
    Mathematical foundations of Quantum cohomology rings were developed by the group of Fukaya, Ono and others. Several developments of mirror symmetry, including the case of toric Calabi-Yau varieties, are obtained. We also obtained several important results on derived categories of sheaves on algebraic varieties.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (S), Kobe University, 24224001
  • Studies on Floer thoery, theory of holomorphic curves and symplectic structures, contact structures
    Grants-in-Aid for Scientific Research
    01 Apr. 2009 - 31 Mar. 2014
    ONO Kaoru; IZUMIYA Shyuichi; JINZENJI Masao; MATSUSHITA Daisuke; ISHIKAWA Goo; YAMAGUCHI Keizo; TAKAKURA Tatsuru
    Symplectic structure is a geometric structure, which appeared in the understanding of Hamilton's equation of motion. In recent years, there has been profound development in the geometric study of symplectic structures. In particular, combined with the mathematical study on mirror symmetry, symplectic geometry
    attracts attentions from many researchers. The investigator has been working on Floer theory, which plays a significant role in symplectic geometry, and its applications. In this research project, we studied Floer theory for Lagrangian torus fibers in toric manifold in a concrete way and obtained various interesting results.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (A), 21244002
  • On constructing of a minimal model of fibred algebraic varieties whose Kodaira dimension is zero
    Grants-in-Aid for Scientific Research
    2011 - 2012
    MATSUSHITA Daisuke; FUJINO Osamu; KAWAKITA Masayuki; TAKAGI Hiromichi
    Let us consider a smooth abelian fibration over a punctured disk or an open set of polydisk which obtained by removing a hypersurface. It is natural question whether these families can be extended over a disk or a polydisk. On 80th, it was announced that we could obtain such a relative compactification with a incomplete proof. Since semidarkness of the proof, there are several results with technical assumptions. By this result, we may get rid of these assumptions and obtain idealistic results.
    Japan Society for the Promotion of Science, Grant-in-Aid for Challenging Exploratory Research, Hokkaido University, 23654002
  • On Lagrangian fibratins of symplectic varieties
    Grants-in-Aid for Scientific Research
    2009 - 2012
    MATSUSHITA Daisuke
    We show that the base space of a Lagrangian fibration is a projective space if the source symplectic variety satisfies certain numerical conditions. We obtain the necessary and sufficient condition of existence of a Lagrangian fibration for all known examples. We also show smoothness of components of the relative moduli space of aLagrangian fibration which parametrize invertible sheaves on each fibre.
    Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (A), Hokkaido University, 21684001
  • New developments and interaction between Algebraic Geometry and Integrable Systems
    Grants-in-Aid for Scientific Research
    2007 - 2011
    SAITO Masa-hiko; NOUMI Masatoshi; YOSHIOKA Kota; YAMADA Yasuhiko; OHTA Yasuhiro; YAMAKAWA Daisuke; FUKAYA Kenji; INABA Michiaki; TAKASAKI Kanehisa; MORI Shigefumi; MUKAI Shigeru; IWASAKI Katsunori; KANEKO Masanobu; HARAOKA Yoshishige; NAMIKAWA Yoshinori; ISHII Akira; FUJINO Osamu; HOSONO Shinobu; MATSUSHITA Daisuke; YOSHINAGA Masahiko; KOIKE Tatsuya; MOCHIZUKI Takuro; IRITANI Hiroshi; HARASHITA Shushi; TODA Yukinobu
    We gave an algebro-geometric construction of the moduli spaces of stable parabolic connections over curves with unramified singularities, and showed the fundamental property of the Riemann-Hilbert correspondences. These results showed the geometric Painleve property of the nonlinear isomonodromic differential equations and established the geometry of isomonodromic deformations of connections, which enables us to investigate the phase space of differential equations deeply such as Okamoto's space of initial conditions for classical Painleve equations. Together with the progress in the field of higher dimensional birational geometry and the geometry related to mirror symmetry, these results reveal deep relations between algebraic geometry and integrable systems.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (S), Kobe University, 19104002
  • Studies on moduli of stable sheaves
    Grants-in-Aid for Scientific Research
    2006 - 2009
    YOSHIOKA Kota; SAITO Masahiko; YAMADA Yasuhiko; NOUMI Masatoshi; NAKAJIMA Hiraku; MASTUSHITA Daisuke; INABA Michiaki
    We derived the wall crossing formula and the blow-up formula of the Donaldson invariants. We also formulated K-theoretic analogue of the Doinaldson invariants and got the wall crossing formula. We studied the betation of the Fourier-Mukai transform and the stability condition ang got a nice result. As an application, we also studied the moduli of stable sheaves on abelian surfaces.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Kobe University, 18340010
  • On the structures of Lagrangian fibrations
    Grants-in-Aid for Scientific Research
    2006 - 2008
    MATSUSHITA Daisuke
    シンプレクティック多様体に入るラグランジアンファイブレーションについて, 特異ファイバーの構造を決定した。またラグランジアンファイブレーションを保ったまま変形出来るシンプレクティック多様体がそのモジュライ空間の中で余次元1の族をなすことを示した。さらにシンプレクティック多様体の双有理的な特質の一つを見出した。
    Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (A), Hokkaido University, 18684001
  • Study on Floer theory and symplectic geometry
    Grants-in-Aid for Scientific Research
    2006 - 2008
    KAORU Ono; KEIZO Yamaguchi; SHYUICHI Izumiya; GOO Ishikawa; MASAO Jinzenji; DAISUKE Matsushita; KENJI Fukaya; HIROSHI Ohta
    Lagrange部分多様体のFloer理論の枠組みおよび基礎付けを深谷氏、Oh氏、太田氏との共同研究で行った。Lagrange部分多様体のFloer理論のシンプレクティック幾何学へのいくつかの応用も得た。また、トーリック多様体のLagrangeトーラスファイバーのFloer理論にも着手し、Hamilton displaceablityやdisplacement energyについての結果を得た。
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), Hokkaido University, 18340014
  • Study of generating functions viewed from group theory and category theory
    Grants-in-Aid for Scientific Research
    2001 - 2004
    YOSHIDA Tomoyuki; YAMASHITA Hiroshi; MATSUSHITA Daisuke; TAKEGAHARA Yugen; YAMADA Hirohumi; YAMAKI Hiroyoshi
    1.Asai-Yoshida's conjecture on the number of group homomorphisms has a connection with p-adic anallysis (Yoshida, Takegahara, K.Conrad, etc.). Furthermore, Yoshida solved the conjecture for the homomorphisms from the fundamental group of a compact Riemann surface whose importence in quantum field theory was pointed by M.Mulase.
    2.Yoshida and Oda accomplished a fundamental theory of crossed Burnside rings of finite groups.
    3.Yoshida, Sasaki, Oda study cohomology theory of finite groups, especially Hochschild cohomology, crossed Mackey functors and quantum doubles of group algebra.
    4.Yoshida, Bannai and Keisuke Shiromoto sutudies combinatorics, in particular, distance regular graphs, designs and code theory, especially an application of homological algebra to the theory of codes on a ring.
    5.Koshitani studies modular representation thoery of finite groups and gave an affirmative answer to the Broue conjecture for groups with some special defect groups.
    6.Nakamura and Yamashita studied some related areas (algebraic geometry and representation theory) and gave some interested results, especially a relation with finite simple groups.
    7.We invited three mathematicians from abroad.
    ・2001 FAN Yun(Wuhan U.) Talk on Broue conjecture(Kyushu Univ.)
    ・2003 Keith CONRAD(Connecticut U.) Talk of p-adic analysis, number theory(Hokkaido U., Kyoto U.)
    ・2004 Segre BOUC(CNRS) Talk on Dade groups and Burnside rings (Hokaido U., Kyoto U.)
    A large number of results of this research has been printed and published. The remainder results will be serially published. The investigator gave some talks related to this research in some conferences--
    "Generating functions and related topics" (Sapporo 2001), "20-th Symposium on Algebraic Combinatorics (Kyoto 2002), "Extended Group Seminar" (Sapporo 2002,2004, and so on.
    Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (B), HOKKAIDO UNIVERSITY, 13440001
  • 正則シンプレクティック多様体
    1997
    Competitive research funding