Advance

MATSUI Yutaka

    Department of Science　Professor
Last Updated :2024/04/25

Researcher Information

Degree

  • Master(Mathematical Sciences)（The University of Tokyo）

Research funding number

  • 10510026

J-Global ID

Research Interests

  • Algebraic analysis   Microlocal analysis   Constructible sheaves   Constructible functions   D-modules   Multicomplex analysis   Prime number theorem   

Research Areas

  • Natural sciences / Basic analysis

Academic & Professional Experience

  • 2021/04 - Today  Kindai UniversityFaculty of Science and Engineering Department of ScienceProfessor
  • 2012/04 - 2021/03  Kindai UniversityFaculty of Science and Engineering, Department of Science准教授
  • 2008/04 - 2012/03  Kindai UniversityFaculty of Science and Engineering, Department of Science講師
  • 2007/04 - 2008/03  The University of TokyoGraduate School of Mathematical SciencesCOE拠点形成特任研究員

Education

  • 2004/04 - 2007/03  東京大学大学院  数理科学研究科  数理科学専攻 博士課程
  • 2002/04 - 2004/03  東京大学大学院  数理科学研究科  数理科学専攻 修士課程
  •        - 2004  The University of Tokyo  Graduate School, Division of Mathematical Sciences  Mathematical Sciences
  • 2000/04 - 2002/03  The University of Tokyo  Faculty of Science  Department of Mathematics
  •        - 2002  The University of Tokyo  Faculty of Science

Association Memberships

  • 日本数学会   Mathematical Society of Japan   

Published Papers

  • Asymptotic behavior of composite numbers with three constrained prime factors of general type
    MARUYA, Yuta; MATSUI Yutaka
    Kyushu J. Math. 掲載決定 2023/08 [Refereed]
     
    In this paper, we study the asymptotic behavior of the counting function of composite numbers with three constrained prime factors. Our constraint is that the largest prime factor is bounded above by a general increasing function with respect to either the smallest or the second smallest prime factor.
  • Generalized self-inversive bicomplex polynomials with respect to the j-conjugation
    MATSUI Yutaka; SATO Yuhei
    Bulletin of the Korean Mathematical Society 58 (4) 885 - 895 2021/07 [Refereed]
     
    In this paper, we study a kind of self-inversive polynomials in bicomplex algebra. For a bicomplex polynomial, this is the study of a relation between a kind of symmetry of its coefficients and a kind of symmetry of zeros. For our deep study, we define several new levels of self-inversivity. We prove some functional equations for standard ones, a decomposition theorem for generalized ones and a comparison theorem. Although we focus the j-conjugation in our study, our argument can be applied for other conjugations.
  • Characterization theorems of Riley type for bicomplex holomorphic functions
    MATSUI Yutaka; SATO Yuhei
    Communications of the Korean Mathematical Society 35 (3) 825 - 841 2020/07 [Refereed]
     
    We characterize bicomplex holomorphic functions from several estimates. Originally, Riley studied such problems in local case. In our study, we treat global estimates on various unbounded domains. In many cases, we can determine the explicit form of a function.
  • Hyperbolic Localization and Lefschetz fixed point formulas for higher dimensional fixed point sets
    IKE Yuichi; MATSUI Yutaka; TAKEUCHI Kiyoshi
    Int. Math. Res. Not. 2018 (15) 4852 - 4898 2018/08 [Refereed]
  • A range characterization of topological Radon transforms on Grassmann manifolds
    MATSUI Yutaka
    Rev. Roumaine Math. Rures Appl. 60 (4) 423 - 440 2015/12 [Refereed]
  • Yutaka Matsui; Kiyoshi Takeuchi
    HOKKAIDO MATHEMATICAL JOURNAL HOKKAIDO UNIV, DEPT MATHEMATICS 44 (3) 313 - 326 0385-4035 2015/10 [Refereed]
     
    We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues lambda not equal 1 in the monodromies at infinity of polynomial maps.
  • An inversion formula of Schapira type for topological Radon transforms of definable functions
    MATSUI Yutaka
    RIMS Kokyuroku Bessatsu B52 85 - 96 2014/10 [Refereed]
  • Yutaka Matsui; Kiyoshi Takeuchi
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES KYOTO UNIV, PUBLICATIONS RESEARCH INST MATHEMATICAL SCIENCES 50 (2) 207 - 226 0034-5318 2014/06 [Refereed]
     
    By calculating the equivariant mixed Hodge numbers of motivic Milnor fibers introduced by Denef-Loeser, we obtain explicit formulas for the Jordan normal forms of Milnor monodromies. The numbers of the Jordan blocks will be described by the Newton polyhedron of the polynomial.
  • Naoya Hayashi; Yutaka Matsui
    Communications of the Korean Mathematical Society 29 (1) 97 - 108 1225-1763 2014 [Refereed]
     
    In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeo- metric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions. © 2014 The Korean Mathematical Society.
  • Yutaka Matsui; Kiyoshi Takeuchi
    International Mathematics Research Notices 2013 (8) 1691 - 1746 1073-7928 2013 [Refereed]
     
    By introducing motivic Milnor fibers at infinity of polynomial maps, we propose some methods for the study of nilpotent parts of monodromies at infinity. The numbers of Jordan blocks in the monodromy at infinity will be described by the Newton polyhedron at infinity of the polynomial. © 2012 The Author(s).
  • 多項式写像とA-超幾何関数の無限遠点におけるモノドロミー
    竹内 潔; 松井 優
    数学 64 (3) 225 - 253 2012/07 [Refereed]
  • Yutaka Matsui; Kiyoshi Takeuchi
    MATHEMATISCHE ZEITSCHRIFT SPRINGER 268 (1-2) 409 - 439 0025-5874 2011/06 [Refereed]
     
    By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.
  • Yutaka Matsui; Kiyoshi Takeuchi
    TOHOKU MATHEMATICAL JOURNAL TOHOKU UNIVERSITY 63 (1) 113 - 136 0040-8735 2011/03 [Refereed]
     
    We apply sheaf-theoretical methods to monodromy zeta functions of Milnor fibrations. Classical formulas due to Kushnirenko, Varchenko and Oka, etc. on polynomials over the complex affine space will be generalized to polynomial functions over any toric variety. Moreover our results enable us to calculate the monodromy zeta functions of any constructible sheaf.
  • Yutaka Matsui; Kiyoshi Takeuchi
    ADVANCES IN MATHEMATICS ACADEMIC PRESS INC ELSEVIER SCIENCE 226 (2) 2040 - 2064 0001-8708 2011/01 [Refereed]
     
    We give explicit formulas for the dimensions and the degrees of A-discriminant varieties introduced by Gelfand, Kapranov and Zelevinsky. Our formulas can be applied also to the case where the A-discriminant varieties are higher-codimensional and their degrees are described by the geometry of the configurations A. Moreover combinatorial formulas for the Euler obstructions of general (not necessarily normal) toric varieties will be also given. (C) 2010 Elsevier Inc. All rights reserved.
  • Yutaka Matsui; Kiyoshi Takeuchi
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES OXFORD UNIV PRESS 2010 (5) 882 - 913 1073-7928 2010 [Refereed]
     
    We introduce new Lagrangian cycles that encode local contributions of Lefschetz numbers of constructible sheaves into geometric objects. We study their functorial properties and apply them to Lefschetz fixed-point formulas with higher-dimensional fixed-point sets.
  • Yutaka Matsui; Kiyoshi Takeuchi
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY AMER MATHEMATICAL SOC 136 (7) 2365 - 2373 0002-9939 2008 [Refereed]
     
    We give a simpler and purely topological proof of Ernstrom's class formula (1997) for the degree of dual varieties. Our new proof also allows us to obtain a formula describing the degrees of the associated varieties studied by Gelfand, Kapranov and Zelevinsky (1994).
  • MATSUI Yutaka; TAKEUCHI Kiyoshi
    RIMS Kokyuroku Bessatsu Kyoto University B10 149 - 165 1881-6193 2008 [Refereed]
  • Microlocal study of Lefschetz fixed point formulas
    MATSUI Yutaka; TAKEUCHI Kiyoshi
    Journal of Siberian Federal University. Mathematical & Physics 1 13 - 24 2008 [Refereed]
  • Topological Radon transforms and their applications
    MATSUI Yutaka; TAKEUCHI Kiyoshi
    RIMS Kokyuroku Bessatsu B5 225 - 240 2008/01 [Refereed]
  • Yutaka Matsui; Kiyoshi Takeuchi
    ADVANCES IN MATHEMATICS ACADEMIC PRESS INC ELSEVIER SCIENCE 212 (1) 191 - 224 0001-8708 2007/06 [Refereed]
     
    Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Asterisque 130 (1985) 193-209] and Kash i wara-Schapi ra [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernstrom in the complex case [L. Ernstrom, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces. (C) 2006 Elsevier Inc. All rights reserved.
  • Yutaka Matsui; Kiyoshi Takeuchi
    REAL AND COMPLEX SINGULARITIES WORLD SCIENTIFIC PUBL CO PTE LTD 248 - + 2007 [Refereed]
     
    By reformulating a result of Ernstrom [6] in terms of Chow groups, we obtain a class formula, i.e. a formula for the degrees of dual varieties, which is applicable also for projective varieties with positive dual defect. Various generalized Plucker-Teissier-Kleiman type formulas will be obtained. By our approach, topological invariants such as Milnor numbers along the singular locus of the original projective variety naturally appear in the class formulas.
  • Yutaka Matsui
    PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES KYOTO UNIV 42 (2) 551 - 580 0034-5318 2006/06 [Refereed]
     
    P. Schapira studied Radon transforms of constructible functions and obtained a formula related to an inversion formula. We generalize this formula to more complicated cases including Radon transformations between any Grassmann manifolds. In particular, we give an inversion formula for the Radon transformation and characterize images of Radon transforms of characteristic functions of Schubert cells.

Books etc

  • 線形代数学30講改訂増補版
    井原健太郎; 鄭仁大; 中村弥生; 松井優 (Joint work)培風館 2023/03
  • 微分積分学30講改訂増補版
    井原健太郎; 鄭仁大; 中村弥生; 松井優 (Joint work)培風館 2023/03
  • 白熱！無差別級数学バトル 近畿大学数学コンテスト問題集
    大野 泰生; 松井 優 (Joint editor)日本評論社 2013/02

MISC

Research Grants & Projects

  • 位相的ラドン変換の超局所解析と特異点理論への応用
    日本学術振興会：科学研究費
    Date (from‐to) : 2019/04 -2024/03 
    Author : 松井優
  • 位相的ラドン変換の超局所解析と特異点理論への応用
    日本学術振興会：科学研究費
    Date (from‐to) : 2015/04 -2019/03 
    Author : 松井 優
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2013/04 -2016/03 
    Author : Takeuchi Kiyoshi; MATSUI Yutaka
     
    We studied monodromies at infinity of polynomial maps. Especially for the maps which are not tame at infinity, by proving a vanishing theorem on the cohomology groups of generic fibers, we described the Jordan normal forms of their monodromies at infinity in many cases. As a byproduct of this study, we obtained also a description of the bifurcation sets of polynomial maps. Moreover, a formula for the characteristic polynomials of the monodromies at infinity of confluent A-hypergeometric functions was obtained. As for the monodromy conjecture, we confirmed it for polynomials which are non-degenerate at the origin in many cases.
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2010/04 -2014/03 
    Author : AOKI Takashi; SUZUKI Takao; IZUMI Shuzo; MATSUI Yutaka; NAKAMURA Yayoi; HONDA Naofumi; KAWAI Takahiro; TAKEI Yoshitsugu; KOIKE Tatsuya
     
    In this research, we have investigated the global properties of solutions to differential equations with a large parameter from the view point of the exact WKB analysis. There are three main results. Firstly, we have constructed the exponential-asymptotic (instanton-type) solutions, namely general formal solutions, to the equations which belong to the first Painleve hierarchies. Secondly, we have classified the topological types of the Stokes curves of the Gauss equation in terms of the parameters of the equation. Thirdly we have defined and computed explicit forms of the Voros coefficients of Gauss equation with a large parameter and obtained the Borel sums go them. We have obtained the formulas that describe parametric Stokes phenomena of WKB solutions.
  • 位相的ラドン変換の超局所解析と特異点理論への応用
    日本学術振興会：科学研究費
    Date (from‐to) : 2011/04 -2014/03 
    Author : 松井 優
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2010 -2012 
    Author : TAKEUCHI Kiyoshi; MATSUI Yutaka
     
    By using the theory of motivic Milnor fibers, we obtained some formulas which express the Jordan normal forms of monodromies at infinity of polynomial maps. Moreover we generalized this result to the case of polynomial maps from complete intersection varieties. By using the theory of rapid decay homologies we also obtained the integral representations of confluent A-hypergeometric functions. By this result we calculated their asymptotic expansions and Stokes multipliers at infinity.
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2009 -2011 
    Author : TAJIMA Shinichi; NAKAMURA Yayoi; OHARA Katsuyoshi; MATSUI Yutaka
     
    Algebraic local cohomology classes attached to hypersurface isolated singularities are considered in the context of algebraic analysis. A new algorithm of computing parametric algebraic local cohomology classes is derived. A new framework to study logarithmic vector fields and associated holonomic D-modules is constructed. An efficient algorithm to compute spectral decomposition of square matrices is derived by analyzing resolvent.
  • 構成可能関数の超局所解析とその特異点理論への応用
    日本学術振興会：科学研究費
    Date (from‐to) : 2008/04 -2010/03 
    Author : 松井 優
  • Japan Society for the Promotion of Science：Grants-in-Aid for Scientific Research
    Date (from‐to) : 2006 -2008 
    Author : AOKI Takashi; HONDA Naofumi; OHNO Yasuo; NAKAMURA Yayoi; MATSUI Yutaka; HONDA Naofumi; NAKAMURA Yayoi
     
    大きなパラメータを自然な形で含む連立非線型微分方程式系の形式解を構成するためには,主要部を決定する代数方程式系を解く必要がある.方程式の階数や方程式の個数が大きい場合は代数方程式系が複雑なものとなり,一見したところでは主要部が決定可能かどうかの判定は困難である.本研究では,この間題に関して主要部が決定可能であることを保証する幾つかの条件を与えた.これらの条件を実際の例に適用して重要な方程式系に対する形式解の存在が証明された.
  • 日本学術振興会：科学研究費助成事業
    Date (from‐to) : 2005 -2006 
    Author : 松井 優
     
    本研究はD加群の解層,更には一般の構成可能層の指数を表す構成可能函数の代数的な積分変換(ラドン変換)についてその像の特徴付けを行うものである.これまで研究では,組み合わせ論的な観点からの研究を行い,グラスマン多様体のシューベルト胞体の特性函数の変換像をヤング図形を用いて表記する結果を得ていた.また昨年度は超局所解析的な考察を行い,実射影空間とその双対空間の間の構成可能函数の積分変換の像の特徴付けを行った.即ち,複素の場合エルンストレムによってすでに得られていた結果の簡潔な証明を与えるとともに,実の場合にこの結果を拡張した.具体的には,実射影空間上滑らかな多様体の特性函数のラドン変換の超局所的な像(特性サイクル)が代数幾何で古典的に知られている双対多様体の次元や主曲率を用いて記述できることを明らかにした.この場合ラドン変換像とは元の多様体の超平面切断の幾何学的オイラー数を表すが,この結果によりラドン変換像の値の変化を双対多様体の幾何特に特異点の様子によって完全に決定できる.本年度はこの結果を実射影空間から実グラスマン多様体への構成可能関数の積分変換に対する結果に拡張した.この場合,双対多様体の拡張版であるk-双対多様体の次元や主曲率を用いて結果を記述できることを明らかにした.またそのために,k-双対多様体の微分幾何学的な性質をいくつか調べた.
  • 構成可能関数のRadon変換
    Date (from‐to) : 2003 -2006
  • Radon Transforms of constructible functions
    Date (from‐to) : 2003 -2006

Other link

researchmap


Copyright © MEDIA FUSION Co.,Ltd. All rights reserved.