Updated on 2024/10/07

写真b

 
SUGIYAMA Kennichi
 
*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*
Senior Specially Appointed Professor
Degree
理学博士 （ 東京大学 ）
Research Theme*

  • 整数論に限らず、数学の様々な分野に現れるゼータ関数の性質を調べることをテーマとする。主に、(a)3次元球面内の双曲結び目のAlexander多項式とその補空間に対して定義されるRuelleのゼータ関数との関係、(b)有限グラフに対して定義される伊原ゼータ関数と有限体上定義された代数曲線に伴うHasse-Weilの合同ゼータ関数に共通する性質、について研究している。

    • Research Interests

  • Number Theory

  • Geometry

    • Campus Career*
    • 4 2024 - Present 
      College of Science   Department of Mathematics   Senior Specially Appointed Professor
    • 4 2024 - Present 
      Graduate School of Science   Master's Program in Mathematics   Senior Specially Appointed Professor
    • 4 2024 - Present 
      Graduate School of Science   Doctoral Program in Mathematics   Senior Specially Appointed Professor
    • 4 2015 - 3 2024 
      College of Science   Department of Mathematics   Professor
    • 4 2015 - 3 2024 
      Graduate School of Science   Master's Program in Mathematics   Professor
    • 4 2015 - 3 2024 
      Graduate School of Science   Doctoral Program in Mathematics   Professor

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    Research Areas

    • Natural Science / Geometry

    Research History

    • 4 2015 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2015 - Present 
      RIKKYO UNIVERSITY   Graduate School of Science Field of Study: Mathematics   Professor

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    • 4 2015 - Present 
      RIKKYO UNIVERSITY   College of Science Department of Mathematics   Professor

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    Education

    • - 3 1987 
      The University of Tokyo   Graduate School, Division of Natural Science

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      Country： Japan

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    • - 3 1982 
      The University of Tokyo   Faculty of Science

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      Country： Japan

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    Committee Memberships

    • 9 2008 - Present 
      Mathematical society of Japan   an extended secretary of geometry

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      Committee type：Academic society

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    • 9 2008 - Present 
      日本数学会   幾何学分科会拡大幹事

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      Committee type：Academic society

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    Papers

    • On a generalization of Deuring's results Peer-reviewed

      Ken-ichi Sugiyama

      FINITE FIELDS AND THEIR APPLICATIONS26 ( C ) 69 - 85   3 2014

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

      Using the Dieudonne theory we will study a reduction of an abelian variety with complex multiplication at a prime. Our results may be regarded as generalization of the classical theorem due to Deuring for CM-elliptic curves. We will also discuss a sufficient condition for a prime at which the reduction of a CM-curve is maximal. (C) 2013 Elsevier Inc. All rights reserved.

      DOI： 10.1016/j.ffa.2013.11.004

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    • On geometric analogues of the Birch and Swinnerton-Dyer conjecture for low dimensional hyperbolic manifolds Invited Peer-reviewed

      Ken-ichi Sugiyama

      Contemporary Mathematics484   267 - 286   2009

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

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    • On geometric analogues of the Iwasawa main conjecture for a hyperbolic threefold Invited Peer-reviewed

      Ken-ichi Sugiyama

      Adv. Stud. in Pure Math.55   117 - 136   2009

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

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    • An analog of the Iwasawa conjecture for a compact hyperbolic threefold Peer-reviewed

      Ken-ichi Sugiyama

      JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK613   35 - 50   12 2007

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：WALTER DE GRUYTER & CO  

      For a local system on a compact hyperbolic threefold, under a cohomological assumption, we will show that the order of its twisted Alexander polynomial and of the Ruelle L-function at s = 0 coincide. Moreover we will show that their leading constants are also identical. These results may be considered as a solution of a geomeric analogue of the Iwasawa conjecture in the algebraic number theory.

      DOI： 10.1515/CRELLE.2007.090

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    • On geometric Iwasawa conjecture from a viewpoint of the arithmetic geometry Invited Peer-reviewed

      Ken-ichi Sugiyama

      RIMS Kokyuroku Bessatsu4   235 - 247   2007

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

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    • Some remarks on the Brylinski-Radon and the Fourier transforms Peer-reviewed

      K Sugiyama

      JOURNAL OF FUNCTIONAL ANALYSIS235 ( 2 ) 543 - 558   6 2006

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

      We will study a relationship between the Brylinski-Radon and the Fourier transforms of a monodromic perverse sheaf. In fact we will show that they are equivalent modulo a constant perverse sheaf. As an application, we will discuss a relation between the Sklyanin transform and the Brylinski-Radon transform. (c) 2005 Elsevier Inc. All rights reserved.

      DOI： 10.1016/j.jfa.2005.11.009

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    • On the Hodge conjecture and the Tate conjecture for the Hilbert schemes of an abelian surface Peer-reviewed

      KI Sugiyama

      MATHEMATISCHE NACHRICHTEN279 ( 1-2 ) 217 - 231   2006

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：WILEY-V C H VERLAG GMBH  

      We will show the Hodge conjecture and the Tate conjecture are true for the Hilbert schemes of points on an abelian surface or on a Kummer surface. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

      DOI： 10.1002/mana.200410357

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    • A geometric analogue of the birch and Swinnerton-Dyer conjecture over the complex number field Peer-reviewed

      KI Sugiyama

      JOURNAL OF DIFFERENTIAL GEOMETRY68 ( 1 ) 73 - 98   9 2004

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

      We will define a Ruelle-Selberg type zeta function for a certain lomathcal system over a Riemann surface whose genus is greater than or equal to three. Also, we will investigate its property, especially their special values. As an application, we will show that a geometric analogue of BSD conjecture is true for a family of abelian varieties which has only semi-stable reductions defined over the complex number field.

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    • Einstein-Kaehler metrics on minimal varieties of general type and an inequality between Chern numbers Invited Peer-reviewed

      Ken-ichi Sugiyama

      Adv. Stud. in Pure Math.18 ( 1 ) 417 - 443   1990

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

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    • On tangent sheaves of minimal varieties Invited

      Ken-ichi Sugiyama

      Adv. Stud. in Pure Math.18 ( 2 ) 85 - 103   1990

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

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    • A GEOMETRY OF KAHLER CONES Peer-reviewed

      K SUGIYAMA

      MATHEMATISCHE ANNALEN281 ( 1 ) 135 - 144   1988

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

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    • An asymptotic estimate of dimension of harmonic spinors Peer-reviewed

      Ken-ichi Sugiyama

      J. Math. Soc. Japan40 ( 2 ) 319 - 330   1988

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

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    • LOWER BOUNDS OF THE ESSENTIAL SPECTRUM OF THE LAPLACE-BELTRAMI OPERATOR AND ITS APPLICATION TO COMPLEX-GEOMETRY Invited Peer-reviewed

      K SUGIYAMA

      LECTURE NOTES IN MATHEMATICS1339   226 - 247   1988

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER VERLAG  

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    • ON COMPLETE KAHLER-MANIFOLDS WITH FAST CURVATURE DECAY

      K SUGIYAMA

      OSAKA JOURNAL OF MATHEMATICS22 ( 2 ) 261 - 275   1985

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      Language：English   Publishing type：Research paper (scientific journal)   Publisher：OSAKA JOURNAL OF MATHEMATICS  

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    Books and Other Publications

    • 線型代数学

      杉山健一（ Role： Sole author）

      日本評論社  3 2006 

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      Language：Japanese Book type：Scholarly book

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    • フーリエ解析学講義

      杉山健一（ Role： Sole author）

      講談社サイエンティフィック  12 2003 

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      Language：Japanese Book type：Scholarly book

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    Presentations

    • On a generalization of Deuring's results Invited International conference

      Ken-ichi Sugiyama

      Low dimensional topology and number theory VI  18 3 2014 

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      Language：English   Presentation type：Oral presentation (general)  

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    • On a geometric analog of the Iwasawa conjecture Invited International conference

      Ken-ichi Sugiyama

      Low dimensional topology and number theory  3 2009 

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      Language：English   Presentation type：Oral presentation (general)  

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    • On a special value of Ruelle L-function and a regulator Invited

      Ken-ichi Sugiyama

      SFB478  7 2008 

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      Language：English   Presentation type：Oral presentation (general)  

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    • A geometric analog of the Birch and Swinnerton-Dyer conjecture for a hyperbolic threefold Invited International conference

      Ken-ichi Sugiyama

      Geometry and Quantization  9 2007 

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      Language：English   Presentation type：Oral presentation (general)  

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    • A geometric analog of the Birch and Swinnerton-Dyer conjecture for a hyperbolic threefold Invited International conference

      Ken-ichi Sugiyama

      Spectral Analysis in Geometry and Number Theory  8 2007 

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      Language：English   Presentation type：Oral presentation (general)  

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    • A geometric analog of the Birch and Swinnerton-Dyer conjecture for a hyperbolic threefold Invited International conference

      Ken-ichi Sugiyama

      MSJ-IHES joint workshop  11 2006 

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      Language：English   Presentation type：Oral presentation (general)  

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    • Non-abelian class field theory over the field of complex numbers and its application to threefolds Invited International conference

      Ken-ichi Sugiyama

      Geometric quantization and related complex geometry  11 2005 

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      Language：English   Presentation type：Oral presentation (general)  

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    Professional Memberships

    Research Projects

    • 非アーベル的な位相的捻れと岩澤多項式の精密化

      日本学術振興会  科学研究費助成事業 

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      4 2010 - 3 2014

      Grant type：Competitive

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    • A special value of the zeta function of a hyperbolic threefold

      Grant-in-Aid for Scientific Research 

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      4 2004 - 3 2014

      Grant type：Competitive

      We describe the special value of the Ruelle L-function of a hyperbolic threefold by a geometric invariant.

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    • ３次元双曲多様体における岩澤予想とその数論への応用

      日本学術振興会  科学研究費助成事業 

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      4 2006 - 3 2010

      Grant type：Competitive

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    Social Contribution

    • 千葉県高等学校教育研究会数学部

      8 2014

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