Updated on 2022/03/27

写真a

 
FURUSHO, Hidekazu
 
Organization
Graduate School of Mathematics Social Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor

Degree 1

  1. 博士(理学) ( 2003.9   京都大学 ) 

Research Interests 2

  1. Algebraic Geometry

  2. Number Theory

Committee Memberships 13

  1. 人事委員会   人事委員  

    2020.4 - 2022.3   

  2. 教務委員会   教務委員  

    2020.4 - 2021.3   

  3. G30教育生活連絡会議委員   G30教育生活連絡会議委員  

    2020.4 - 2021.3   

  4. 日本数学コンクール実行委員会   日本数学コンクール実行委員  

    2019.4 - 2021.3   

  5. 広報・談話会委員会   広報・談話会委員  

    2019.4 - 2020.3   

  6. IR本部会議WGアソシエイトメンバー委員   IR本部会議WGアソシエイトメンバー委員  

    2018.4 - 2019.3   

  7. 図書委員会   図書委員  

    2018.4 - 2019.3   

  8. ホームカミングディ実行委員会   ホームカミングディ実行委員会  

    2018.4 - 2019.3   

  9. IR本部会議WGアソシエイトメンバー委員   IR本部会議WGアソシエイトメンバー委員  

    2017.4 - 2018.3   

  10. 広報談話会委員会   広報談話会委員  

    2015.4 - 2017.3   

  11. 一年生指導委員   一年生指導委員  

    2015.4 - 2016.3   

  12. 日本数学会中部支部評議員   日本数学会中部支部評議員  

    2015.4 - 2016.3   

  13. 広報談話会委員会   広報談話会委員  

    2014.4 - 2015.3   

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Awards 3

  1. 日本数学会代数学賞

    2014.3   日本数学会  

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    Country:Japan

  2. 井上研究奨励賞

    2006.2   井上財団  

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    Country:Japan

  3. 日本数学会建部賢弘奨励賞

    2004.9   日本数学会  

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    Country:Japan

 

Papers 23

  1. The Betti side of the double shuffle theory. I. The harmonic coproducts

    Enriquez Benjamin, Furusho Hidekazu

    SELECTA MATHEMATICA-NEW SERIES   Vol. 27 ( 5 )   2021.11

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  2. p-adic multiple L-functions and cyclotomic multiple harmonic values Reviewed

    Furusho Hidekazu, Jarossay David

    INTERNATIONAL JOURNAL OF NUMBER THEORY   Vol. 16 ( 2 ) page: 361 - 375   2020.3

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

    DOI: 10.1142/S1793042120500190

    Web of Science

  3. Galois action on knots II: proalgebraic string links and knots Invited Reviewed

    Hidekazu Furusho

    Periods in Quantum Field Theory and Arithmetic" Springer Proceedings in Mathematics & Statistics   Vol. 314   page: 541--591   2020.3

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  4. A Stabilizer Interpretation of Double Shuffle Lie Algebras Reviewed

    Enriquez Benjamin, Furusho Hidekazu

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   Vol. 2018 ( 22 ) page: 6870 - 6907   2018.11

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

    DOI: 10.1093/imrn/rnx084

    Web of Science

  5. On the coefficients of the Alekseev-Torossian associator Reviewed

    Furusho Hidekazu

    JOURNAL OF ALGEBRA   Vol. 506   page: 364-378   2018.7

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

    DOI: 10.1016/j.jalgebra.2018.03.023

    Web of Science

  6. DESINGULARIZATION OF COMPLEX MULTIPLE ZETA-FUNCTIONS Reviewed

    Furusho Hidekazu, Komori Yasushi, Matsumoto Kohji, Tsumura Hirofumi

    AMERICAN JOURNAL OF MATHEMATICS   Vol. 139 ( 1 ) page: 147-173   2017.2

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

    Web of Science

  7. Fundamentals of p-adic multiple L-functions and evaluation of their special values Reviewed

    Furusho Hidekazu, Komori Yasushi, Matsumoto Kohji, Tsumura Hirofumi

    SELECTA MATHEMATICA-NEW SERIES   Vol. 23 ( 1 ) page: 39-100   2017.1

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

    DOI: 10.1007/s00029-016-0233-2

    Web of Science

  8. Galois action on knots I: Action of the absolute Galois group Reviewed

    Furusho Hidekazu

    QUANTUM TOPOLOGY   Vol. 8 ( 2 ) page: 295-360   2017

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

    DOI: 10.4171/QT/91

    Web of Science

  9. p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas, Reviewed

    Hidekazu Furusho, Shinichi Kobayashi, Kenichi Bannai

    Nagoya Math Journal   Vol. 219   page: 269-302   2015

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

  10. Around associators Invited Reviewed

    Hidekazu Furusho

    Automorphic forms and Galois representations 2   ( 415 ) page: 105-117   2014

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

  11. Mixed Pentagon, octagon and Broadhurst duality equation Reviewed

    Benjamin Enriquez, Hidekazu Furusho

    Journal of Pure and Applied Algebra   Vol. 216 ( 4 ) page: 982-995   2012

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

  12. Geometric interpretation of double shuffle relation for multiple L-values Reviewed

    Hidekazu Furusho

    Galois-Teichm\"{u}ller theory and Arithmetic Geometry, Advanced Studies in Pure Math   Vol. 63   page: 163-187   2012

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

  13. Double shuffle relation for associators Reviewed

    Hidekazu Furusho

    Annals of Mathematics   Vol. 174 ( 1 ) page: 341-360   2011

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

  14. Pentagon and hexagon equations Reviewed

    Hidekazu Furusho

    Annals of Mathematics   Vol. 171 ( 1 ) page: 545-556   2010

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  15. p-adic multiple zeta values II -- tannakian interpretations Reviewed

    Hidekazu Furusho

    Amer.J.Math   Vol. 129 ( 4 ) page: 1105-1144   2007

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    We establish a tannakian formalism of $p$-adic multiple polylogarithms
    and $p$-adic multiple zeta values introduced in our previous paper
    via a comparison isomorphism between
    a de Rham fundamental torsor and a rigid fundamental torsor
    of the projective line minus three points
    and also discuss its Hodge and \'{e}tale analogues.
    As an application we give a way to erase log poles of
    $p$-adic multiple polylogarithms and introduce
    overconvergent $p$-adic multiple polylogarithms
    which might be $p$-adic multiple analogue of
    Zagier's single-valued complex polylogarithms.

  16. Algebraic cycles and motivic generic iterated integrals Reviewed

    Hidekazu Furusho, Amir Jafari

    Mathematical Research Letters   Vol. 14 ( 6 ) page: 923-942   2007

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

  17. Regularization and generalized double shuffle relations for p-adic multiple zeta values Reviewed

    Hidekazu Furusho, Amir Jafari

    Compositio Math   Vol. 143   page: 1089-1107   2007

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

  18. p-adic multiple zeta values -- a precis. p-adic mathmatical physics Invited Reviewed

    Hidekazu Furusho

    Amer.Inst.Phys   Vol. 826   page: 222-236   2006

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

    This is an expose of the theory of $p$-adic multiple zeta value
    developped by the author.
    This theory is almost parallel to the story of the complex case.
    $p$-adic multiple polylogarithm, which is a $p$-adic function,
    is constructed by Coleman's $p$-adic iterated integration theory.
    $p$-adic multiple zeta value is defined to be its special value at $1$.
    Many nice properties of $p$-adic multiple zeta value is shown.
    $p$-adic KZ equation is also introduced and the $p$-adic Drinfel'd associator
    is constructed from two fundamental solutions of the $p$-adic KZ equation.
    A relation of $p$-adic multiple zeta value with
    the $p$-adic Drinfel'd associator as well as
    its relation with the fundamental group of the projective line minus
    three points is established.

  19. Multiple zeta values and Grothendieck-Teichm\"{u}ller groups Invited Reviewed

    Hidekazu Furusho

    AMS Contemporary Math   Vol. 416   page: 49-82   2006

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

    We get a canonical embedding from the spectrum of the algebra
    of multiple zeta values modulo $\pi^2$ into the graded version of
    the Grothendieck-Teichm\"{u}ller group
    by using relations of the Drinfel'd associator.
    On the other hand, it is known that the
    rational pro-$l$ Galois image algebraic group
    is embedded into the Grothendieck-Teichm\"{u}ller
    pro-algebraic group for each prime $l$.
    Via these embeddings, we get two kinds of relationship
    between the spectrum of the algebra of multiple zeta values and
    the pro-$l$ Galois image algebraic group.

  20. The double shuffle relations for p-adic multiple zeta values Invited Reviewed

    Hidekazu Furusho, Amnon Besser

    AMS Contemporary Math   Vol. 416   page: 9-29   2006

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

    We give a proof of double shuffle relations for $p$-adic multiple zeta values
    by developing higher dimensional version of tangential base points and
    discussing a relationship with two (and one) variable $p$-adic multiple
    polylogarithms.

  21. p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation Reviewed

    Hidekazu Furusho

    Inventiones Mathematicae   Vol. 155 ( 2 ) page: 253-286   2004

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

    Our main aim in this paper is to give a foundation of the theory of
    $p$-adic multiple zeta values.
    We introduce (one variable) $p$-adic multiple polylogarithms
    by Coleman's $p$-adic iterated integration theory.
    We define $p$-adic multiple zeta values to be special values of
    $p$-adic multiple polylogarithms.
    We consider the $p$-adic KZ equation and introduce the
    $p$-adic Drinfel'd associator
    by using certain two fundamental solutions of the $p$-adic KZ equation.
    We show that our $p$-adic multiple polylogarithms appear
    as coefficients of
    a certain fundamental solution of the $p$-adic KZ equation
    and our $p$-adic multiple zeta values appear
    as coefficients of the $p$-adic Drinfel'd associator.
    We show various properties of $p$-adic multiple zeta values,
    which are sometimes analogous to the complex case
    and are sometimes peculiar to the $p$-adic case,
    via the $p$-adic KZ equation.

  22. The multiple zeta value algebra and the stable derivation algebra Reviewed

    Hidekazu Furusho

    Publ. Res. Inst. Math. Sci.   Vol. 39 ( 4 ) page: 695-720   2003

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

  23. Geometric and arithmetic subgroups of the Grothendieck-Teichm\"{u}ller group Reviewed

    Hidekazu Furusho

    Mathematical Research Letters   Vol. 10 ( 1 ) page: 97-108   2003

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

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Books 1

  1. 結び目とGrothendieck-Teichmüller群

    古庄英和, 小谷久寿,新甫洋史( Role: Joint author)

    九州大学マス・フォア・インダストリ研究所  2016.2 

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    Language:Japanese

Presentations 78

  1. Kashiwara-Vergne Lie algebra and Goncharov’s dihedral Lie algebra in mould theory Invited International conference

    Low dimensional topology and number theory XIII  2022.3.17 

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    Event date: 2022.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  2. Associators and an l-adic analogue of Gauss's hypergeometric function Invited International conference

    Hidekazu Furusho

    Johnson homomorphisms and related topics  2022.1.12  Nariya Kawazumi, Gwénaël Massuyeau, Hiroaki Nakamura, Takuya Sakasai, Christine Vespa.

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    Event date: 2022.1

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Zoomによるオンライン開催  

  3. ℓ-進超幾何関数 Invited

    古庄英和

    九大多重ゼータセミナー(拡大版)  2021.11.23  金子昌信

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    Event date: 2021.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:九州大学   Country:Japan  

  4. Artin-Schreier equation and Carlitz multiple polylogarithms Invited International conference

    Hidekazu Furusho

    Japan Europe Number Theory Exchange Seminar  2021.6.1  Henrik Bachmann, Nils Matthes

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    Event date: 2021.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Zoomによるオンライン開催  

  5. ダブルシャッフル群の Betti 対応物 (Benjamin Enriquez 氏 (University of Strasbourg) との共同研究) Invited International coauthorship

    早稲田大学整数論研究集会  2021.3.23  橋本 喜一朗 (早稲田大学),尾崎 学 (早稲田大学),成田 宏秋 (早稲田大学), 坂田 裕 (早稲田大学高等学院),青木 琢哉 (早稲田大学)

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    Event date: 2021.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:早稲田大学数理科学研究所(Zoom によるオンライン開催)   Country:Japan  

  6. Analytic continuation of Carlitz multiple polylogarithms Invited International conference

    Hidekazu Furusho

    NCTS Seminar on Number Theory  2020.12.11  Cheih-yu Chang

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    Event date: 2020.12

    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:NTHU, Online seminar   Country:Taiwan, Province of China  

  7. Four groups related to associators Invited

    Hidekazu Furusho

    2020.2.13 

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    Event date: 2020.2

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

  8. The associator relation and the confluence relations International conference

    Hidekazu Furusho

    Expansions, Lie Algebras, and Invariants,  2019.7.25  Anton Alekseev, Dror Bar-Natan, and Roland van der Veen

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    Event date: 2019.7

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:The Centre de Recherches Mathématiques   Country:Canada  

  9. On a relation of Hirose and Sato Invited International conference

    Hidekazu Furusho

    Multiple zeta values and related topics  2019.6.11  Minoru Hirose (Kyushu University), Masataka Ono (Kyushu University) Tomokazu Onozuka (Kyushu University), Nobuo Sato (Kyushu University)

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    Event date: 2019.6

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Kyushu University   Country:Japan  

  10. Kontsevich's eye, Lie graphs and associators Invited International conference

    Hidekazu Furusho

    Workshop: Johnson homomorphisms and related topics 2019  2019.5.16  Shinobu Hikami, Nariya Kawazumi, Gwénaël Massuyeau, Hiroaki Nakamura, Takuya Sakasai, Christine Vespa

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    Event date: 2019.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Tokyo university   Country:Japan  

  11. 調和余積のBetti対応物とDeligne-寺杣プロジェクト Invited International coauthorship

    関西多重ゼータ研究会  2019.5.11  関西多重ゼータ研究会

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    Event date: 2019.5

    Language:Japanese  

    Venue:大阪体育大学   Country:Japan  

  12. On Relations among Multiple Zeta Values Obtained in Knot Theory Invited International conference

    Hidekazu Furusho

    NCTS Seminar on Number Theory  2019.4.10 

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    Event date: 2019.4

    Language:English   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:National Tsing Hua University,   Country:Taiwan, Province of China  

  13. p-adic multiple L-functions and cyclotomic multiple harmonic values. Invited International conference

    Hidekazu Furusho

    Special Session on Arithmetic and Transcendence of Special Functions and Special Values 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:University of Hawaii at Manoa, Honolulu, USA   Country:United States  

  14. Betti side of the double shuffle theory Invited

    Hidekazu Furusho

    Low dimensional topology and number theory XI 

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    Event date: 2019.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  15. Kontsevich's eye, Lie graphs and associators

    Hidekazu Furusho

    Arithmetic and Algebraic Geometry 2019 

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    Event date: 2019.1

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Tokyo University   Country:Japan  

  16. アイについて... Invited

    古庄 英和

    第26回整数論サマースクール 「多重ゼータ値」 

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    Event date: 2018.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:伊良湖シーパーク&スパ   Country:Japan  

  17. On the coefficients of the Alekseev Torossian associator Invited International conference

    Hidekazu Furusho

    International Workshop on Arithmetic Geometry and Quantum Field Theory 

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    Event date: 2018.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:KIAS, Seoul, South Korea   Country:Korea, Republic of  

  18. On a relation of Hirose and Sato Invited International conference

    Hidekazu Furusho

    Taiwan-Japan Joint Workshop on Multiple Zeta Values 

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    Event date: 2018.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:National Taiwan University   Country:Taiwan, Province of China  

  19. Associators and Kontsevich's eye (1) and (2) Invited

    Hidekazu Furusho

    Algebraic Lie Theory and Representation Theory (ALTReT) 2018 

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    Event date: 2018.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  20. A Betti counterpart of the harmonic coproduct (I) Invited International conference

    Hidekazu Furusho

    Poisson geometry of moduli spaces, associators and quantum field theory 

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    Event date: 2018.4 - 2018.6

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Simons Center for Geometry and Physics, Stony Brook, USA   Country:United States  

  21. A Betti counterpart of the harmonic coproduct (I) Invited International conference

    Hidekazu Furusho

    Periods and Regulators 

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    Event date: 2018.1

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Hausdorff Research Institute for Mathematics, Bonn   Country:France  

  22. p-adic multiple zeta values Invited

    Hidekazu Furusho

    Combinatoire et Theorie de Nombres 

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    Event date: 2017.12

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Institut Camille Jordan, Universite Claude Bernard Lyon 1,   Country:France  

  23. The stabilizer of the harmonic coproduct and Racinet's double shuffle group Invited

    Hidekazu Furusho

    Seminaire tournant de theorie des nombres 

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    Event date: 2017.5

    Language:English   Presentation type:Oral presentation (general)  

    Venue:l'Institut Fourier, Grenoble   Country:France  

  24. Kontsevich's eye and associators I and II Invited

    Hidekazu Furusho

    Geometry of Moduli Space of Low Dimensional Manifolds 

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    Event date: 2016.12

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  25. A stabilizer interpretation of the double shuffle Lie algebra Invited

    Hidekazu Furusho

    Workshop on Grothendieck-Teichmuller Theories 

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    Event date: 2016.7

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Tianjin, China   Country:China  

  26. Complex and p-adic multiple zeta functions International conference

    Hidekazu Furusho

    Low dimensional topology and number theory VIII, 

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    Event date: 2016.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  27. 結び目へのガロア作用

    代数的整数論とその周辺 

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    Event date: 2015.11 - 2015.12

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  28. p-adic multiple L-functions and p-adic multiple polylogarithms International conference

    Hidekazu Furusho

    Zeta Functions of Several Variables and Applications 

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    Event date: 2015.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  29. Desingularization of multiple zeta functions International conference

    Hidekazu Furusho

    GRT, MZVs and associators 

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    Event date: 2015.8

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Switzerland  

  30. 結び目と多重ゼータ値

    関西多重ゼータ研究会 

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    Event date: 2015.5

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  31. p-adic multiple zeta values International conference

    Hidekazu Furusho

    Seminnaire Groupes de Lie et espaces de modules 

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    Event date: 2015.4

    Language:English   Presentation type:Oral presentation (general)  

    Country:Switzerland  

  32. Complex and p-adic multiple zeta functions International conference

    Hidekazu Furusho

    S\'{e}minnaire Quantique 

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    Event date: 2015.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:France  

  33. p-adic multiple zeta values (I)-(IV) International conference

    Hidekazu Furusho

    2015 TIMS Winter School on Number Theory 

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    Event date: 2015.2

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Taiwan, Province of China  

  34. p-adic multiple zeta values International conference

    Hidekazu Furusho

    PMI Number Theory Seminar 

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    Event date: 2015.1

    Language:English   Presentation type:Oral presentation (general)  

    Country:Korea, Republic of  

  35. アソシエーターにまつわるエトセトラ

    東北大学談話会 

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    Event date: 2014.11

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  36. Multiple zeta values and associators International conference

    Hidekazu Furusho

    Tresses et Arithmetique 

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    Event date: 2014.10

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:France  

  37. Four groups related to associators International conference

    Hidekazu Furusho

    Homotopical Algebra, Operads and Grothendieck-Teichmüller groups 

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    Event date: 2014.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:France  

  38. Galois action on knots International conference

    Hidekazu Furusho

    Intelligence of Low-dimensional Topology 

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    Event date: 2014.5

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  39. Various topics around associators

    Hidekazu Furusho

    2014 Mathematical Society of Japan, annual meeting, Award Lecture for 2014 Algebra Prize 

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    Event date: 2014.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  40. Four groups related to associators International conference

    Hidekazu Furusho

    Japanese Turkish Joint Geometry Meeting 

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    Event date: 2013.11

    Language:English   Presentation type:Oral presentation (general)  

    Country:Turkey  

  41. Four groups related to associators International conference

    Hidekazu Furusho

    General Mathematics Seminar 

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    Event date: 2013.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:Luxembourg  

  42. Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions International conference

    Hidekazu Furusho

    Exploratory Workshop, New Approaches To Multiple Zeta Values 

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    Event date: 2013.9 - 2013.10

    Language:English   Presentation type:Oral presentation (general)  

    Country:Spain  

  43. Galois action on knots International conference

    Hidekazu Furusho

    Motivic Galois Groups 

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    Event date: 2013.9

    Language:English   Presentation type:Oral presentation (general)  

    Country:Hungary  

  44. Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions International conference

    Hidekazu Furusho

    Seminar on Algebra, Geometry and Physics 

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    Event date: 2013.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  45. Galois action on knots International conference

    Hidekazu Furusho

    MPI-Oberseminar 

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    Event date: 2013.6

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  46. Galois action on knots International conference

    Hidekazu Furusho

    Higher Structures in Topology and Number Theory 

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    Event date: 2013.4

    Language:English   Presentation type:Oral presentation (general)  

    Country:United Kingdom  

  47. On multiple L-functions and their p-adic analogues International conference

    Hidekazu Furusho

    Grothendieck-Teichm\"{u}ller theory and Multiple Zeta Values 

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    Event date: 2013.4

    Language:English   Presentation type:Oral presentation (general)  

    Country:United Kingdom  

  48. p-adic multiple zeta values International conference

    Hidekazu Furusho

    Introductory Workshop of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads 

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    Event date: 2013.1

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:United Kingdom  

  49. Galois action on knots International conference

    Hidekazu Furusho

    Low-Dimensional Topology and Number Theory 

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    Event date: 2012.8 - 2012.9

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  50. Galois action on knots International conference

    Hidekazu Furusho

    Periods and Motives 

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    Event date: 2012.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Spain  

  51. p-adic multiple polylogarithms International conference

    Hidekazu Furusho

    Polylogarithmes en alg\`{e}bre et en topologie 

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    Event date: 2012.6

    Language:English   Presentation type:Oral presentation (general)  

    Country:France  

  52. On GT-actions International conference

    Hidekazu Furusho

    Colloque à l'occasion des 80 ans de Pierre Cartier 

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    Event date: 2012.6

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:France  

  53. Galois action on knots

    Hidekazu Furusho

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    Event date: 2012.4

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  54. On Galois action on knots International conference

    Hidekazu Furusho

    Low dimensional topology and number theory IV  

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    Event date: 2012.3

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  55. Around associators International conference

    Hidekazu Furusho

    Automorphic forms and Galois representations 

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    Event date: 2011.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:United Kingdom  

  56. Double shuffle for associators International conference

    Hidekazu Furusho

    Mathematische Arbeitstagung 2011 

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    Event date: 2011.6 - 2011.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  57. On Associators International conference

    Hidekazu Furusho

    The motivic fundamental group  

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    Event date: 2011.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Netherlands  

  58. Geometric interpretation of double shuffle relations for multiple L-values

    Hidekazu Furusho

    Various Aspects of Multiple Zeta Values 

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    Event date: 2010.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  59. Motivic Hopf algebra and tree Hopf algebra (joint work with A. Jafari)

    Arithmetic Geometry Workshop 2010 

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    Event date: 2010.8

    Language:Japanese  

  60. Motivic Galois group, Grothendieck-Teichmuller group and double shuffle group

    Des associateurs de Drinfeld \`{a} ceux de Kashiwara-Vergne et lien avec les invariants de noeuds g\'{e}n\'{e}ralis\'{e}s 

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    Event date: 2010.5

    Language:English  

  61. The motivic Galois group, the Grothendieck–Teichm¨uller group and the double shuffle group International conference

    Motives and Homotopy Theory of Schemes 

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    Event date: 2010.5

    Language:English  

  62. The motivic Galois group, the Grothendieck–Teichm¨uller group and the double shuffle group

    Quantum Groups and Quantum Topology 

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    Event date: 2010.4

    Language:English  

  63. Pentagon and hexagon equations

    P-adic Special Functions & Arithmetic Geometry 

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    Event date: 2009.10

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  64. Motivic Galois group,Grothendieck-Teichm¨uller group and double shuffle group

    第54回代数学シンポジウム 

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    Event date: 2009.8

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  65. Double shuffle relation for associators International conference

    Anabelian Geometry 

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    Event date: 2009.8

    Language:English   Presentation type:Oral presentation (invited, special)  

  66. Grothendieck-Teichmuller group International conference

    Séminaire M.A.T. : autour des travaux d'A. Grothendieck 

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    Event date: 2009.1

    Language:English   Presentation type:Oral presentation (invited, special)  

  67. Pentagon and hexagon equations International conference

    Multiple Polylogarithms and Moduli Spaces Day 

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    Event date: 2007.11

    Language:English   Presentation type:Oral presentation (invited, special)  

  68. Pentagon and hexagon equations of GT International conference

    GTEM Workshop Arithmetic of Curves and Covers 

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    Event date: 2007.11

    Language:English  

  69. Pentagon and hexagon equations International conference

    Arithmetic Algebraic Geometry Conference 

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    Event date: 2007.10

    Language:English   Presentation type:Oral presentation (invited, special)  

  70. Double shuffle relations for p-adic multiple zeta values International conference

    Arithmetic Algebraic Geometry 

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    Event date: 2007.9

    Language:English   Presentation type:Oral presentation (general)  

  71. ポリログとフロベニウス

    夏の学校 「多重ゼータ値とモティーフ」 

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    Event date: 2007.7

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  72. p進多重ゼータ値

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    Event date: 2007.7

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  73. Pentagon and Hexagons

    Motives, related topics, applications 

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    Event date: 2007.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  74. p進多重ゼータ値

    名古屋大学多元数理科学研究科談話会 

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    Event date: 2007.2

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  75. p-adic analogue of multiple zeta values International conference

    UK-Japan Winter School, Number Theory, 

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    Event date: 2007.1

    Language:English  

  76. Survey of Drinfel'd's work on GT and its associated quantumn groups

    Arithmetic Galois Theory and Related Moduli Spaces, 

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    Event date: 2006.10

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  77. p-adic multiple zeta values International conference

    Motives and Periods 

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    Event date: 2006.6

    Language:English   Presentation type:Oral presentation (invited, special)  

  78. Algebraic cycles and motivic generic iterated integrals International conference

    Red Lodge Conference 

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    Event date: 2006.4

    Language:English   Presentation type:Oral presentation (invited, special)  

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Research Project for Joint Research, Competitive Funding, etc. 1

  1. ゼータ関数とモティーフの理論の多様性

    2015.9 - 2018.3

    大幸財団第25回自然科学系学術研究助成 

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    Grant type:Competitive

KAKENHI (Grants-in-Aid for Scientific Research) 11

  1. 数論的対象の背後にある幾何学の発見・構築を通じたL関数・ガロア表現の研究

    Grant number:21H00969  2021.4 - 2026.3

    科学研究費助成事業  基盤研究(B)

    安田 正大, 古庄 英和, 山下 剛

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    Authorship:Coinvestigator(s) 

    (A) 法 p 還元の計算を一般の半安定表現に拡張し, 柔軟性の高い整係数 p 進Hodge 理論の構築を目指す. また保型形式の slope を調べる手法を開発し Taylor-Wiles 系の議論を展開する.
    (B) Harder-Raghuram の手法を用いて複シャッフル空間についての代表者による予想を証明する. さらに modular symbol の概念を拡張してモジュラ複体と対応する理論を構築する.
    (C) Hilbert modular 多様体と Kummer 多様体の間の代数的対応を探し出す. さらに Fermat 曲線と関係する場合に, Beilinson 予想の確立を試みる.

  2. Why is the multiple zeta value so ubiquitous?

    Grant number:21H04430  2021.4 - 2026.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A)

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  3. 数論トポロジーと種々のモノドロミー不変量の新たな展開

    Grant number:20H00115  2020.4 - 2025.3

    科学研究費助成事業  基盤研究(A)

    中村 博昭, 角皆 宏, 河澄 響矢, 森下 昌紀, 星 明考, 伊吹山 知義, 古庄 英和, 高橋 浩樹, 小笠原 健

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    Authorship:Coinvestigator(s) 

    本研究では,ガロア・タイヒミュラー群の普遍モノドロミー表現,正則逆ガロア問題に関わるリフトと特殊化,モノドロミー不変量としての種々の数論的関数の醸成,の三つの柱に集約される新しい観点からの方法を導入し,数論トポロジーに対する有機的な構造解析を進める.理論的考察とともに計算機による実例計算とを総合して数論側とトポロジー側との類似性比較に関する詳細な理解を追求するとともに,両者を繋ぐバイパス構築の手がかりに関わる数学的構造の理解の深化を目指す.

  4. モチヴィックガロア群と多重ゼータ値から広がる数学ー整数論からの解放ー

    Grant number:18H01110  2018.4 - 2023.3

    科学研究費助成事業  基盤研究(B)

    古庄 英和, 田坂 浩二, 大野 泰生, 安田 正大

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    Authorship:Principal investigator 

    Grant amount:\12220000 ( Direct Cost: \9400000 、 Indirect Cost:\2820000 )

    論文(2018)ではKontsevichの目上の接続より構成されるAlekseev-Torossian associatorと呼ばれる非可換形式的べき級数の係数をLieグラフのKontsevichの重み形式の反復積分を用いて明示的に書き下す手法を与えた。またStrasbourg大学のBenjamin Enriquez氏と調和余積とdouble shuffle群のBetti対応物について共同研究を行ない共著のプレプリントを書いた。Geneve大学のDavid Jarossay氏と共同研究を行なった。彼との共著のプレプリントでは、円分多重調和値(cyclotomic multiple harmonic values)をp進多重L値の無限和で書けることを示した。プレプリント(2018)では佐藤信夫氏と広瀬稔氏がみつけた多重ゼータ値の合流関係式が結合子関係式が等価になることを示した。
    7月には、外国人研究者を招聘しMini-Workshop「Elliptic multiple zeta values and mixed elliptic motives」を名古屋大学で開催した。
    研究分担者である田坂氏はHecke固有形式を2重Eisenstein級数の線形和に一意的に分解する公式を与えた。またMatthes氏との共同研究ではBrownと Ecalleによる極化複シャッフルリー代数の元の構成方法の比較を行なった。大野氏は、拡張されたArakawa-Kaneko型多重ゼータ関数とその特殊値への従来理論の拡張について研究を進めた。また安田氏は、複シャッフル関係式と整数係数の一般線形群の関係についてのGoncharovの議論の解明を行った。
    合流関係式と結合子関係式が等価なことがわかった。
    Enriquez氏との共同研究に大きな進展があった。
    Jarossay氏との共同研究が稔りプレプリントにまとめ上げた。
    今まで書いたプレプリントを改良し証明の簡易化に努める。また積極的に研究集会・セミナーに出向き、今まで得られた研究の発表を行う。
    昨年度は多重ゼータ値の整数論的側面を重点的に研究をしてきたが、今後は整数論以外の分野とのつながりを視野に入れて研究をしていく。

  5. 多重ゼータ値と多重Eisenstein級数の代数的, 幾何的な研究

    Grant number:16F16021  2016.4 - 2018.3

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    Authorship:Other 

    多重ゼータ値とはここ四半世紀で研究が盛んになった研究対象であり、多重Eisenstein級数とはGangl, Kaneko Zagier (2006)により導入された二重Eisenstein級数を一般化した級数のことである。Bachamann氏は外国人特別研究員として採用されていた1年間、国内のさまざまなセミナー、研究集会に足繁く出向き国内の若手の研究者たちと複数の共同研究を同時進行で行い、この多重ゼータ値と多重Eisenstein級数について精力的に研究を続けてきた。主だった業績として以下の4つが挙げられる:
    1).多重Eisenstein級数の微分に関する研究:多重Eisenstein級数は、depthが1,2,3の場合において多重Eisenstein級数に関連するある種のq級数が微分作用素で閉じていることを計算により示した。
    2).補間Schur多重ゼータ値の研究:多重ゼータ値や多重ゼータスター値を一般化した補間多重ゼータ値という多項式とYoung図形より構成されるSchur多重ゼータ値が知られている。これら二者をつなげる補間Schur多重ゼータ値という多項式を導入し基本的な性質を導いた。
    3).円分的有限多重ゼータ値の研究:円分的有限多重ゼータ値を導入して、これの基本的な代数的構造の基本的性質、特殊値、有限多重ゼータ値のq類似とのつながりについての結果を得た。
    4).Schur多重ゼータ値の和公式の類似の研究:多重ゼータ値や多重ゼータスター値と同様にSchur多重ゼータ値に対しても和公式の類似が成り立つことを示した。
    翌年度、交付申請を辞退するため、記入しない。
    翌年度、交付申請を辞退するため、記入しない。

  6. Motivic Galois group(Fostering Joint International Research)

    Grant number:15KK0159  2016 - 2019

    Fund for the Promotion of Joint International Research (Fostering Joint International Research)

    FURUSHO HIDEKAZU

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    Authorship:Principal investigator 

    Grant amount:\14300000 ( Direct Cost: \11000000 、 Indirect Cost:\3300000 )

    To make clearer a relationship of the motivic Galois group with various fields of mathematics, I conducted researches, particularly on multiple zeta values and associators, and obtained the following results:
    geometric interpretation of the harmonic coproduct of multiple zeta values and constructions of its Betti counterpart, a method to calculate coefficients of the Alekseev-Torossian associator, relationship of associator relations and relations among multiple zeta values obtained in knot theory, relations between p-adic multiple L-functions and cyclotomic multiple harmonic values.

  7. Adelic new methods on arithemetic geometry and their applications to p-adic Hodge theory and multiple L-functions

    Grant number:15H03610  2015.4 - 2020.3

    Yasuda Seidai

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    The research representative and Go Yamashita have constructed families of Wach modules of rank two and applied them to the study of crystalline deformation rings of dimension two. He and Satoshi Kondo have constructed lifts of the zeta elements in motivic cohomologies of Drinfeld modular varieties to their integral models satisfying norm relations, and have constructed a theory of topoi related to monoids. He and Yusuke Sugiyama have introduced a new notion of pseudo-tameness and, by using them, have proved that any algebraic curve over an algebraically closed field has a tame morphism to the projective line. He has introduced the derived double shuffle spaces and has applied them to show a double shuffle analogue of Broadhurst-Kreimer conjecture in depth four. He has found that a suitable quotient of a Hilber modular surface related to the L-function of a certain curve of genus is a Kummer surface.

  8. Research on number theoretic properties of zeta functions in several variables

    Grant number:15K04788  2015.4 - 2018.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    TSUMURA Hirofumi, MATSUMOTO Kohji, KOMORI Yasushi, FURUSHO Hidekazu

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    The main aim in this research is to study what is called the zeta function which plays an important role in number theory and investigate their properties. In particular, we studied zeta functions in several variables mainly from the viewpoint of the analytic aspect. We studied the Witten zeta function in several variables which was defined based on Witten's work, and also the Arakawa-Kaneko zeta function defined by Tsuneo Arakawa and Masanobu Kaneko. Our main result is consider the number theoretic properties of these zeta functions,and consequently we obtained unknown properties of them and gave new results.

  9. Studies on arithmetic invariants arising from mutual interactions between Galois groups and fundamental groupoids

    Grant number:26287006  2014.4 - 2019.3

    Nakamura Hiroaki

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    We found various properties of arithmetic functions arising from Galois representations in arithmetic fundamental groupoids. We investigated behaviors of Galois-polylogarithmic functions and derived a formula that relates their normalized special values on p-adic inertia group with standard p-adic polylogarithmic values. Elaborating the composition law for the Eisenstein invariants of universal monodromy representation in affine elliptic curves, we established a new foundation toward subsequent studies in arithmetic Galois monodromy theory.

  10. A study on algebraic and analytic behavior of multiple zeta-functions and multiple automorphic L-functions

    Grant number:25287002  2013.4 - 2018.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    Matsumoto Kohji, TSUMURA HIROFUMI, KANEKO MASANOBU, OHNO YASUO, SHOJI MAYUMI, FURUSHO HIDEKAZU, YAMASAKI YOSHINORI, UMEGAKI YUMIKO, NAKAMURA TAKASHI

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    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    The present research has dealt with various multiple series, such as multiple zeta-functions of Euler-Zagier type, a more general class of zeta-functions of root systems, and also the same type of series with Fourier coefficients of modular forms on the numerators. The main results obtained in the period of the present research are the structure theory and functional relations for zeta-functions of root systems, or more general multiple zeta-functions associated with Lie groups; evaluation of values of multiple series involving hyperbolic functions; numerical computations on the zeros multiple zeta-functions; the proof of two types of functional equations for double zeta-functions involving Fourier coefficients of modular forms on the numerator; the idea of desingularized multiple zeta-functions and the development of the theory of p-adic multiple zeta-functions.

  11. モチヴィックガロア群-数論幾何学を越えて-

    2012.4 - 2016.3

    科学研究費補助金  若手研究(A)

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    Authorship:Principal investigator 

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Teaching Experience (On-campus) 10

  1. 線形代数学II

    2018

  2. 線形代数学I

    2018

  3. 代数学要論I

    2016

  4. 線形代数学II

    2016

  5. 線形代数学I

    2016

  6. 線形代数学II

    2015

  7. 線形代数学I

    2015

  8. 代数学要論I

    2015

  9. 数理科学展望III /数理科学展望I(英語)

    2012

  10. 代数学特論I

    2010

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Teaching Experience (Off-campus) 3

  1. 数学特別講義H

    2014.4 - 2015.3 Tohoku University)

  2. 数理科学特別講義VII

    2012.4 - 2013.3 Kyushu University)

  3. 数理科学特別講義Ⅷ

    2011.4 - 2012.3 The University of Tokyo)

 

Social Contribution 3

  1. 出前講義、向陽高校

    Role(s):Lecturer

    2020.11

  2. NHKカルチャー, 数学散策

    Role(s):Lecturer

    NHKカルチャー  NHKカルチャー, 数学散策  2019.2

  3. NHKカルチャー, 数学散策

    Role(s):Lecturer

    NHKカルチャー  NHKカルチャー, 数学散策  NHKカルチャー  2018.7

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    Audience: General