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Motivic Galois group(Fostering Joint International Research)

Research Project

Project/Area Number 15KK0159
Research Category

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

Allocation TypeMulti-year Fund
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

FURUSHO HIDEKAZU  名古屋大学, 多元数理科学研究科, 教授 (60377976)

Project Period (FY) 2016 – 2019
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥14,300,000 (Direct Cost: ¥11,000,000、Indirect Cost: ¥3,300,000)
Keywordsモチヴィックガロア群 / 多重ゼータ値 / associators / double shuffle関係式 / モチッヴィクガロア群 / associator / Teichmuller-Legoの哲学 / Double shuffle関係式 / モチヴィック基本群 / Kashiwara-Vergne予想
Outline of Final Research Achievements

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.

Academic Significance and Societal Importance of the Research Achievements

モチヴィックガロア群の研究は数論幾何学のみならず、様々な分野と関連していることが概念的に指摘されている。多重ゼータ値等の非常に具体的な対象を通じて研究することで、この繋がりはより直接的になり、またより明らかなものになる。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (39 results)

All 2020 2019 2018 2017 2016

All Int'l Joint Research (1 results) Journal Article (11 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 11 results,  Acknowledgement Compliant: 1 results) Presentation (27 results) (of which Int'l Joint Research: 11 results,  Invited: 22 results)

  • [Int'l Joint Research] 高等数学研究所(IRMA)(フランス)2017

    • Related Report
      2019 Annual Research Report
  • [Journal Article] On relations among multiple zeta values obtained in knot theory2020

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      the Advanced Lectures in Mathematics (ALM) book series

      Volume: 印刷中

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Galois action on knots II: proalgebraic string links and knots2020

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      Periods in Quantum Field Theory and Arithmetic", Springer Proceedings in Mathematics & Statistics

      Volume: 314 Pages: 541-591

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] p-adic multiple L-functions and cyclotomic multiple harmonic values2019

    • Author(s)
      Furusho Hidekazu、Jarossay David
    • Journal Title

      International Journal of Number Theory

      Volume: 16 Issue: 02 Pages: 361-375

    • DOI

      10.1142/s1793042120500190

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the coefficients of the Alekseev-Torossian associator2018

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      Journal of Algebra

      Volume: 506 Pages: 364-378

    • DOI

      10.1016/j.jalgebra.2018.03.023

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Stabilizer Interpretation of Double Shuffle Lie Algebras2018

    • Author(s)
      Hidekazu Furusho, Benjamin Enriquez
    • Journal Title

      International Mathematics Research Notices

      Volume: 22 Issue: 22 Pages: 6870-6907

    • DOI

      10.1093/imrn/rnx084

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the coefficients of the Alekseev Torossian associator2018

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      Journal of Algebra

      Volume: 印刷中

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] On relations among multiple zeta values obtained in knot theory2018

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      proceedings of "Teichmuller theory and its impact"

      Volume: 印刷中

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Galois action on knots II: proalgebraic string links and knots2018

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      to appear in "Periods in Quantum Field Theory and Arithmetic"

      Volume: 印刷中

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Galois action on knots I: Action of the absolute Galois group2017

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      Quantum Topology

      Volume: 8 Pages: 295-360

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers2017

    • Author(s)
      Hidekazu Furusho, Yasushi Komori, Kohji Matsumoto, Hirofumi Tsumura
    • Journal Title

      RIMS Kokyuroku bessatsu

      Volume: B6 Pages: 26-66

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A stabilizer interpretation of double shuffle Lie algebras2017

    • Author(s)
      Benjamin Enriquez, Hidekazu Furusho
    • Journal Title

      IMRN

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Four groups related to associators2020

    • Author(s)
      Hidekazu Furusho
    • Organizer
      The 15th Kagoshima Algebra-Analysis-Geometry Seminar
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] The associator relation and the confluence relations2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Expansions, Lie Algebras, and Invariants
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On a relation of Hirose and Sato2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Workshop: Multiple zeta values and related topics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Kontsevich's eye, Lie graphs and associators2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Workshop: Johnson homomorphisms and related topics 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] $p$-adic multiple zeta values2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Algebra, Combination and Number Theory seminar
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] 調和余積のBetti対応物とDeligne-寺杣プロジェクト2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      関西多重ゼータ研究会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On relations among multiple zeta values obtained in knot theory2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      NCTS Seminar on Number Theory
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] $p$-adic multiple $L$-functions and cyclotomic multiple harmonic values2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Spring Central and Western Joint Sectional Meeting of the AMS, Special Session on Arithmetic and Transcendence of Special Functions and Special Values
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Betti side of the double shuffle theory2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Low dimensional topology and number theory XI
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Kontsevich's eye, Lie graphs and associators2019

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Arithmetic and Algebraic Geometry 2019
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the coefficients of the Alekseev Torossian associator2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      International Workshop on Arithmetic Geometry and Quantum Field Theory
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On a relation of Hirose and Sato2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A Betti counterpart of the harmonic coproduct (I)2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Poisson geometry of moduli spaces, associators and quantum field theory
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On a relation of Hirose and Sato2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      解析数論セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] アイについて...2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      第26回整数論サマースクール
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Associators and Kontsevich's eye 1 & 22018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Algebraic Lie Theory and Representation Theory (ALTReT) 2018
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] A Betti counterpart of the harmonic coproduct (I)2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminnaire Quantique
    • Related Report
      2017 Research-status Report
  • [Presentation] A Betti counterpart of the harmonic coproduct (I)2018

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Periods and Regulators
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] p-adic multiple zeta values2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Combinatoire et Theorie de Nombres
    • Related Report
      2017 Research-status Report
  • [Presentation] A Betti counterpart of the harmonic coproduct2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminnaire de Geometrie et Quantification
    • Related Report
      2017 Research-status Report
  • [Presentation] On coefficients of Alekseev-Torossian associator2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminnaire et Groupe de travail de GAAO
    • Related Report
      2017 Research-status Report
  • [Presentation] The stabilizer of the harmonic coproduct and Racinet's double shuffle group2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminaire tournant de theorie des nombres
    • Related Report
      2017 Research-status Report
  • [Presentation] A stabilizer interpretation de double shuffle Lie algebras2017

    • Author(s)
      Benjamin Enriquez
    • Organizer
      Hot Topics: Galois Theory of Periods and Applications
    • Place of Presentation
      MSRI
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On coefficients of Alekseev-Torossian associator2017

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminnaire Quantique
    • Place of Presentation
      Strasbourg大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Une interpretation des algebres de double battage en termes de stabilisateurs2017

    • Author(s)
      Benjamin Enriquez
    • Organizer
      Seminnaire Quantique
    • Place of Presentation
      Strasbourg大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Kontsevich's eye and associators2016

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Geometry of Moduli Space of Low Dimensional Manifolds
    • Place of Presentation
      数理解析研究所
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Une interpretation des algebres de double battage en termes de stabilisateurs2016

    • Author(s)
      Benjamin Enriquez
    • Organizer
      Seminaire et Geometrie et quantification
    • Place of Presentation
      Institut Henri Poincare
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2016-10-04   Modified: 2021-02-19  

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