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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

Research Project

Project/Area Number 18H01110
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionNagoya University

Principal Investigator

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

Co-Investigator(Kenkyū-buntansha) 田坂 浩二  愛知県立大学, 情報科学部, 准教授 (30780762)
大野 泰生  東北大学, 理学研究科, 教授 (70330230)
安田 正大  北海道大学, 理学研究院, 教授 (90346065)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Granted (Fiscal Year 2022)
Budget Amount *help
¥12,220,000 (Direct Cost: ¥9,400,000、Indirect Cost: ¥2,820,000)
Fiscal Year 2022: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2021: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2020: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2018: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Keywords多重ゼータ値 / モチヴィックガロア群 / Teichmuller-Legoの哲学 / double shuffle関係式 / associators / モチッヴィクガロア群 / Kashiwara-Vergne予想 / ダブルシャッフル関係式
Outline of Annual Research Achievements

7月にカナダのCRM研究所のプログラム「Expansions, Lie Algebras, and Invariants」に参加し、Enriquez氏と共同研究を続けRacinetが2002年に提出したdouble shuffle群のBetti側に対応する群の正体を明らかにした。1年前に発見した調和余積のBetti対応物を用いてde Rham側と同様な簡明な表示を与えることができた。この結果をpreprintにまとめ発表した。今までの「Double shufle関係式のBetti側の理論」に関する一連の共著論文(3本)をようやく書き終えたことになるが、読み直してみると複雑に入り組んでいた議論のいくつかが簡略化できそうなことに気づいたので、引き続き議論の整備をし改訂を行っていくことにした。
11月には「多重ゼータ値の諸相」の国際集会を数理解析研究所で主催した。多重ゼータ値を研究する研究者を各方面から招聘した。Enriquez氏もこの集会に招聘し共同研究のサーベイ発表してもらった。
研究分担者の田坂氏は楕円モジュラー形式の新形式を二重Eisenstein級数の基底で表示する明示公式を得た。大野氏はArakawa-Kaneko多重ゼータ関数の特殊値に関する和公式を構成した。安田氏はグラフの圏を適当に局所化することによって得られる対称性の観点から複シャッフル空間に関する Goncharovの仕事の再解釈を行なった。

Current Status of Research Progress
Current Status of Research Progress

3: Progress in research has been slightly delayed.

Reason

共著の改訂に結構時間が取られた。春休みに予定していたフランス出張が新型コロナ感染症の流行のため、叶わず直接対面で討論することができなくて不自由した。

Strategy for Future Research Activity

当面コロナ禍のためにオンラインが主になると思うが研究集会・セミナーに参加し、行った共同研究及び新しく得られた研究結果の発表を行う。また今までの研究とは違った方向になるが、近年正標数の整数論の研究者達との交流をするようになってきたのでこの方面の研究にも参画していく。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(54 results)

All 2020 2019 2018 Other

All Int'l Joint Research (6 results) Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (39 results) (of which Int'l Joint Research: 17 results,  Invited: 29 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Strasbourg大学(フランス)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] ナイメーヘン・ラドバウド大学(オランダ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 上海大学(中国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 国立台湾大学/国立精華大学(その他の国・地域)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Strasbourg大学(フランス)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Geneve大学(スイス)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Hecke eigenform and double Eisenstein series2020

    • Author(s)
      KOJI TASAKA
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 148 Pages: 53-58

    • DOI

      10.1090/proc/14680

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Interpolation between Arakawa-Kaneko and Kaneko-Tsumura multiple zeta functions2020

    • Author(s)
      Yasuo Ohno and Hirotsugu Wayama
    • Journal Title

      Commentarii Mathematici Univ. St. Pauli

      Volume: 68 Pages: 83-91

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recurrence formulas for poly-Bernoulli polynomials2020

    • Author(s)
      Yasuo Ohno and Yoshitaka Sasaki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 84 Pages: 353-360

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Interpolated multiple zeta functions of Arakawa-Kaneko type2020

    • Author(s)
      Yasuo Ohno and Hirotsugu Wayama
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 84 Pages: 361-366

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Ecalle’s and Brown’s polar solutions to the double shuffle equations modulo products2019

    • Author(s)
      Nils Matthes, Koji Tasaka
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 印刷中

    • NAID

      130007871386

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Hecke eigenform and double Eisenstein series2019

    • Author(s)
      Koji Tasaka
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [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 Annual Research 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 Pages: 6870-6907

    • DOI

      10.1093/imrn/rnx084

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Four groups related to associators2020

    • Author(s)
      Hidekazu Furusho
    • Organizer
      第 15 回代数・解析・幾何学セミナー
    • 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 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
      第45回関西多重ゼータ研究会
    • Related Report
      2019 Annual Research Report
    • 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
    • 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] 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] Finite and symmetric colored multiple zeta values2019

    • Author(s)
      田坂浩二
    • Organizer
      多重ゼータ値の諸相
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On Arakawa-Kaneko type zeta functions2019

    • Author(s)
      Yasuo Ohno
    • Organizer
      Multiple zeta values and related topics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 多重ゼータ値の母関数について2019

    • Author(s)
      大野泰生
    • Organizer
      RIMS共同研究(公開型)可積分系数理の深化と展開
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Relations among multiple zeta values and Arakawa-Kaneko zeta functions2019

    • Author(s)
      Yasuo Ohno
    • Organizer
      Frontiers in Mathematical Science Research Workshop ---Joint workshop with Tohoku University and Shanghai University
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Depth graded structures2019

    • Author(s)
      Seidai Yasuda
    • Organizer
      Multiple zeta values and related topics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / 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 Annual Research 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 Annual Research 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 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On special values of the multiple zeta functions of Arakawa-Kaneko type2019

    • Author(s)
      Yasuo Ohno
    • Organizer
      RIKEN Number Theory Seminar
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Hecke固有形式と2重Eisenstein級数2019

    • Author(s)
      田坂浩二
    • Organizer
      2019年日本数学会年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Period polynomial relations for double zeta values2019

    • Author(s)
      田坂浩二
    • Organizer
      第12回ゼータ若手研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] ヘッケ固有形式と2重アイゼンシュタイン級数2019

    • Author(s)
      田坂浩二
    • Organizer
      第12回東京電機大学講演会
    • Related Report
      2018 Annual Research Report
  • [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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research 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 Annual Research Report
    • Invited
  • [Presentation] Interpolation of Arakawa-Kaneko and Kaneko-Tsumura multiple zeta functions2018

    • Author(s)
      Yasuo Ohno
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Bernoulli多項式のアルゴリズムと多重ゼータ値2018

    • Author(s)
      大野泰生
    • Organizer
      2018大分鹿児島整数論研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 2色半順序集合と荒川-金子型ゼータ関数の特殊値2018

    • Author(s)
      大野泰生・川﨑菜穂
    • Organizer
      2018年度 応用数学合同研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Modular complexes and dimensions of derived double shuffle modules2018

    • Author(s)
      安田 正大
    • Organizer
      第17回北陸数論研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Derived double shuffle Lie algebra and the Steinberg modules2018

    • Author(s)
      Seidai Yasuda
    • Organizer
      NTCS Seminar on Numner Theory
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 「p進多重ゼータ値」から「有限多重ゼータ値」へ2018

    • Author(s)
      安田 正大
    • Organizer
      第26回整数論サマースクール「多重ゼータ値」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] レベル付き2重ゼータ値のモジュラー関係式について2018

    • Author(s)
      田坂浩二
    • Organizer
      関西多重ゼータ研究会
    • Related Report
      2018 Annual Research Report
  • [Presentation] The Gangl-Kaneko-Zagier relation and the Ihara-Takao relation2018

    • Author(s)
      田坂浩二
    • Organizer
      九大多重ゼータセミナー
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Broadhurst-Kreimer予想について2018

    • Author(s)
      田坂浩二
    • Organizer
      第26回整数論サマースクール
    • Related Report
      2018 Annual Research Report
  • [Presentation] Multiple zeta values and modular forms2018

    • Author(s)
      田坂浩二
    • Organizer
      Taiwan-Japan Joint Workshop on Multiple Zeta Values
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Anatomical decomposition of zeta elements2018

    • Author(s)
      田坂浩二
    • Organizer
      慶應義塾大学代数セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] 4点抜き射影直線上の反復積分の和公式2018

    • Author(s)
      田坂浩二
    • Organizer
      名古屋解析数論セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] 多重ゼータ値と複シャッフルリー代数の極化2018

    • Author(s)
      田坂浩二
    • Organizer
      九大多重ゼータセミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] 様々な多重ゼータ値の統一理論に向けて2018

    • Author(s)
      田坂浩二
    • Organizer
      愛知数論セミナー
    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Various aspects of multiple zeta values2019

    • Related Report
      2019 Annual Research Report

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Published: 2018-04-23   Modified: 2022-07-01  

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