motivic Galois group

• Project/Area Number: 24684001
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: Furusho Hidekazu 名古屋大学, 多元数理科学研究科, 准教授 (60377976)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥10,660,000 (Direct Cost: ¥8,200,000、Indirect Cost: ¥2,460,000); Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2013: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
• Keywords: モチヴィック基本群 / Teichmuller-Legoの哲学 / 多重ゼータ値 / Kashiwara-Vergne予想 / 結び目理論 / モチヴィックガロア群 / 多重ゼータ / 結び目 / 基本群 / アソシエーター

Outline of Final Research Achievements

This research was mainly focused on the study of associators and multiple zeta values which are essential in the study of motivic Galois group of unramified mixed Tate motives:1. We pursued various topics related to associators, in particular a relationship caused by associators between knot theory and number theory. We revealed a hidden arithmetic structure of the space of knots by constructing an action of the absolute Galois group of the rational number field. 2. In our joint work with analytic number theorists, we produced a method of desingularization of complex multiple zeta functions and also a construction of p-adic multiple zeta functions.

Research Products

• [Journal Article] $p$-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas (2015)
  • Author(s): Hidekazu Furusho, Kenichi Bannai and Shinichi Kobayashi
  • Journal Title: Nagoya Math. J Volume: 219 Pages: 269-302
  • DOI: 10.1215/00277630-2891995
  • Peer Reviewed / Open Access
• [Journal Article] Around associators (2014)
  • Author(s): Hidekazu Furusho
  • Journal Title: London Math.Soc. Lecture Note Ser Volume: 415 Pages: 105-117
  • Peer Reviewed
• [Journal Article] On profinite knots and Galois action there (2014)
  • Author(s): Hidekazu Furusho
  • Journal Title: 数理解析研究所講究録 Volume: 1911 Pages: 76-85
  • Open Access
• [Journal Article] Geometric interpretation of double shuffle relation for multiple L-values (2012)
  • Author(s): Hidekazu Furusho
  • Journal Title: Advanced Studies in Pure Math 63 Volume: 63 Pages: 163-187
  • Peer Reviewed
• [Presentation] Complex and p-adic multiple zeta functions (2016)
  • Author(s): Hidekazu Furusho
  • Organizer: Low dimensional topology and number theory VIII
  • Place of Presentation: IMAQ Seminar Room, Innovation Plaza
  • Year and Date: 2016-03-22
  • Int'l Joint Research / Invited
• [Presentation] 結び目へのガロア作用 (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: 代数的整数論とその周辺
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2015-11-30
  • Invited
• [Presentation] p-adic multiple L-functions and p-adic multiple polylogarithms (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: Zeta Functions of Several Variables and Applications
  • Place of Presentation: Nagoya university
  • Year and Date: 2015-09-09
  • Int'l Joint Research / Invited
• [Presentation] Desingularization of multiple zeta functions (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: GRT, MZVs and associators
  • Place of Presentation: Les Diables, Switzerland
  • Year and Date: 2015-08-20
  • Int'l Joint Research
• [Presentation] p-adic multiple zeta values (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: Seminnaire Groupes de Lie et espaces de modules
  • Place of Presentation: Universite de Geneve
  • Year and Date: 2015-08-02
  • Invited
• [Presentation] 結び目と多重ゼータ値 (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: 関西多重ゼータ研究会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-05-16
  • Invited
• [Presentation] Complex and p-adic multiple zeta functions (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: S\'{e}minnaire Quantique
  • Place of Presentation: IRMA, Strasbourg
  • Year and Date: 2015-03-30
  • Invited
• [Presentation] p-adic multiple zeta values (I)-(IV) (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: 2015 TIMS Winter School on Number Theory,
  • Place of Presentation: Taida Institute for Mathematical Science, National Taiwan University
  • Year and Date: 2015-02-09 – 2015-02-12
  • Invited
• [Presentation] p-adic multiple zeta values (2015)
  • Author(s): Hidekazu Furusho
  • Organizer: PMI Number Theory Seminar
  • Place of Presentation: Department of Mathematics, POSTECH
  • Year and Date: 2015-01-05
  • Invited
• [Presentation] アソシエーターにまつわるエトセトラ (2014)
  • Author(s): Hidekazu Furusho
  • Organizer: 東北大学談話会
  • Place of Presentation: 東北大学理学部数学科
  • Year and Date: 2014-11-17
  • Invited
• [Presentation] Multiple zeta values and associators (I)-(III) (2014)
  • Author(s): Hidekazu Furusho
  • Organizer: Tresses et Arithmetique
  • Place of Presentation: Centre International de Rencontres Math\'{e}matiques, Luminy
  • Year and Date: 2014-10-13 – 2014-10-16
  • Invited
• [Presentation] Four groups related to associators (2014)
  • Author(s): Hidekazu Furusho
  • Organizer: Homotopical Algebra, Operads and Grothendieck-Teichm\"{u}ller groups,
  • Place of Presentation: Universit\'{e} Nice Sophia Antipolis, Laboratoire J.A. Dieudonn\'{e}, Nice
  • Year and Date: 2014-09-11
  • Invited
• [Presentation] Galois action on knots (2014)
  • Author(s): Hidekazu Furusho
  • Organizer: Intelligence of Low-dimensional Topology
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2014-05-22
  • Invited
• [Presentation] 結び目と多重ゼータ値 (2014)
  • Author(s): Hidekazu furusho
  • Organizer: 解析数論セミナー
  • Place of Presentation: 名古屋大学多元数理科学研究科
  • Year and Date: 2014-04-08
  • Invited
• [Presentation] アソシエーターとその周辺 (2014)
  • Author(s): Hidekazu Furusho
  • Organizer: 日本数学会
  • Place of Presentation: 学習院大学
  • Invited
• [Presentation] p-adic multiple zeta values (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Introductory Workshop of Grothendieck-T eichmiiller Groups, Deformation and Operads
  • Place of Presentation: Isaac Newton Institute for Mathematical Sciences, UK
  • Year and Date: 2013-01-09
• [Presentation] On multiple L-functions and their p-adic analogues (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Grothendieck-Teichm\"{u}ller theory and Multiple Zeta Values of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads
  • Place of Presentation: Isaac Newton Institute for Mathematical Sciences
  • Invited
• [Presentation] Galois action on knots (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Higher Structures in Topology and Number Theory
  • Place of Presentation: Clay Mathematics Institute workshop, Mathematical Institute
  • Invited
• [Presentation] Galois action on knots (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: MPI-Oberseminar
  • Place of Presentation: Max Planck Institute for Mathematics
  • Invited
• [Presentation] Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Seminar on Algebra, Geometry and Physics
  • Place of Presentation: Max Planck Institute for Mathematics
  • Invited
• [Presentation] Galois action on knots (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Motivic Galois Groups
  • Place of Presentation: Alfred Renyi Institute of Mathematics
  • Invited
• [Presentation] Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Exploratory Workshop, New Approaches To Multiple Zeta Values
  • Place of Presentation: Instituto de Ciencias Matematicas Universidad Autonoma de Madrid,
  • Invited
• [Presentation] p-adic multiple zeta values (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Joint UAM-ICMAT Seminar, Algebra and Combinatorics
  • Place of Presentation: Instituto de Ciencias Matematicas Universidad Autonoma de Madrid,
  • Invited
• [Presentation] Four groups related to associators (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: General Mathematics Seminar
  • Place of Presentation: University of Luxembourg
  • Invited
• [Presentation] Four groups related to associators (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: Japanese Turkish Joint Geometry Meeting
  • Place of Presentation: Galatasaray University
  • Invited
• [Presentation] Quatre groupes reliés aux associateurs (2013)
  • Author(s): Hidekazu Furusho
  • Organizer: S\'{e}minnaire d'alg\`{e}bre
  • Place of Presentation: Institut Camille Jordan, Universit\'{e} Claude Bernard Lyon 1
  • Invited
• [Presentation] Galois action on knots (2012)
  • Author(s): Hidekazu Furusho
  • Organizer: Low-Dimensional Topology and Number Theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
  • Year and Date: 2012-08-30
• [Presentation] Galois action on knots (2012)
  • Author(s): Hidekazu Furusho
  • Organizer: Periods and Motives, A Modern Perspective on Renormalization
  • Place of Presentation: Institute de Ciencias Matematicas Universidad Autonoma de Madrid, Spain
  • Year and Date: 2012-07-05
• [Presentation] p-adic multiple polylogarithms (2012)
  • Author(s): Hidekazu Furusho
  • Organizer: Polylogarithmes en algebre et en topologie
  • Place of Presentation: Laboratoire J A. Dieudonne, Nice, France
  • Year and Date: 2012-06-16
• [Presentation] On GT-actions (2012)
  • Author(s): Hidekazu Furusho
  • Organizer: Colloque a l'occasion des 80 ans de Pierre Cartier, Dialogues autour de l'alg&bre, la geomtrie et les fonctions multizetas
  • Place of Presentation: IHES, France
  • Year and Date: 2012-06-11
• [Book] 結び目とGrothendieck-Teichmuller群 (2016)
  • Author(s): 古庄英和 著 ; 小谷久寿, 新甫洋史記述.
  • Total Pages: 111
  • Publisher: 九州大学マス・フォア・インダストリ研究所