• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

motivic Galois group

Research Project

Project/Area Number 24684001
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypePartial Multi-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, 准教授 (60377976)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥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.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • Research Products

    (35 results)

All 2016 2015 2014 2013 2012

All Journal Article (4 results) (of which Peer Reviewed: 3 results,  Open Access: 2 results) Presentation (30 results) (of which Int'l Joint Research: 3 results,  Invited: 24 results) Book (1 results)

  • [Journal Article] $p$-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas2015

    • Author(s)
      Hidekazu Furusho, Kenichi Bannai and Shinichi Kobayashi
    • Journal Title

      Nagoya Math. J

      Volume: 219 Pages: 269-302

    • DOI

      10.1215/00277630-2891995

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Around associators2014

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      London Math.Soc. Lecture Note Ser

      Volume: 415 Pages: 105-117

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On profinite knots and Galois action there2014

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      数理解析研究所講究録

      Volume: 1911 Pages: 76-85

    • Related Report
      2014 Annual Research Report
    • Open Access
  • [Journal Article] Geometric interpretation of double shuffle relation for multiple L-values2012

    • Author(s)
      Hidekazu Furusho
    • Journal Title

      Advanced Studies in Pure Math 63

      Volume: 63 Pages: 163-187

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Complex and p-adic multiple zeta functions2016

    • 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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] p-adic multiple L-functions and p-adic multiple polylogarithms2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Zeta Functions of Several Variables and Applications
    • Place of Presentation
      Nagoya university
    • Year and Date
      2015-09-09
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Desingularization of multiple zeta functions2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      GRT, MZVs and associators
    • Place of Presentation
      Les Diables, Switzerland
    • Year and Date
      2015-08-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] p-adic multiple zeta values2015

    • 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
    • Related Report
      2015 Annual Research Report
    • 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
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Complex and p-adic multiple zeta functions2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      S\'{e}minnaire Quantique
    • Place of Presentation
      IRMA, Strasbourg
    • Year and Date
      2015-03-30
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] p-adic multiple zeta values2015

    • Author(s)
      Hidekazu Furusho
    • Organizer
      PMI Number Theory Seminar
    • Place of Presentation
      Department of Mathematics, POSTECH
    • Year and Date
      2015-01-05
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Four groups related to associators2014

    • 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
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2014

    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] p-adic multiple zeta values2013

    • 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
    • Related Report
      2012 Annual Research Report
  • [Presentation] On multiple L-functions and their p-adic analogues2013

    • 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
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Higher Structures in Topology and Number Theory
    • Place of Presentation
      Clay Mathematics Institute workshop, Mathematical Institute
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      MPI-Oberseminar
    • Place of Presentation
      Max Planck Institute for Mathematics
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Seminar on Algebra, Geometry and Physics
    • Place of Presentation
      Max Planck Institute for Mathematics
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Motivic Galois Groups
    • Place of Presentation
      Alfred Renyi Institute of Mathematics
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Exploratory Workshop, New Approaches To Multiple Zeta Values
    • Place of Presentation
      Instituto de Ciencias Matematicas Universidad Autonoma de Madrid,
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] p-adic multiple zeta values2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Joint UAM-ICMAT Seminar, Algebra and Combinatorics
    • Place of Presentation
      Instituto de Ciencias Matematicas Universidad Autonoma de Madrid,
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Four groups related to associators2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      General Mathematics Seminar
    • Place of Presentation
      University of Luxembourg
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Four groups related to associators2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Japanese Turkish Joint Geometry Meeting
    • Place of Presentation
      Galatasaray University
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Quatre groupes reliés aux associateurs2013

    • Author(s)
      Hidekazu Furusho
    • Organizer
      S\'{e}minnaire d'alg\`{e}bre
    • Place of Presentation
      Institut Camille Jordan, Universit\'{e} Claude Bernard Lyon 1
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Galois action on knots2012

    • Author(s)
      Hidekazu Furusho
    • Organizer
      Low-Dimensional Topology and Number Theory
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach, Germany
    • Year and Date
      2012-08-30
    • Related Report
      2012 Annual Research Report
  • [Presentation] Galois action on knots2012

    • 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
    • Related Report
      2012 Annual Research Report
  • [Presentation] p-adic multiple polylogarithms2012

    • 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
    • Related Report
      2012 Annual Research Report
  • [Presentation] On GT-actions2012

    • 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
    • Related Report
      2012 Annual Research Report
  • [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
    • Related Report
      2015 Annual Research Report

URL: 

Published: 2012-04-24   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi