Welcome to Hidekazu Furusho's Home Page.

Research Interests

  • periods: (p-adic) multiple zeta value, (p-adic) (multiple) polylogarithm, (p-adic) iterated integration.
  • analytic aspect of multiple zeta functions.
  • mixed Tate motive, motivic Galois group, motivic fundamental group.
  • (p-adic) Knizhnik-Zamolodchikov equation, Yang-Baxter equation, (braided) monoidal (tensor) category.
  • associators, Grothendieck-Teichmuller group, Lego-Teichmuller philosophy.
  • (quasi-triangular) (quasi-Hopf) quantum group, deformation quantization, Kashiwara-Vergne conjecture.
  • quantum topology: Kontsevich (knot) invariant, quantum (knot) invariant...

    Research Experience

  • April 2013-March 2014, Member at Max Planck Institute for Mathematics, Bonn, Germany.
  • January 2013-April 2013, Member at Isaac Newton Institute for Mathematical Sciences, Cambridge, UK.
  • April 2010-, Associate Professor at Nagoya University, Nagoya, Japan.
  • October 2007-September 2009, JSPS Postdoctoral Fellowships for Research Abroad in \'{E}cole Normale Sup\'{e}rieure, Paris, France.
  • September 2004-August 2005, Member at Institute for Advanced Study, Princeton, USA.
  • February 2004- March 2010, Assistant Professor (permanent one) at Nagoya University, Nagoya, Japan.
  • September 2003. Ph.D from RIMS, Kyoto, Japan.

    Awards

  • March. 2014, Algebra Prize of Math. Soc. Japan.
  • February. 2007, Inoue Research Award for Young Scientists.
  • September. 2004, Takebe Prize of Math. Soc. Japan.

    Paper

  • On relations among multiple zeta values obtained in knot theory.
  • Galois action on knots II: proalgebraic string links and knots.
  • Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type, (with Y.Komori, K.Matsumoto and H.Tsumura).
  • Fundamentals of p-adic multiple L-functions and evaluation of their special values (with Y.Komori, K.Matsumoto and H.Tsumura).
  • Desingularization of complex multiple zeta-functions (with Y.Komori, K.Matsumoto and H.Tsumura).
  • Galois action on knots I: Action of the absolute Galois group.
  • p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas, (with S.Kobayashi and K.Bannai.), to appear in Nagoya Mathematical Journal.
  • Around associators, Automorphic forms and Galois representations, 2, 105-117, London Math.Soc. Lecture Note Ser. 415 (2014), Cambridge Univ. Press, Cambridge.
  • Geometric interpretation of double shuffle relation for multiple L-values, Galois-Teichm\"{u}ller theory and Arithmetic Geometry, Advanced Studies in Pure Math 63 (2012), 163-187.
  • Mixed Pentagon, octagon and Broadhurst duality equation, (with B.Enriquez), Journal of Pure and Applied Algebra, Vol 216, Issue 4, (2012), 982-995.
  • Double shuffle relation for associators, Annals of Mathematics, Vol. 174 (2011), No. 1, 341-360.
  • Pentagon and hexagon equations, Annals of Mathematics, Vol. 171 (2010), No. 1, 545-556.
  • Algebraic cycles and motivic generic iterated integrals (with A.Jafari), Mathematical Research Letters,(2007) Vol 14, No.6, 923-942.
  • Regularization and generalized double shuffle relations for p-adic multiple zeta values, (with A.Jafari), Compositio Math. Vol 143, (2007), 1089-1107.
  • p-adic multiple zeta values II -- tannakian interpretations, Amer.J.Math, Vol 129, No 4, (2007),1105-1144.
  • p-adic multiple zeta values -- a pr\'{e}cis. p-adic mathematical physics, 2nd international conference, Amer.Inst.Phys, (2006), Conf. Proc. Vol 826, 222-236.
  • The double shuffle relations for p-adic multiple zeta values, (with A.Besser). AMS Contemporary Math, Vol 416, (2006), 9-29.
  • Multiple zeta values and Grothendieck-Teichm\"{u}ller groups, AMS Contemporary Math, Vol 416, (2006), 49-82.
  • p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation, Inventiones Mathematicae, Volume 155, Number 2, 253-286, (2004).
  • Geometric and arithmetic subgroups of the Grothendieck-Teichm\"{u}ller group, Mathematical Research Letters, (2003) Volume 10, Number 1, 97-108.
  • The multiple zeta value algebra and the stable derivation algebra, Publ. Res. Inst. Math. Sci. Vol 39. no 4. (2003). 695-720.

    Research Surveys

  • On profinite knots and Galois action there, RIMS-kokyuroku No. 1911, Intelligence of Low-dimensional Topology (2014),76-85, problems,135-136.
  • Galois action on knots, Oberwolfach Reports, Report No. 42/2012, Low-Dimensional Topology and Number Theory, 2556-2557.
  • On the construction of $p$-adic multiple $L$-functions and their special values (with H.Tsumura), (Japanese), report on 5th Multiple Zeta Values seminar, 2012.
  • Four groups related to associators, Report on Mathematische Arbeitstagung 24th June-1st July.2011.
  • Mixed pentagon equation and double shuffle relation, RIMS-kokyuroku No 1813, Various Aspects of Multiple Zeta Values (2012), 109-122.
  • The Grothendieck-Teichm\"{u}ller group, the double shuffle group and the motivic Galois group, RIMS-kokyuroku No.1714, Quantum Groups and quantum Topology (2010), 63-79.
  • The motivic Galois group, the Grothendieck-Teichm\"{u}ller group and the double shuffle group, Oberwolfach Reports, Report No. 23/2010, Motives and Homotopy Theory of Schemes, 1406-1408.
  • The motivic Galois group, the Grothendieck-Teichm\"{u}ller group and the double shuffle group, 54th Algebra Symposium Report (2009), 139-150.
  • Proof of double shuffle relations for p-adic multiple zeta values, RIMS-kokyuroku No.1523, Automorphic representations, L-functions, and periods, (2006), 12-24.
  • On motivic iterated integrals in generic positions (joint work with A. Jafari), RIMS-kokyuroku No.1521, Algebraic number theory and related topics, (2006), 70-85.
  • Grothendieck-Teichmuller group (Japanese), 12th Summer School on Number theory (2004), 97-104.
  • Polylog and Frobenius (Japanese), 49th Algebra Symposium Report (2004), 72-85.
  • The double shuffle relations for p-adic multiple zeta values (joint work with Amnon Besser) (Japanese) typewritten file available, Waseda University Number Theory Conference Report (2004), 69-76.
  • A note on weights of l-adic polylogarithms and p-adic polylogarithms, on 2004.2.29
  • Introduction to p-adic multiple zeta values (Japanese), RIMS-kokyuroku No.1324, Algebraic number theory and related topics, (2003), 33-46.
  • A note on the explicit formula for a certain solution of the KZ-like differential equation, on 2002.12.30.
  • On defining equations of three variants of the Grothendieck-Teichm\"{u}ller group, RIMS-kokyuroku No.1267, Communications in Arithmetic Fundamental Groups , (2002), 189-196.
  • The Multiple Zeta Value Algebra And The Stable Derivation Algebra (Japanese), RIMS-kokyuroku No. 1200, Algebraic number theory and related topics, (2001), 137-148.

    Upcoming Talk

  • Kansai Multiple Zeta Values Workshop, Kyoto Sangyo University, Kyoto, Japan, 16th. May. 2015.

    Previous Talks

  • 2015 TIMS Winter School on Number Theory, Taida Institute for Mathematical Science, National Taiwan University, Taipei, Taiwan, 9th-13th. February. 2015.
  • PMI Number Theory Seminar, Department of Mathematics, POSTECH, Pohang, South Korea, 5th. January. 2015.
  • Intensive Lectures, Tohoku University, Sendai, Japan, 18th-21st. November. 2014.
  • Colloquium, Tohoku University, Sendai, Japan, 17th. November. 2014.
  • Tresses et Arithmetique, Centre International de Rencontres Math\'{e}matiques, Luminy, France, 13th-17th. October. 2014.
  • Homotopical Algebra, Operads and Grothendieck-Teichm\"{u}ller groups, Universit\'{e} Nice Sophia Antipolis, Laboratoire J.A. Dieudonn\'{e}, Nice, France, 9th-12th. September. 2014.
  • Intelligence of Low-dimensional Topology, RIMS, Kyoto, Japan, 21st-24th. May. 2014.
  • Seminar on Analytic Number Theory, Nagoya University, Nagoya, Japan, 8th. April. 2014.
  • MSJ Spring Meeting 2014, Gakushuin University, Tokyo, Japan, 15th-18th. March. 2014.
  • S\'{e}minnaire d'alg\`{e}bre, Institut Camille Jordan, Universit\'{e} Claude Bernard Lyon 1, Lyon, France, 12th December. 2013.
  • Japanese Turkish Joint Geometry Meeting, Galatasaray University, \.{I}stanbul, Turkey, 21st-24th. November. 2013.
  • General Mathematics Seminar, University of Luxembourg, Luxembourg, Luxembourg, 22nd October. 2013.
  • Joint UAM-ICMAT Seminar, Algebra and Combinatorics, Instituto de Ciencias Matem\'{a}ticas Universidad Aut\'{o}noma de Madrid, Madrid, Spain, 4th October, 2013.
  • Exploratory Workshop, New Approaches To Multiple Zeta Values, Instituto de Ciencias Matem\'{a}ticas Universidad Aut\'{o}noma de Madrid, Madrid, Spain, 30th September-2nd October, 2013.
  • Motivic Galois Groups, Alfr\'{e}d R\'{e}nyi Institute of Mathematics, Budapest, Hungary, 2nd-6th. September. 2013.
  • Seminar on Algebra, Geometry and Physics, Max Planck Institute for Mathematics, Bonn, Germany, 16th. July. 2013.
  • MPI-Oberseminar, Max Planck Institute for Mathematics, Bonn, Germany, 13th. June. 2013.
  • Higher Structures in Topology and Number Theory, Clay Mathematics Institute workshop, Mathematical Institute, University of Oxford, Oxford, UK, 15th-16th. April. 2013.
  • Grothendieck-Teichm\"{u}ller theory and Multiple Zeta Values of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8th-12th. April. 2013.
  • Lecture of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 13th. February. 2013.
  • Introductory Workshop of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8th-10th. January. 2013.
  • Tuesday Seminar on Topology, Tokyo University, Tokyo, Japan, 6th. November. 2012.
  • Low-Dimensional Topology and Number Theory, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, 26th. August.-1st. September. 2012.
  • Periods and Motives, A Modern Perspective on Renormalization, Instituto de Ciencias Matem\'{a}ticas Universidad Aut\'{o}noma de Madrid, Madrid, Spain, 2nd-6th. July. 2012.
  • String seminar, Nagoya University, Nagoya, Japan, 28th. June. 2012.
  • Polylogarithmes en alg\`{e}bre et en topologie, Laboratoire J.A. Dieudonn\'{e}, Nice, France, 14th-16th. June. 2012.
  • Colloque \`{a} l'occasion des 80 ans de Pierre Cartier, Dialogues autour de l'alg\`{e}bre, la g\'{e}omtri\'{e} et les fonctions multiz\^{e}tas, IHES, Paris, France, 11th-12th. June. 2012.
  • Colloquium in Mathematics, Kyushu University, Hakata, Japan, 26th. April. 2012.
  • Intensive Lectures, Kyushu University, Hakata, Japan, 23rd-27th. April. 2012.
  • Low dimensional topology and number theory IV, Kyushu University, Fukuoka, JAPAN, 12th-15th March. 2012.
  • 5th Multiple Zeta Values seminar, Kyushu University, Hakata, Japan, 27th-29th. January. 2012.
  • Algebra seminar, Tohoku University, Sendai, Japan, 15th. December. 2011.
  • Intensive Lectures, Tokyo University, Tokyo, Japan, 14th-18th. November. 2011.
  • Automorphic forms and Galois representations, Durham University, Durham, UK, 18th-28th July. 2011.
  • Mathematische Arbeitstagung 2011, Universit\"{a}t Bonn and the Max-Planck-Institute for Mathematics, Bonn, Germany, 24th-30th June. 2011.
  • The motivic fundamental group, Lorentz Center, Leiden, Netherlands, 23rd-27th May. 2011.
  • Workshop on L-functions, Kyushu University, Fukuoka, Japan, 21st-23rd April.2011.
  • Low dimensional topology and number theory III, Nishijin Plaza, Fukuoka, JAPAN, 14th-17th March. 2011.
  • S\'{e}minnaire Quantique, IRMA, Strasbourg, France, 6th. December. 2010.
  • Development of Galois-Teichm\"{u}ller Theory and Anabelian Geometry, RIMS, Kyoto, Japan, 25th-30th October. 2010.
  • Various Aspects of Multiple Zeta Values, RIMS, Kyoto, Japan, 6th-9th September. 2010.
  • Arithmetic Geometry Workshop 2010, Naha, Okinawa, Japan, 2nd-6th August. 2010.
  • Des associateurs de Drinfeld \`{a} ceux de Kashiwara-Vergne et lien avec les invariants de noeuds g\'{e}n\'{e}ralis\'{e}s, l'Universit\'{e} Montpellier 2, Montpellier, France, 3rd-4th June. 2010.
  • Motives and Homotopy Theory of Schemes, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, 16th-22nd May, 2010.
  • Quantum Groups and Quantum Topology, RIMS, Kyoto, Japan, 19th-20th. April. 2010.
  • S\'{e}minnaire Quantique, IRMA, Strasbourg, France, 22nd. February. 2010.
  • Analytic Number Theory Seminar, Nagoya University, Nagoya, Japan, 27th. January. 2010.
  • Arithmetic Geometry Seminar, Nagoya University, Nagoya, Japan, 26th. January. 2010.
  • $p$-adic Special Functions and Arithmetic Geometry, Yutomorikurabu, Zaoh, Japan, 28th-31st. October. 2009.
  • Anabelian Geometry, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 24th-28th. August 2009.
  • 54th Algebra Symposium, Meiji University, Tokyo, Japan, 3rd-6th. August. 2009.
  • S\'{e}minnaire The\'{o}rie de Galois Dif\'{e}rentielle, Laboratoire Paul Painlev\'{e}, UFR de Math\'{e}matiques, Universite de Lille 1, Lille, France, 16th. March. 2009.
  • Autour des travaux d'A. Grothendieck, l'Universit\'{e} Montpellier 2, Montpellier, France, 21st-23rd. January. 2009.
  • S\'{e}minnaire Quantique, IRMA, Strasbourg, France, 8th. December. 2008.
  • S\'{e}minnaire de G\'{e}om\'{e}trie et Dynamique, Groupe de travail de Renormalisation -Supersym\'{e}trie, math\'{e}matiques \`{a} Jussieu; Jussieu / Chevaleret, Paris, France, 27th. November. 2008.
  • S\'{e}minnaire d'alg\`{e}bre, Institut Camille Jordan, Universit\'{e} Claude Bernard Lyon 1, Lyon, France, 20th. November. 2008.
  • S\'{e}minnaire Groupes de Lie et espaces de modules, Section de math\'{e}matiques, Universit\'{e} de Gen\`{e}ve, Geneva, Switzerland, 14th. October. 2008.
  • Nottingham Number theory seminar, School of Mathematical Sciences, University of Nottingham, Nottingham, UK, 4th. June. 2008.
  • S\'{e}minnaire Quantique, IRMA, Strasbourg, France, 17th. March. 2008.
  • S\'{e}minnaire Polylogarithmes et Multiz\^{e}ta, math\'{e}matiques \`{a} Jussieu; Jussieu / Chevaleret, Paris, France, 10th. March. 2008.
  • Number theory lunch seminar, Max Planck Institute for Mathematics, Bonn, Germany, 19th. December. 2007.
  • G\"{a}ste und G\"{a}stvortage im Wintersemester 2007/08, Universitat Regensburg, Regensburg, Germany, 14th. December. 2007.
  • Multiple Polylogarithms and Moduli Spaces Day, Durham University, Durham, UK, 5th. December. 2007.
  • GTEM Workshop Arithmetic of Curves and Covers, UFR de Math\'{e}matiques, Universite de Lille 1, Lille, France, 21st-23rd. November. 2007.
  • Groupe de Travail de G\'{e}om\'{e}trie Arithm\'{e}tique, IRMAR, Universite de Rennes 1, Rennes, France, 13rd. November. 2007.
  • Seminar, Padova university, Padova, Italy, 19th. October. 2007.
  • Seminar, Padova university, Padova, Italy, 16th. October. 2007.
  • Arithmetic Algebraic Geometry Conference, Cetraro, Italy, 7th-13th, October. 2007. slides available.
  • Arithmetic Algebraic Geometry, Adam Mickiewicz University, Poznan, Poland, 3rd-7th, September. 2007.
  • Summer School; Multiple Zeta Values and Motives, Tohoku University, Sendai, Miyagi, Japan, 26th-28th.July. 2007.
  • Analytic Number Theory Seminar, Nagoya University, Nagoya, Japan, 4th. April. 2007.
  • Motives, related topics, applications, Hiroshima University, Hiroshima, Japan, 5th-9th. March. 2007. slides available.
  • Colloquium, Nagoya university, Nagoya, Japan, 21st. February, 2007.
  • Conference on zeta for younger researchers, Nagoya University, Nagoya, Japan, 17th-18th. February. 2007.
  • UK-Japan Winter School, Number Theory, University of Cambridge, Centre for Mathematical Sciences, Cambridge, UK, 7th-10th. January 2007.
  • Arithmetic Galois Theory and Related Moduli Spaces, RIMS, Kyoto University, Kyoto, Japan, 23rd-27th and 30th-31st. October. 2006. slides available.
  • Seminar, Harish-Chandra Research Institute, Allahabad, India, 4th. August. 2006.
  • Number Theory Seminar, TIFR, Mumbai, India, 26th. July. 2006.
  • Special Mathematics Colloquium, TIFR, Mumbai, India, 19th. July. 2006.
  • Motives and Periods, University of British Columbia, Vancouver, Canada, 5th-12th. June. 2006.
  • Red Lodge Conference, Red Lodge, Montana, USA, 3rd-7th. April. 2006. slides available.
  • Number Theory Seminar, Nagoya university, Nagoya, Japan, 22nd. February, 2006.
  • Automorphic representations, L-functions, and periods, RIMS, Kyoto, Japan, 23rd-27th. January, 2006, slides available.
  • Japan-Korea Joint Number Theory Seminar, KAIST, Daejeon, South Korea, 5th-8th, January, 2006.
  • Workshop on Motives, Tokyo University, Tokyo, Japan, 19th-22nd, December. 2005, slides available.
  • Algebraic Number Theory and Related Topics, RIMS, Kyoto, Japan, 5th-9th. December. 2005, slides available.
  • Hodge Theory Seminar, Duke University, Durham, USA, 26th. October. 2005.
  • JHU Number Theory Seminar, Johns Hopkins University, Baltimore, USA, 21th. October. 2005.
  • 2nd International Conference on p-adic Mathematical Physics, Institute of Physics, Belgrade, Serbia and Montenegro, 15th-21th, September, 2005, slides available.
  • Member seminar, Simonyi Hall, IAS, Princeton, USA, 7th, March, 2005.
  • Algebra Seminar, University of Pennsylvania, Philadelphia, USA, 14th, February, 2005.
  • Short Talks by Postdoctoral Members, Simonyi Hall, IAS, Princeton, USA, 23rd-29th, September, 2004.
  • Summer School on Number theory, Fukuyama, Japan, 23rd-27th, August, 2004. slides available.
  • 49th Algebra Symposium, Sendai International Center, Sendai, Japan, 2nd-5th, August, 2004. slides available.
  • Algebra Seminar, Hiroshima University, Hiroshima, Japan, 31st. May. 2004.
  • Underground Seminar, Nagoya University, Nagoya, Japan, 26th. May. 2004.
  • Conference on Number Theory, Waseda University, Tokyo, Japan, 17th-19th. March. 2004.
  • Kagawa seminar, Kagawa University, Kagawa, Japan, 20th-21st. December. 2003.
  • Okayama little workshop, Okayama University, Okayama, Japan, November. 13rd-14th. 2003.
  • Noncommutative aspects of number theory , University of Durham, Durham, UK, 28th. August - 5th. September. 2003, slides available.
  • Padova University, Padova, Italy, 2nd - 3rd. July. 2003.
  • Journee Groupes Fondamentaux et Polylogs, Universite de Paris 6, Institut Mathematique de Jussieu, Paris, France, 20th. June, 2003.
  • RIMS Number Theory Seminar, A short survey talk on Monster, especially on Conway-Norton conjecture, Kyoto, Japan, 29th. May. 2003.
  • UC Berkeley Number Theory Seminar, University of California, Berkeley, USA, 14th. May. 2003.
  • Arithmetic application of moduli degeneration, University of California, Irvine, USA, 7th-10th. May. 2003.
  • Tokyo University Monthly Seminar on Number Theory of Modular Forms, Tokyo University, Tokyo, Japan, 26th. April. 2003.
  • p-adic methods in number theory, Nagoya University, Nagoya, Japan, 9th-10th. April. 2003.
  • Conference on Primes and Knots ( JAMI-conference), Japan-U.S. Mathematics Institute, Johns Hopkins University, Baltimore, USA, 6th-16th. March. 2003.
  • Ben-Gurion University Number Theory and Algebraic Geometry Seminar , Beer Sheva, Israel, 26th. February. 2003 .
  • Algebraic Geometry seminar, Einstein Institute, Hebrew University, Jerusalem, Israel, 20th. February. 2003.
  • RIMS Number Theory Seminar, Kyoto, Japan, 10th. February. 2003.
  • Algebraic Number Theory and Related Topics, RIMS, Kyoto, Japan, 2nd-6th. December. 2002.
  • Waseda University Number Theory seminar, Tokyo, Japan, 25th. October. 2002.
  • Number Theory Workshop, Hiroshima University, Hiroshima, Japan, 29th-31th. July. 2002.
  • Workshop on Homotopy Theory of Algebraic Varieties and the Milnor Conjecture, Yatsugatake Izumigo, Japan, 5th-8th. July. 2002.
  • RIMS Number Theory seminar, RIMS, Kyoto, Japan, 22th. April. 2002.
  • Arithmetic Aspects of Fundamental Groups , EURESCO Conference, Acquafredda di Maratea (near Naples), Italy, 1st-6th. September. 2001.
  • Various aspects on multiple zeta values, RIMS, Kyoto, Japan, 4th-6th. June. 2001.
  • Workshop on Hodge theory, Galois theory, moduli and arithmetic geometry, Kyoto University, Graduate School of Human and Environmental Studies Room No. G226, Kyoto, Japan, 21st-24th. May. 2001.
  • $\pi_1$ festival, Tokyo Metropolitan University, Tokyo, Japan, 14th-15th. March. 2001.
  • RIMS Number Theory seminar,Kyoto, Japan, 19th. February. 2001.
  • Algebraic Number Theory and Related Topics, RIMS, Kyoto, Japan, 18th-22th. December. 2000.
  • Kyushu University Multiple Zeta Values Seminar, Hakata, Japan, 6th-7th. November. 2000.
  • Tokyo Metropolitan University Number Theory Seminar, Tokyo, Japan, 24th-26th. July. 2000. slides available.

    Organised Workshop

  • Japan-Korea Number Theory Seminar 2011, Nagoya University, Nagoya, Japan, 9th-12th. November. 2011.
  • Summer School; Multiple Zeta Values and Motives, Tohoku University, Sendai, Miyagi, Japan, 26th-28th.July. 2007.

    Computation Tables

  • Table of Multiple Zeta Values up to Weight 12
  • Drinfel'd Associator up to degree 4
  • The Fundamental Solution of KZ equation up to degree 4

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