Welcome to Hidekazu Furusho's Home Page.

Research Interests

  • (p-adic) multiple zeta value, (p-adic) (multiple) polylogarithm, (p-adic) iterated integration.
  • mixed Tate motive, motivic Galois group, motivic fundamental group.
  • (p-adic) Knizhnik-Zamolodchikov equation, Grothendieck-Teichmuller group, Teichmuller-Lego philosophy.
  • quantum group, Yang-Baxter equation, deformation quantization, quasi-triangular quasi-Hopf QUE-algebra, Kashiwara-Vergne conjecture, knot invariant......

    Research Experience

  • April 2010-, Associate Professor at Nagoya University, Nagoya, Japan.
  • October 2007-September 2009, JSPS Postdoctoral Fellowships for Research Abroad in Ecole Normale Suerieieu, 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

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

    Paper

  • Double shuffle relation for associators.
  • p-adic Eisenstein-Kronecker functions and the elliptic polylogarithm for CM elliptic curves, (with S.Kobayashi and K.Bannai).
  • 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, detailed/corrected version.
  • The multiple zeta value algebra and the stable derivation algebra, Publ. Res. Inst. Math. Sci. Vol 39. no 4. (2003). 695-720.

    Articles

  • The motivic Galois group, the Grothendieck-Teichm\"{u}ller group and the double shuffle group, 54th Algebra Symposium Report (2009).
  • 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 Invited Talk

  • Quantum Groups and Quantum Topology, RIMS, Kyoto, Japan, 19th-20th. April. 2010.

    Previous Invited Talks

  • 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.
  • S\'{e}minnaire M.A.T. : 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.