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 ,
to appear in Quantum Topology.
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
GRT, MZVs and associators, Les Diables,Switzerland, 20th-29th. August. 2015.
Previous Talks
Kansai Multiple Zeta Values Workshop ,
Kyoto Sangyo University, Kyoto, Japan, 16th. May. 2015.
S\'{e}minnaire Groupes de Lie et espaces de modules ,
Section de math\'{e}matiques, Universit\'{e} de Gen\`{e}ve, Geneva, Switzerland, 2nd. April. 2015.
S\'{e}minnaire Quantique ,
IRMA, Strasbourg, France, 30th. March. 2015.
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
Address:
Graduate School of Mathematics ,
Nagoya University , Chikusa-ku, Furo-cho, Nagoya 464-8602 Japan
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