Organization
Graduate School of Mathematics Division of Mathematics Social Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Professor
FURUSHO, Hidekazu
Degree 1
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博士（理学） （ 2003.9 京都大学 ）
Research Interests 2
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Algebraic Geometry
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Number Theory
Committee Memberships 13
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教務委員会 教務委員
2022.4 - 2024.3
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教務委員会 教務委員
2020.4 - 2021.3
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G30教育生活連絡会議委員 G30教育生活連絡会議委員
2020.4 - 2021.3
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日本数学コンクール実行委員会 日本数学コンクール実行委員
2019.4 - 2021.3
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広報・談話会委員会 広報・談話会委員
2019.4 - 2020.3
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図書委員会 図書委員
2018.4 - 2019.3
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ホームカミングディ実行委員会 ホームカミングディ実行委員会
2018.4 - 2019.3
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ＩＲ本部会議ＷＧアソシエイトメンバー委員 ＩＲ本部会議ＷＧアソシエイトメンバー委員
2018.4 - 2019.3
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ＩＲ本部会議ＷＧアソシエイトメンバー委員 ＩＲ本部会議ＷＧアソシエイトメンバー委員
2017.4 - 2018.3
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広報談話会委員会 広報談話会委員
2015.4 - 2017.3
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一年生指導委員 一年生指導委員
2015.4 - 2016.3
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日本数学会中部支部評議員 日本数学会中部支部評議員
2015.4 - 2016.3
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広報談話会委員会 広報談話会委員
2014.4 - 2015.3
Awards 3
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日本数学会代数学賞
2014.3 日本数学会
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井上研究奨励賞
2006.2 井上財団
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日本数学会建部賢弘奨励賞
2004.9 日本数学会
Papers 28
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The Betti side of the double shuffle theory. III. Bitorsor structures Reviewed
Enriquez Benjamin, Furusho Hidekazu
SELECTA MATHEMATICA-NEW SERIES Vol. 29 ( 2 ) 2023.4
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The Betti side of the double shuffle theory. II. Double shuffle relations for associators Reviewed
Enriquez Benjamin, Furusho Hidekazu
SELECTA MATHEMATICA-NEW SERIES Vol. 29 ( 1 ) 2023.2
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THE PENTAGON EQUATION AND THE CONFLUENCE RELATIONS Reviewed
Furusho Hidekazu
AMERICAN JOURNAL OF MATHEMATICS Vol. 144 ( 4 ) page： 873 - 894 2022.8
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On relations among multiple zeta values obtained in knot theory Invited Reviewed
Hidekazu Furusho
the Advanced Lectures in Mathematics (ALM) book series Vol. 49 page： 73 - 89 2022
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Analytic continuation of multiple polylogarithms in positive characteristic Reviewed
Furusho Hidekazu
TUNISIAN JOURNAL OF MATHEMATICS Vol. 4 ( 3 ) 2022
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The Betti side of the double shuffle theory. I. The harmonic coproducts Reviewed
Enriquez Benjamin, Furusho Hidekazu
SELECTA MATHEMATICA-NEW SERIES Vol. 27 ( 5 ) 2021.11
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p-adic multiple L-functions and cyclotomic multiple harmonic values Reviewed
Furusho Hidekazu, Jarossay David
INTERNATIONAL JOURNAL OF NUMBER THEORY Vol. 16 ( 2 ) page： 361 - 375 2020.3
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Galois action on knots II: proalgebraic string links and knots Invited Reviewed
Hidekazu Furusho
Periods in Quantum Field Theory and Arithmetic" Springer Proceedings in Mathematics & Statistics Vol. 314 page： 541--591 2020.3
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A Stabilizer Interpretation of Double Shuffle Lie Algebras Reviewed
Enriquez Benjamin, Furusho Hidekazu
INTERNATIONAL MATHEMATICS RESEARCH NOTICES Vol. 2018 ( 22 ) page： 6870 - 6907 2018.11
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On the coefficients of the Alekseev-Torossian associator Reviewed
Furusho Hidekazu
JOURNAL OF ALGEBRA Vol. 506 page： 364-378 2018.7
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DESINGULARIZATION OF COMPLEX MULTIPLE ZETA-FUNCTIONS Reviewed
Furusho Hidekazu, Komori Yasushi, Matsumoto Kohji, Tsumura Hirofumi
AMERICAN JOURNAL OF MATHEMATICS Vol. 139 ( 1 ) page： 147-173 2017.2
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Fundamentals of p-adic multiple L-functions and evaluation of their special values Reviewed
Furusho Hidekazu, Komori Yasushi, Matsumoto Kohji, Tsumura Hirofumi
SELECTA MATHEMATICA-NEW SERIES Vol. 23 ( 1 ) page： 39-100 2017.1
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Galois action on knots I: Action of the absolute Galois group Reviewed
Furusho Hidekazu
QUANTUM TOPOLOGY Vol. 8 ( 2 ) page： 295-360 2017
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p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas, Reviewed
Hidekazu Furusho, Shinichi Kobayashi, Kenichi Bannai
Nagoya Math Journal Vol. 219 page： 269-302 2015
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Around associators Invited Reviewed
Hidekazu Furusho
Automorphic forms and Galois representations 2 ( 415 ) page： 105-117 2014
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Mixed Pentagon, octagon and Broadhurst duality equation Reviewed
Benjamin Enriquez, Hidekazu Furusho
Journal of Pure and Applied Algebra Vol. 216 ( 4 ) page： 982-995 2012
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Geometric interpretation of double shuffle relation for multiple L-values Reviewed
Hidekazu Furusho
Galois-Teichm\"{u}ller theory and Arithmetic Geometry, Advanced Studies in Pure Math Vol. 63 page： 163-187 2012
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Double shuffle relation for associators Reviewed
Hidekazu Furusho
Annals of Mathematics Vol. 174 ( 1 ) page： 341-360 2011
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Pentagon and hexagon equations Reviewed
Hidekazu Furusho
Annals of Mathematics Vol. 171 ( 1 ) page： 545-556 2010
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p-adic multiple zeta values II -- tannakian interpretations Reviewed
Hidekazu Furusho
Amer.J.Math Vol. 129 ( 4 ) page： 1105-1144 2007
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Algebraic cycles and motivic generic iterated integrals Reviewed
Hidekazu Furusho, Amir Jafari
Mathematical Research Letters Vol. 14 ( 6 ) page： 923-942 2007
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Regularization and generalized double shuffle relations for p-adic multiple zeta values Reviewed
Hidekazu Furusho, Amir Jafari
Compositio Math Vol. 143 page： 1089-1107 2007
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p-adic multiple zeta values -- a precis. p-adic mathmatical physics Invited Reviewed
Hidekazu Furusho
Amer.Inst.Phys Vol. 826 page： 222-236 2006
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Multiple zeta values and Grothendieck-Teichm\"{u}ller groups Invited Reviewed
Hidekazu Furusho
AMS Contemporary Math Vol. 416 page： 49-82 2006
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The double shuffle relations for p-adic multiple zeta values Invited Reviewed
Hidekazu Furusho, Amnon Besser
AMS Contemporary Math Vol. 416 page： 9-29 2006
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p-adic multiple zeta values I -- p-adic multiple polylogarithms and the p-adic KZ equation Reviewed
Hidekazu Furusho
Inventiones Mathematicae Vol. 155 ( 2 ) page： 253-286 2004
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The multiple zeta value algebra and the stable derivation algebra Reviewed
Hidekazu Furusho
Publ. Res. Inst. Math. Sci. Vol. 39 ( 4 ) page： 695-720 2003
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Geometric and arithmetic subgroups of the Grothendieck-Teichm\"{u}ller group Reviewed
Hidekazu Furusho
Mathematical Research Letters Vol. 10 ( 1 ) page： 97-108 2003
Books 1
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結び目とGrothendieck-Teichmüller群
古庄英和, 小谷久寿，新甫洋史（ Role： Joint author）
九州大学マス・フォア・インダストリ研究所 2016.2
Presentations 83
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Associateurs et theorie des moules Invited International conference
Hidekazu Furusho
Seminnaire Quantique 2023.3.14
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On l-adic and p-adic hypergeometric functions
Hidekazu Furusho
L-functions and Motives in Niseko 2022 2022.9.11 Masanori Asakura (Hokkaido University), Noriyuki Otsubo (Chiba University) , Seidai Yasuda (Hokkaido University)
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Mould理論とKashiwara-Vergne Lie代数 II Invited
古庄英和
リーマン面に関連する位相幾何学 2022.9.6 河澄響矢 (東大数理) 田所勇樹 (木更津高専) 久野雄介 (津田塾大学) 佐藤正寿 (東京電機大学)
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調和余積の 2 種類の固定化部分群について Invited International coauthorship
古庄英和
多重ゼータ値の諸相 2022.5.20 田坂 浩二
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On two stabilizers related to harmonic coproducts Invited International coauthorship International conference
Hidekazu Furusho
Seminnaire Quantique 2022.4.27
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Kashiwara-Vergne Lie algebra and Goncharov’s dihedral Lie algebra in mould theory Invited International conference
Low dimensional topology and number theory XIII 2022.3.17
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Associators and an l-adic analogue of Gauss's hypergeometric function Invited International conference
Hidekazu Furusho
Johnson homomorphisms and related topics 2022.1.12 Nariya Kawazumi, Gwénaël Massuyeau, Hiroaki Nakamura, Takuya Sakasai, Christine Vespa.
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ℓ-進超幾何関数 Invited
古庄英和
九大多重ゼータセミナー（拡大版） 2021.11.23 金子昌信
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Artin-Schreier equation and Carlitz multiple polylogarithms Invited International conference
Hidekazu Furusho
Japan Europe Number Theory Exchange Seminar 2021.6.1 Henrik Bachmann, Nils Matthes
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ダブルシャッフル群の Betti 対応物 (Benjamin Enriquez 氏 (University of Strasbourg) との共同研究) Invited International coauthorship
早稲田大学整数論研究集会 2021.3.23 橋本 喜一朗 （早稲田大学），尾崎 学 （早稲田大学），成田 宏秋 （早稲田大学）， 坂田 裕 （早稲田大学高等学院），青木 琢哉 （早稲田大学）
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Analytic continuation of Carlitz multiple polylogarithms Invited International conference
Hidekazu Furusho
NCTS Seminar on Number Theory 2020.12.11 Cheih-yu Chang
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Four groups related to associators Invited
Hidekazu Furusho
2020.2.13
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The associator relation and the confluence relations International conference
Hidekazu Furusho
Expansions, Lie Algebras, and Invariants, 2019.7.25 Anton Alekseev, Dror Bar-Natan, and Roland van der Veen
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On a relation of Hirose and Sato Invited International conference
Hidekazu Furusho
Multiple zeta values and related topics 2019.6.11 Minoru Hirose (Kyushu University), Masataka Ono (Kyushu University) Tomokazu Onozuka (Kyushu University), Nobuo Sato (Kyushu University)
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Kontsevich's eye, Lie graphs and associators Invited International conference
Hidekazu Furusho
Workshop: Johnson homomorphisms and related topics 2019 2019.5.16 Shinobu Hikami, Nariya Kawazumi, Gwénaël Massuyeau, Hiroaki Nakamura, Takuya Sakasai, Christine Vespa
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調和余積のBetti対応物とDeligne-寺杣プロジェクト Invited International coauthorship
関西多重ゼータ研究会 2019.5.11 関西多重ゼータ研究会
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On Relations among Multiple Zeta Values Obtained in Knot Theory Invited International conference
Hidekazu Furusho
NCTS Seminar on Number Theory 2019.4.10
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p-adic multiple L-functions and cyclotomic multiple harmonic values. Invited International conference
Hidekazu Furusho
Special Session on Arithmetic and Transcendence of Special Functions and Special Values
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Betti side of the double shuffle theory Invited
Hidekazu Furusho
Low dimensional topology and number theory XI
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Kontsevich's eye, Lie graphs and associators
Hidekazu Furusho
Arithmetic and Algebraic Geometry 2019
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アイについて... Invited
古庄 英和
第26回整数論サマースクール 「多重ゼータ値」
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On the coefficients of the Alekseev Torossian associator Invited International conference
Hidekazu Furusho
International Workshop on Arithmetic Geometry and Quantum Field Theory
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On a relation of Hirose and Sato Invited International conference
Hidekazu Furusho
Taiwan-Japan Joint Workshop on Multiple Zeta Values
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Associators and Kontsevich's eye (1) and (2) Invited
Hidekazu Furusho
Algebraic Lie Theory and Representation Theory (ALTReT) 2018
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A Betti counterpart of the harmonic coproduct (I) Invited International conference
Hidekazu Furusho
Poisson geometry of moduli spaces, associators and quantum field theory
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A Betti counterpart of the harmonic coproduct (I) Invited International conference
Hidekazu Furusho
Periods and Regulators
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p-adic multiple zeta values Invited
Hidekazu Furusho
Combinatoire et Theorie de Nombres
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The stabilizer of the harmonic coproduct and Racinet's double shuffle group Invited
Hidekazu Furusho
Seminaire tournant de theorie des nombres
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Kontsevich's eye and associators I and II Invited
Hidekazu Furusho
Geometry of Moduli Space of Low Dimensional Manifolds
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A stabilizer interpretation of the double shuffle Lie algebra Invited
Hidekazu Furusho
Workshop on Grothendieck-Teichmuller Theories
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Complex and p-adic multiple zeta functions International conference
Hidekazu Furusho
Low dimensional topology and number theory VIII,
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結び目へのガロア作用
代数的整数論とその周辺
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p-adic multiple L-functions and p-adic multiple polylogarithms International conference
Hidekazu Furusho
Zeta Functions of Several Variables and Applications
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Desingularization of multiple zeta functions International conference
Hidekazu Furusho
GRT, MZVs and associators
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結び目と多重ゼータ値
関西多重ゼータ研究会
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p-adic multiple zeta values International conference
Hidekazu Furusho
Seminnaire Groupes de Lie et espaces de modules
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Complex and p-adic multiple zeta functions International conference
Hidekazu Furusho
S\'{e}minnaire Quantique
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p-adic multiple zeta values (I)-(IV) International conference
Hidekazu Furusho
2015 TIMS Winter School on Number Theory
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p-adic multiple zeta values International conference
Hidekazu Furusho
PMI Number Theory Seminar
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アソシエーターにまつわるエトセトラ
東北大学談話会
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Multiple zeta values and associators International conference
Hidekazu Furusho
Tresses et Arithmetique
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Four groups related to associators International conference
Hidekazu Furusho
Homotopical Algebra, Operads and Grothendieck-Teichmüller groups
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Galois action on knots International conference
Hidekazu Furusho
Intelligence of Low-dimensional Topology
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Various topics around associators
Hidekazu Furusho
2014 Mathematical Society of Japan, annual meeting, Award Lecture for 2014 Algebra Prize
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Four groups related to associators International conference
Hidekazu Furusho
Japanese Turkish Joint Geometry Meeting
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Four groups related to associators International conference
Hidekazu Furusho
General Mathematics Seminar
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Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions International conference
Hidekazu Furusho
Exploratory Workshop, New Approaches To Multiple Zeta Values
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Galois action on knots International conference
Hidekazu Furusho
Motivic Galois Groups
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Desingularization of complex multiple zeta-functions and fundamentals of p-adic multiple L-functions International conference
Hidekazu Furusho
Seminar on Algebra, Geometry and Physics
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Galois action on knots International conference
Hidekazu Furusho
MPI-Oberseminar
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Galois action on knots International conference
Hidekazu Furusho
Higher Structures in Topology and Number Theory
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On multiple L-functions and their p-adic analogues International conference
Hidekazu Furusho
Grothendieck-Teichm\"{u}ller theory and Multiple Zeta Values
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p-adic multiple zeta values International conference
Hidekazu Furusho
Introductory Workshop of Grothendieck-Teichm\"{u}ller Groups, Deformation and Operads
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Galois action on knots International conference
Hidekazu Furusho
Low-Dimensional Topology and Number Theory
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Galois action on knots International conference
Hidekazu Furusho
Periods and Motives
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p-adic multiple polylogarithms International conference
Hidekazu Furusho
Polylogarithmes en alg\`{e}bre et en topologie
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On GT-actions International conference
Hidekazu Furusho
Colloque à l'occasion des 80 ans de Pierre Cartier
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Galois action on knots
Hidekazu Furusho
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On Galois action on knots International conference
Hidekazu Furusho
Low dimensional topology and number theory IV
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Around associators International conference
Hidekazu Furusho
Automorphic forms and Galois representations
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Double shuffle for associators International conference
Hidekazu Furusho
Mathematische Arbeitstagung 2011
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On Associators International conference
Hidekazu Furusho
The motivic fundamental group
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Geometric interpretation of double shuffle relations for multiple L-values
Hidekazu Furusho
Various Aspects of Multiple Zeta Values
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Motivic Hopf algebra and tree Hopf algebra (joint work with A. Jafari)
Arithmetic Geometry Workshop 2010
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Motivic Galois group, Grothendieck-Teichmuller group and double shuffle group
Des associateurs de Drinfeld \`{a} ceux de Kashiwara-Vergne et lien avec les invariants de noeuds g\'{e}n\'{e}ralis\'{e}s
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The motivic Galois group, the Grothendieck–Teichm¨uller group and the double shuffle group International conference
Motives and Homotopy Theory of Schemes
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The motivic Galois group, the Grothendieck–Teichm¨uller group and the double shuffle group
Quantum Groups and Quantum Topology
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Pentagon and hexagon equations
P-adic Special Functions & Arithmetic Geometry
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Motivic Galois group,Grothendieck-Teichm¨uller group and double shuffle group
第54回代数学シンポジウム
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Double shuffle relation for associators International conference
Anabelian Geometry
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Grothendieck-Teichmuller group International conference
Séminaire M.A.T. : autour des travaux d'A. Grothendieck
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Pentagon and hexagon equations International conference
Multiple Polylogarithms and Moduli Spaces Day
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Pentagon and hexagon equations of GT International conference
GTEM Workshop Arithmetic of Curves and Covers
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Pentagon and hexagon equations International conference
Arithmetic Algebraic Geometry Conference
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Double shuffle relations for p-adic multiple zeta values International conference
Arithmetic Algebraic Geometry
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ポリログとフロベニウス
夏の学校 「多重ゼータ値とモティーフ」
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p進多重ゼータ値
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Pentagon and Hexagons
Motives, related topics, applications
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p進多重ゼータ値
名古屋大学多元数理科学研究科談話会
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p-adic analogue of multiple zeta values International conference
UK-Japan Winter School, Number Theory,
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Survey of Drinfel'd's work on GT and its associated quantumn groups
Arithmetic Galois Theory and Related Moduli Spaces,
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p-adic multiple zeta values International conference
Motives and Periods
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Algebraic cycles and motivic generic iterated integrals International conference
Red Lodge Conference
Research Project for Joint Research, Competitive Funding, etc. 1
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ゼータ関数とモティーフの理論の多様性
2015.9 - 2018.3
大幸財団第25回自然科学系学術研究助成
Grant type：Competitive
KAKENHI (Grants-in-Aid for Scientific Research) 11
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Why is the multiple zeta value so ubiquitous?
Grant number：21H04430 2021.4 - 2026.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (A)
Authorship：Coinvestigator(s)
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数論的対象の背後にある幾何学の発見・構築を通じたL関数・ガロア表現の研究
Grant number：21H00969 2021.4 - 2026.3
科学研究費助成事業 基盤研究(B)
安田 正大, 古庄 英和, 山下 剛
Authorship：Coinvestigator(s)
(A) 法 p 還元の計算を一般の半安定表現に拡張し, 柔軟性の高い整係数 p 進Hodge 理論の構築を目指す. また保型形式の slope を調べる手法を開発し Taylor-Wiles 系の議論を展開する.
(B) Harder-Raghuram の手法を用いて複シャッフル空間についての代表者による予想を証明する. さらに modular symbol の概念を拡張してモジュラ複体と対応する理論を構築する.
(C) Hilbert modular 多様体と Kummer 多様体の間の代数的対応を探し出す. さらに Fermat 曲線と関係する場合に, Beilinson 予想の確立を試みる. -
Grant number：20H00115 2020.4 - 2025.3
科学研究費助成事業 基盤研究(A)
中村 博昭, 角皆 宏, 河澄 響矢, 森下 昌紀, 星 明考, 伊吹山 知義, 古庄 英和, 高橋 浩樹, 小笠原 健
Authorship：Coinvestigator(s)
本研究では，ガロア・タイヒミュラー群の普遍モノドロミー表現，正則逆ガロア問題に関わるリフトと特殊化，モノドロミー不変量としての種々の数論的関数の醸成，の三つの柱に集約される新しい観点からの方法を導入し，数論トポロジーに対する有機的な構造解析を進める．理論的考察とともに計算機による実例計算とを総合して数論側とトポロジー側との類似性比較に関する詳細な理解を追求するとともに，両者を繋ぐバイパス構築の手がかりに関わる数学的構造の理解の深化を目指す．
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モチヴィックガロア群と多重ゼータ値から広がる数学ー整数論からの解放ー
Grant number：18H01110 2018.4 - 2023.3
科学研究費助成事業 基盤研究(B)
古庄 英和, 田坂 浩二, 大野 泰生, 安田 正大
Authorship：Principal investigator
Grant amount：\12220000 （ Direct Cost: \9400000 、 Indirect Cost：\2820000 ）
論文(2018)ではKontsevichの目上の接続より構成されるAlekseev-Torossian associatorと呼ばれる非可換形式的べき級数の係数をLieグラフのKontsevichの重み形式の反復積分を用いて明示的に書き下す手法を与えた。またStrasbourg大学のBenjamin Enriquez氏と調和余積とdouble shuffle群のBetti対応物について共同研究を行ない共著のプレプリントを書いた。Geneve大学のDavid Jarossay氏と共同研究を行なった。彼との共著のプレプリントでは、円分多重調和値(cyclotomic multiple harmonic values)をp進多重L値の無限和で書けることを示した。プレプリント(2018)では佐藤信夫氏と広瀬稔氏がみつけた多重ゼータ値の合流関係式が結合子関係式が等価になることを示した。
7月には、外国人研究者を招聘しMini-Workshop「Elliptic multiple zeta values and mixed elliptic motives」を名古屋大学で開催した。
研究分担者である田坂氏はHecke固有形式を2重Eisenstein級数の線形和に一意的に分解する公式を与えた。またMatthes氏との共同研究ではBrownと Ecalleによる極化複シャッフルリー代数の元の構成方法の比較を行なった。大野氏は、拡張されたArakawa-Kaneko型多重ゼータ関数とその特殊値への従来理論の拡張について研究を進めた。また安田氏は、複シャッフル関係式と整数係数の一般線形群の関係についてのGoncharovの議論の解明を行った。
合流関係式と結合子関係式が等価なことがわかった。
Enriquez氏との共同研究に大きな進展があった。
Jarossay氏との共同研究が稔りプレプリントにまとめ上げた。
今まで書いたプレプリントを改良し証明の簡易化に努める。また積極的に研究集会・セミナーに出向き、今まで得られた研究の発表を行う。
昨年度は多重ゼータ値の整数論的側面を重点的に研究をしてきたが、今後は整数論以外の分野とのつながりを視野に入れて研究をしていく。 -
多重ゼータ値と多重Ｅｉｓｅｎｓｔｅｉｎ級数の代数的， 幾何的な研究
Grant number：16F16021 2016.4 - 2018.3
Authorship：Other
多重ゼータ値とはここ四半世紀で研究が盛んになった研究対象であり、多重Eisenstein級数とはGangl, Kaneko Zagier (2006)により導入された二重Eisenstein級数を一般化した級数のことである。Bachamann氏は外国人特別研究員として採用されていた１年間、国内のさまざまなセミナー、研究集会に足繁く出向き国内の若手の研究者たちと複数の共同研究を同時進行で行い、この多重ゼータ値と多重Eisenstein級数について精力的に研究を続けてきた。主だった業績として以下の４つが挙げられる：
1).多重Eisenstein級数の微分に関する研究：多重Eisenstein級数は、depthが1,2,3の場合において多重Eisenstein級数に関連するある種のq級数が微分作用素で閉じていることを計算により示した。
2).補間Schur多重ゼータ値の研究：多重ゼータ値や多重ゼータスター値を一般化した補間多重ゼータ値という多項式とYoung図形より構成されるSchur多重ゼータ値が知られている。これら二者をつなげる補間Schur多重ゼータ値という多項式を導入し基本的な性質を導いた。
3).円分的有限多重ゼータ値の研究：円分的有限多重ゼータ値を導入して、これの基本的な代数的構造の基本的性質、特殊値、有限多重ゼータ値のq類似とのつながりについての結果を得た。
4).Schur多重ゼータ値の和公式の類似の研究：多重ゼータ値や多重ゼータスター値と同様にSchur多重ゼータ値に対しても和公式の類似が成り立つことを示した。
翌年度、交付申請を辞退するため、記入しない。
翌年度、交付申請を辞退するため、記入しない。 -
Motivic Galois group(Fostering Joint International Research)
Grant number：15KK0159 2016 - 2019
Fund for the Promotion of Joint International Research (Fostering Joint International Research)
FURUSHO HIDEKAZU
Authorship：Principal investigator
Grant amount：\14300000 （ Direct Cost: \11000000 、 Indirect Cost：\3300000 ）
To make clearer a relationship of the motivic Galois group with various fields of mathematics, I conducted researches, particularly on multiple zeta values and associators, and obtained the following results:
geometric interpretation of the harmonic coproduct of multiple zeta values and constructions of its Betti counterpart, a method to calculate coefficients of the Alekseev-Torossian associator, relationship of associator relations and relations among multiple zeta values obtained in knot theory, relations between p-adic multiple L-functions and cyclotomic multiple harmonic values. -
Adelic new methods on arithemetic geometry and their applications to p-adic Hodge theory and multiple L-functions
Grant number：15H03610 2015.4 - 2020.3
Yasuda Seidai
Authorship：Coinvestigator(s)
The research representative and Go Yamashita have constructed families of Wach modules of rank two and applied them to the study of crystalline deformation rings of dimension two. He and Satoshi Kondo have constructed lifts of the zeta elements in motivic cohomologies of Drinfeld modular varieties to their integral models satisfying norm relations, and have constructed a theory of topoi related to monoids. He and Yusuke Sugiyama have introduced a new notion of pseudo-tameness and, by using them, have proved that any algebraic curve over an algebraically closed field has a tame morphism to the projective line. He has introduced the derived double shuffle spaces and has applied them to show a double shuffle analogue of Broadhurst-Kreimer conjecture in depth four. He has found that a suitable quotient of a Hilber modular surface related to the L-function of a certain curve of genus is a Kummer surface.
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Research on number theoretic properties of zeta functions in several variables
Grant number：15K04788 2015.4 - 2018.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
TSUMURA Hirofumi, MATSUMOTO Kohji, KOMORI Yasushi, FURUSHO Hidekazu
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid)
The main aim in this research is to study what is called the zeta function which plays an important role in number theory and investigate their properties. In particular, we studied zeta functions in several variables mainly from the viewpoint of the analytic aspect. We studied the Witten zeta function in several variables which was defined based on Witten's work, and also the Arakawa-Kaneko zeta function defined by Tsuneo Arakawa and Masanobu Kaneko. Our main result is consider the number theoretic properties of these zeta functions,and consequently we obtained unknown properties of them and gave new results.
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Studies on arithmetic invariants arising from mutual interactions between Galois groups and fundamental groupoids
Grant number：26287006 2014.4 - 2019.3
Nakamura Hiroaki
Authorship：Coinvestigator(s)
We found various properties of arithmetic functions arising from Galois representations in arithmetic fundamental groupoids. We investigated behaviors of Galois-polylogarithmic functions and derived a formula that relates their normalized special values on p-adic inertia group with standard p-adic polylogarithmic values. Elaborating the composition law for the Eisenstein invariants of universal monodromy representation in affine elliptic curves, we established a new foundation toward subsequent studies in arithmetic Galois monodromy theory.
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Grant number：25287002 2013.4 - 2018.3
Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Matsumoto Kohji, TSUMURA HIROFUMI, KANEKO MASANOBU, OHNO YASUO, SHOJI MAYUMI, FURUSHO HIDEKAZU, YAMASAKI YOSHINORI, UMEGAKI YUMIKO, NAKAMURA TAKASHI
Authorship：Collaborating Investigator(s) (not designated on Grant-in-Aid)
The present research has dealt with various multiple series, such as multiple zeta-functions of Euler-Zagier type, a more general class of zeta-functions of root systems, and also the same type of series with Fourier coefficients of modular forms on the numerators. The main results obtained in the period of the present research are the structure theory and functional relations for zeta-functions of root systems, or more general multiple zeta-functions associated with Lie groups; evaluation of values of multiple series involving hyperbolic functions; numerical computations on the zeros multiple zeta-functions; the proof of two types of functional equations for double zeta-functions involving Fourier coefficients of modular forms on the numerator; the idea of desingularized multiple zeta-functions and the development of the theory of p-adic multiple zeta-functions.
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モチヴィックガロア群－数論幾何学を越えて－
2012.4 - 2016.3
科学研究費補助金 若手研究(A)
Authorship：Principal investigator
Teaching Experience (On-campus) 10
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線形代数学II
2018
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線形代数学I
2018
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線形代数学II
2016
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線形代数学I
2016
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代数学要論I
2016
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線形代数学II
2015
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線形代数学I
2015
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代数学要論I
2015
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数理科学展望III ／数理科学展望I(英語)
2012
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代数学特論I
2010
Teaching Experience (Off-campus) 3
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数学特別講義H
2014.4 - 2015.3 （Tohoku University）
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数理科学特別講義VII
2012.4 - 2013.3 （Kyushu University）
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数理科学特別講義Ⅷ
2011.4 - 2012.3 （The University of Tokyo）
Social Contribution 3
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出前講義、向陽高校
Role(s)：Lecturer
2020.11
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NHKカルチャー, 数学散策
Role(s)：Lecturer
NHKカルチャー NHKカルチャー, 数学散策 2019.2
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NHKカルチャー, 数学散策
Role(s)：Lecturer
NHKカルチャー NHKカルチャー, 数学散策 NHKカルチャー 2018.7