九州大学 研究者情報
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基本情報 研究活動 教育活動 社会活動
森下 昌紀(もりした まさのり) データ更新日:2019.06.28



主な研究テーマ
数論的位相幾何学
キーワード:結び目と素数
1998.12.
研究業績
主要著書
1. Masanori Morishita, Knots and Primes -- An Introduction to Arithmetic Topology, Springer, 2011.12, 結び目と素数の類似に基づき, 結び目理論(3次元位相幾何学)と数論の間の類似性・関連性を論じた..
2. 森下昌紀, 結び目と素数, 現代数学シリーズ 15, シュプリンガー・ジャパン, 2009.04.
主要原著論文
1. Hikaru Hirano, Masanori Morishita, Arithmetic topology in Ihara theory II: Milnor invariants, dilogarithmic Heisenberg coverings and triple power residue symbols, J. Number Theory 198 (2019), 211–238., 2019.03.
2. Fumiya Amano, Yasushi Mizusawa, Masanori Morishita, On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field, Research in Number Theory, 4, (2018), 4:7.
3. Takahiro Kitayama, Masanori Morishita, Ryoto Tange, Yuji Terashima, On certain L-functions for deformations of knot group representations, Transactions of AMS., Number 5, (2018), 3171–3195.
4. Hisatoshi Kodani, Masanori Morishita, Yuji Terashima, Arithmetic topology in Ihara theory, Publ. Res. Inst. Math. Sci. 53 (2017), no. 4, 629–688, Publ. Res. Inst. Math. Sci. , 53, 4, 629-688, 2017.12.
5. Masanori Morishita, Yuji Terashima, p-Johnson homomorphisms and pro-p groups, Journal of Algebra, 479 (2017), 102-136, Journal of Algebra, 479 (2017), 102-136.
6. Masanori Morishita, Yu Takakura, Yuji Terashima, Jun Ueki, On the universal deformations for SL_2-representations of knot groups, Tohoku Math. J., 69 (2017), 67-84, Tohoku Math. J., 69 (2017), 67-84.
7. Fumiya Amano, Hisatoshi Kodani, Masanori Morishita, Takayuki Sakamoto, Takafumi Yoshida, Redei's triple symbols and modular forms, Tokyo J. Math. Vol. 36, no.2, 2013.
8. Junhyeung Kim, Hisatoshi Kodani, Masanori Morishita, Nilpotent class field theory for manifolds, Proceedings of Japan Academy, 89, 1, 15-19, 2013.01.
9. Masanori Morishita, Analogies between knots and primes, 3-manifolds and number rings , Sugaku expositions, 23, 1, 1--30, 2010.07.
10. M. Morishita, Y. Terashima, Chern-Simons variation and Deligne cohomology, in: Spectral Analysis in Geometry and Number Theory on Prof. Toshikazu Sunada's 60th birthday, Contemporary Math., AMS..
11. M. Morishita, Milnor invariants and l-class groups, in Geometry and Dynamics of Groups and Spaces, In Memory of Alexander Reznikov, Progress in Math., Birkhauser, 589-603, 2008., Vol.265, 589-603, 2008.04.
12. M. Morishita, Y. Terashima, Geometry of polysymbols, Mathematical Research Letters, 15, 95-116, 2008., 2008.04.
13. M. Morishita, Y. Terashima, Arithmetic topology after Hida theory, Proceedings of `Intelligence of Low Dimensional Topology' in `Knots and Everything', Vol. 40, 213-222, 2006.07.
14. 森下昌紀, 素数と結び目の類似について, 数学, 日本数学会/岩波, vol.58, no.1 pp.40-63, 2006.01.
15. J. Hillman, D. Matei and M. Morishita, Pro-p link groups and p-homology groups, Contemporary Math., Vol. 416, 121-136, 2006.10.
16. M.Morishita, On the Alexander stratification in the deformation space of Galois characters, Kyushu J. Math., vol.60, pp.405-414, 2006.01.
17. M.Morishita, Milnor invariants and Massey products for prime numbers, Compositio Math., vol.140, pp.69-83, 2004.01.
18. M.Morishita, On capitulation problem for 3-manifolds, Proceedings "Galois theory and Modular forms", Developments in Math., 11, Kluwer Acad. Publ. pp.305-313, 2003.01.
19. M.Morishita, On certain analogies between knots and primes, J.Reine Angew. Math., vol.550, pp.141-167, 2002.01.
主要総説, 論評, 解説, 書評, 報告書等
1. 森下 昌紀, 平方剰余と結び目, 数学セミナー, 日本評論社, 2016.01.
2. 森下昌紀, 結び目と素数 -- 数論的位相幾何学 --, 「日本の現代数学」, 数学書房, 2010.06.
3. 森下昌紀, 数論と結び目不変量, 数理科学, サイエンス社, 2009.10.
4. 森下昌紀, あきらめないで, 数学の道しるべ5~研究者の道とは何か~, 数理科学, サイエンス社, 72-77, 2008.12.
5. 森下昌紀, 幾何学と数論--結び目群とGalois群の表現のモジュライ--., 数理科学, サイエンス社, 8月号, 2005.08.
6. 森下昌紀, 素数と結び目, 数学のたのしみ、日本評論社, 秋号, 2004.09.
7. 森下昌紀, 数論と3次元トポロジー, 数理科学、サイエンス社, 34-40, 2003.06.
主要学会発表等
1. Masanori Morishita, Arithmetic topology in Ihara theory: Milnor invariants, Heisenberg coverings and triple power residue symbols, Profinite monodromy, Galois representations and Complex functions, in honor of Professor Yasutaka Ihara's 80th birthday, 2018.05.
2. Masanori Morishita, On 3-dimensional foliated dynamial systems and Hilbert reciprocity law, Arithmetic and Analysis in honor of Christopher Deninger's 60th birthday, Muenster University, Germany, 2018.04.
3. 森下昌紀, On local symbols and the reciprocity law for foliated dynamical systems on 3-manifolds, 代数的整数論とその周辺, 京都大学数理解析研究所, 2017.12.
4. Masanori Morishita, Milnor invariants in Ihara theory and triple power residue symbols, Low-dimensional Topology and Number Theory, Oberwolfach, Germany, 2017.08.
5. Masanori Morishita, On local symbols and the reciprocity law for foliated dynamical systems on 3-manifolds, Arithmetic Chern-Simons Theory, Leiden University, Holland, 2017.05, [URL].
6. Masanori Morishita, Arithmetic topology on deformations of knot group representations, Number Theory and Quantum Field Theory, CGP of IBS, 2016.08, [URL].
7. Masanori Morishita, Arithmetic topology in Ihara theory, Grothendieck-Teichmuller theory, Chern Institute, 2016.07.
8. Masanori Morishita, Arithmetic Milnor invariants and multiple power residue symbols in number fields, 代数的整数論とその周辺, 2014.12.
9. 森下 昌紀, Johnson-Kawazumi maps in non-Abelian Iwasawa theory, Workshop: Johnson homomorphisms, University of Tokyo, 2013.06.
10. 森下 昌紀, 結び目理論と整数論 -- 数論的位相幾何学, Encounter with Mathematics, 中央大学, 2013.05.
11. Masanori Morishita, Milnor invariants and Maass wave forms, Quantum Topology and Hyperbolic Geometry, Nha Trang, Vietnam, 2013.05.
12. Masanori Morishita, Johnson maps in non-Abelian Iwasawa theory, JAMI conference, In honor of Professor Takashi Ono, Johns Hopkins University,U.S.A, 2013.04.
13. 森下 昌紀, Johnson maps in non-Abelian Iwasawa theory, 早稲田大学整数論研究集会, 2013.03.
14. 森下 昌紀, Redei記号の多重化とMaass波動形式,
Johnson maps in non-Abelian Iwasawa theory, 北陸数論研究集会, 2012.12.
15. M. Morishita, Knots and Primes - An Introduction to Atithmetic Topology, Japan-Taiwan Joint Conference on Number Theory, 2012.09.
16. M. Morishita, Johnson maps in non-Abelian Iwasawa theory, Oberwolfach workshop "Low dimensional topology and number theory", 2012.08.
17. M. Morishita, Knots and Primes, Tata Institute of Fundamental Research, 2012.02.
18. 森下昌紀, 数論的位相幾何学と数論的場の理論, 代数学シンポジウム, 2011.08.
19. 森下昌紀, 結び目と素数 - 数論的位相幾何学入門, 仙台シンポジウム, 2011.08.
20. M. Morishita(Joint with Y. Terashima), The universal deformation and the associated homological invariants for hyperbolic knots
, Oberwolfach workshop, Low dimensional topology and number theory, 2010.08.
21. M. Morishita, Analogies between knot theory and number theory, Lectures at KAIST, 2010.02, [URL].
22. 森下昌紀, 結び目と素数 -- 双曲幾何と肥田理論の類似性について, 日本数学会幾何学分科会, 2009.03.
23. M. Morishita, Analogies between knot theory and number theory, Invited lectures at Mathematics Center, University of Heidelberg, 2008.11.
24. M. Morishita (Joint with Y. Terashima), Chern-Simons variation and Hida-Mazur theory, ``Low Dimensional Topology and Number Theory'', Banff, Canada, 2007.10.
25. M. Morishita(Joint with Y. Terashima), Chern-Simons variation and Hida-Mazur theory, Spectral Analysis in Geometry and Number Theory on Prof. Toshikazu Sunada's 60th birthday, 2007.08.
26. M. Morishita, Arithmetic Topology after Iwasawa-Hida theory, Geometry and Dynamics of Groups and Spcaces, Alexander Reznikov memorial conference, Max Planck Inst., 2006.09.
27. 森下昌紀, 結び目と素数の類似について, 日本数学会トポロジー分科会, 2006.03.
28. M.Morishita, Analogies between knots and primes, 3-manifolds and number fields, AMS National Meeting (No.983), Special Session "Primes and Knots", Baltimore, 2003.01.
29. M.Morishita, Number theory and 3-dimensional topology, JAMI conference, Baltimore, 2003, 2003.03, [URL].
30. M.Morishita, J.Hillman and D. Matei, Pro-$p$ link groups and $p$-homology groups, Workshop on Topology and Geometry, Hiroshima, 2003.04.
31. M. Morishita, Higher linking symbols, Conference on ``Analogies between number fields and function fields'', Netherland, 2004.04.
32. M.Morishita, and Y. Terashima, Geometry of polysymbols, Conference on Algebraic number theory and related topics, Kyoto, 2005.12.
学会活動
所属学会名
日本数学会
学会大会・会議・シンポジウム等における役割
2019.03~2019.03, Low dimensional topology and number theory XI, 主催者.
2018.03~2018.03, Low dimensional topology and number theory X, 主催者.
2009.03~2009.03, Low dimensional topology and number theory I, 主催者.
2010.03~2010.03, Low dimensional topology and number theory II, 主催者.
2011.03~2011.03, Low dimensional topology and number theory III, 主催者.
2012.03~2012.03, Low dimensional topology and number theory IV, 主催者.
2013.03~2013.03, Low dimensional topology and number theory V, 主催者.
2014.03.18~2014.03.21, Low dimensional topology and number theory VI, 主催者.
2015.03~2015.03, Low dimensional topology and number theory VII, 主催者.
2016.03~2016.03, Low dimensional topology and number theory VIII, 主催者.
2017.03~2017.03, Low dimensional topology and number theory IX, 主催者.
学術論文等の審査
年度 外国語雑誌査読論文数 日本語雑誌査読論文数 国際会議録査読論文数 国内会議録査読論文数 合計
2018年度      
2013年度      
2012年度      
その他の研究活動
海外渡航状況, 海外での教育研究歴
Muenster University, Germany, 2018.04~2018.04.
Leiden University, Holland.
Center of Geometry and Physics, Institute of Basic Science, Korea.
Chern Institute of Mathematics, China.
Nha Trang College of Education, Vietnam, 2013.05~2013.05.
Johns Hopkins University, UnitedStatesofAmerica, 2013.04~2013.04.
National Center for Theoretical Science, Taiwan, 2012.09~2012.09.
Mathematisches Forschungsinstitut Oberwolfach , Germany, 2012.08~2012.08.
University of Sydney, Australia.
University of Toronto, Canada.
Johns Hopkins University, UnitedStatesofAmerica.
Max Planck Institute, Germany.
Korea Institute for Advanced Study, Korea.
University of Heidelberg, Germany.
Korea Advanced Institute of Science and Technology, Korea.
Mathematisches Forschungsinstitut Oberwolfach, Germany.
Pusan University, Korea.
Tata Institute of Fundamental Research, India.
National Center for Theoretical Science, Taiwan.
研究資金
科学研究費補助金の採択状況(文部科学省、日本学術振興会)
2017年度~2020年度, 基盤研究(B), 代表, 数論的位相幾何学の深化と新展開.
2012年度~2015年度, 基盤研究(B), 代表, 数論的位相幾何学の発展と数論的場の理論.
2009年度~2011年度, 基盤研究(B), 代表, 数論的位相幾何学の発展と応用.
2007年度~2008年度, 基盤研究(C), 代表, 数論的位相幾何学の育成.
2005年度~2006年度, 基盤研究(C), 代表, 数論的位相幾何学の基礎づけと育成.
2003年度~2004年度, 基盤研究(C), 代表, 代数的整数論と3次元トポロジーの相互啓発的研究.
2001年度~2002年度, 基盤研究(C), 代表, 素数と結び目、代数体の数論と3次元トポロジーの類似・融合.

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