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Masanori Morishita Last modified date:2018.06.21



Graduate School
Undergraduate School


E-Mail
Fax
092-802-4487
Academic Degree
Ph. D
Field of Specialization
Arithmetic Topology
Outline Activities
Summary of the research: Study of Arithmetic Topology:
I am working on the interaction between number theory and 3-dimensional topology from the view point of the analogy between primes and knots. I have obtained foundational results in arithmetic topology.
Research
Research Interests
  • Arithmetic Topology
    keyword : Knots and Primes
    1998.12.
Academic Activities
Books
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..
Papers
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Junhyeung Kim, Hisatoshi Kodani, Masanori Morishita, Nilpotent class field theory for manifolds, Proceedings of Japan Academy, 89, 1, 15-19, 2013.01.
8. Masanori Morishita, Analogies between knots and primes, 3-manifolds and number rings , Sugaku expositions, 23, 1, 1--30, 2010.07.
9. 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..
10. 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.
11. M. Morishita, Y. Terashima, Geometry of polysymbols, Mathematical Research Letters, 15, 95-116, 2008., 2008.04.
12. 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.
13. J. Hillman, D. Matei and M. Morishita, Pro-p link groups and p-homology groups, Contemporary Math., Vol. 416, 121-136, 2006.10.
14. M.Morishita, On the Alexander stratification in the deformation space of Galois characters, Kyushu J. Math., vol.60, pp.405-414, 2006.01.
15. M.Morishita, Milnor invariants and Massey products for prime numbers, Compositio Math., vol.140, pp.69-83, 2004.01.
16. 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.
17. M.Morishita, On certain analogies between knots and primes, J.Reine Angew. Math., vol.550, pp.141-167, 2002.01.
Presentations
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, [URL].
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, [URL].
3. Masanori Morishita, Milnor invariants in Ihara theory and triple power residue symbols, Low-dimensional Topology and Number Theory, Oberwolfach, Germany, 2017.08.
4. 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], We show some fundamental results concerning $3$-dimensional foliated dynamical systems (FDS$^3$ for short) introduced by Deninger. Firstly, we classify FDS$^3$'s into three types. For each type, we determine the structures of the underlying $3$-manifold and leaves and construct concrete examples of FDS$^3$'s which have countably infinitely many closed orbits. Secondly, as an application of our classification, we show the existence of FDS$^3$-meromorphic functions. Finally, by using the integration theory for smooth Deligne cohomology, we introduce geometric analogues of local symbols and show a Hilbert type reciprocity law for an FDS$^3$. Our results answer the question posed by Deninger..
5. Masanori Morishita, Arithmetic topology on deformations of knot group representations, Number Theory and Quantum Field Theory, CGP of IBS, 2016.08, [URL], Following after the deformation theory of Galois representations, we will discuss deformations for knot group representations and associated invariants..
6. Masanori Morishita, Arithmetic topology in Ihara theory, Grothendieck-Teichmuller theory, Chern Institute, 2016.07, Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further, following after some issues and their inter-relations in the theory of braids and links such as Milnor invariants, Johnson homomorphisms, Magnus-Gassner cocycles and Alexander invariants, and study relations with arithmetic in Ihara theory. .
7. 森下 昌紀, Johnson-Kawazumi maps in non-Abelian Iwasawa theory, Workshop: Johnson homomorphisms, University of Tokyo, 2013.06.
8. Masanori Morishita, Milnor invariants and Maass wave forms, Quantum Topology and Hyperbolic Geometry, Nha Trang, Vietnam, 2013.05.
9. 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.
10. M. Morishita, Analogies between knots and primes,
3-manifolds and number fields,
AMS National Meeting (No.983), Baltimore, Special Session
"Primes and Knots", 2003, January..
11. M. Morishita, Number theory and 3-dimensional topology,
Japan-U.S Mathematical Institute, Baltimore, U.S.A.,
JAMI conference, 2003, March., [URL].
12. M. Morishita, Higher linking symbols,
Conference on "Analogies between number fields and
function fields", Texel Island (The Netherlands),
2004, April..
13. M. Morishita, Higher linking symbols,
Conference on "Analogies between number fields and
function fields", Texel Island (The Netherlands),
2004, April..
14. M. Morishita and Y. Terashima, Geometry of polysymbols,
Conference on Algebraic number theory and related topics,
RIMS, Kyoto Univ., 2005, December..
Educational
Educational Activities
Educational Activities
 
Linear algebra, Calculus, Algebra, Number Theory, Topology, Complex function theory
Intensive Lectures: Kyushu Univ. (2002), Kyoto Univ.(2005), Tohoku Univ.(2007),
Tokyo Univ.(2007), University of Heidelberg(2008),
KAIST(2009), Busan University(2010)
Other Educational Activities
  • 2011.11.
Social
Professional and Outreach Activities
Annual meeting of AMS, Special Session`Primes and Knots' Organizer(2003)
Japan-U.S Mathematical Institute Conference `Primes and Knots' Organizer(2003)
Lectures at high schools in Ishikawa and Fukui (2003, 2004)wa-ku.