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.

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**

**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)

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

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