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Deepening and new developments of arithmetic topology

Research Project

Project/Area Number 17H02837
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionKyushu University

Principal Investigator

Morishita Masanori  九州大学, 数理学研究院, 教授 (40242515)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥10,140,000 (Direct Cost: ¥7,800,000、Indirect Cost: ¥2,340,000)
Fiscal Year 2020: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2018: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Keywords結び目 / 素数 / 代数体 / 3次元多様体 / 数論的位相幾何学 / 数論的位相的場の理論 / Deninger葉層力学系 / 整数環 / 素イデアル / 場の理論
Outline of Final Research Achievements

My research achievements is concerned with deepening and new developments of arithmetic topology.The outline is as follows.(1) I solved the problem posed by Deninger jointly with J. Kim, T. Noda and Y. Terashima.Namely, we showed a dynamical analog of Hilbert reciprocity law for 3-dimensional foliated dynamical system. Moreover we gave a classification of 3-dimensiona foliated dynamical systems. We published the paper on this research and I gave invited talks at conferences in Germany and US etc. (2) I constructed an arithmetic analog of (2+1)-dimensional Dijkgraaf-Witten topological quantum field theory for number rings jointly with H. Hirano and J. Kim.We published the paper on this research and I gave invited online talks at various conference and seminars. I also held the workshop at Edinburgh ``Gauge fields in Arithmetic, Topology and Physics".

Academic Significance and Societal Importance of the Research Achievements

研究成果の学術的意義は、数論的位相幾何学という数学における新分野の創始とその深化および新展開である。社会的意義として、研究成果を査読付き国際誌に発表したこと、国内外で行われた国際研究集会で招待講演を行ったこと、さらに、本研究を契機として、2023年3月にスコットランドで「Gauge fields in Arithmetic, Topology and Physics」と題するコンファレンスを主催したこと、毎年国際研究集会「Low dimensional topology and number theory」を主催していることがあげられる。

Report

(5 results)
  • 2022 Final Research Report ( PDF )
  • 2020 Annual Research Report
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (22 results)

All 2023 2022 2021 2019 2018 2017 Other

All Int'l Joint Research (1 results) Journal Article (6 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 6 results) Presentation (12 results) (of which Int'l Joint Research: 8 results,  Invited: 12 results) Funded Workshop (3 results)

  • [Int'l Joint Research] ICMS(その他の国・地域(スコットランド))

    • Related Report
      2020 Annual Research Report
  • [Journal Article] On arithmetic Dijkgraaf-Witten theory2023

    • Author(s)
      J. Kim, H. Hirano, M. Morishita
    • Journal Title

      Communications in Number Theory and Physics

      Volume: 17 Pages: 1-61

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On adjoint homological Selmer modules for SL_2-representations of knot groups2022

    • Author(s)
      T. Kitayama, M. Morishita, R. Tange, Y. Terashima
    • Journal Title

      Internaational Mathematical Research Notices

      Volume: rnac255

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] On 3-dimensional foliated dynamical systems and Hilbert type reciprocity law,2021

    • Author(s)
      J. Kim, M. Morishita, T. Noda, Y. Terashima
    • Journal Title

      Muenster Journal of Mathematics,

      Volume: 14 Pages: 323-348

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Arithmetic topology in Ihara theory II: Milnor invariants, dilogarithmic Heisenberg coverings and triple power residue symbols2019

    • Author(s)
      Hirano Hikaru、Morishita Masanori
    • Journal Title

      Journal of Number Theory

      Volume: 198 Pages: 211-238

    • DOI

      10.1016/j.jnt.2018.10.010

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On mod 3 triple Milnor invariants and triple cubic residue symbols in the Eisenstein number field2018

    • Author(s)
      Amano Fumiya、Mizusawa Yasushi、Morishita Masanori
    • Journal Title

      Research in Number Theory

      Volume: 4 Issue: 1 Pages: 1-29

    • DOI

      10.1007/s40993-018-0100-7

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On certain $L$-functions for deformations of knot group representations2017

    • Author(s)
      Kitayama Takahiro、Morishita Masanori、Tange Ryoto、Terashima Yuji
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 370 Issue: 5 Pages: 3171-3195

    • DOI

      10.1090/tran/7037

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Symbols on 3-manifolds and conformal field theory2023

    • Author(s)
      Masanori Morishita
    • Organizer
      ICMS, Edinburgh, Workshop“Gauge Fields in Arithmetic, Topology and Physics”,
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Arithmetic topology and arithmetic TQFT2022

    • Author(s)
      Masanori Morishita
    • Organizer
      Feza Guersey Institute, Higher Structures Seminar
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] Arithmetic topology and Arithmetic TQFT2022

    • Author(s)
      Masanori Morishita
    • Organizer
      Muenster University, Seminar
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On arithmetic Dijkgraaf-Witten theory2021

    • Author(s)
      森下昌紀
    • Organizer
      10th Pan Asian Number Theory Cnference
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On arithmetic Dijkgraaf-Witten theory2021

    • Author(s)
      Masanori Morishita
    • Organizer
      Institute of Mathematics of the Romanian Academy, Geometric Method in Algabra and Topology Seminar
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On arithmetic topology and arithmetic Dijkgraaf-Witten theory2021

    • Author(s)
      Masanori Morishita
    • Organizer
      東京大学カブリ数物連携宇宙機構, Mathematics - String Seminar
    • Related Report
      2020 Annual Research Report
    • Invited
  • [Presentation] On 3-dimensional foliated dynamical systems and Hilbert type reciprocity law2019

    • Author(s)
      Masanori Morishita
    • Organizer
      JAMI conference, Johns Hopkins University
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On 3-dimensional foliated dynamical systems and Hilbert reciprocity law2019

    • Author(s)
      Masanori Morishita
    • Organizer
      Arithmetic and Analysis on the occasion of Deninger's 60th birthday
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Arithmetic topology in Ihara theory: Milnor invariants, Heisenberg covers and triple power residue symbols2019

    • Author(s)
      Masanori Morishita
    • Organizer
      Profinite monodromy, Galois representations, and Complex functions in honor of Professor Yasutaka Ihara's 80th birthday
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On 3-dimensional foliated dynamical systems and Hilbert reciprocity law2018

    • Author(s)
      Masanori Morishita
    • Organizer
      Arithmetic and Analysis in honor of Deninger's 60th birthday
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On local symbols and the reciprocity law for foliated dynamical systems on 3-manifolds2017

    • Author(s)
      Masanori Morishita
    • Organizer
      Workshop on Arithmetic Chern-Simons Theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Milnor invariants in Ihara theory and triple power residue symbols2017

    • Author(s)
      Masanori Morishita
    • Organizer
      Low dimensional topology and number theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] Low dimensional topology and number theory XIII2021

    • Related Report
      2020 Annual Research Report
  • [Funded Workshop] Low dimensional topology and number theory XI, Osaka University2019

    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] Low dimensional topology and number theory X2018

    • Related Report
      2017 Annual Research Report

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Published: 2017-04-28   Modified: 2024-01-30  

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