Morifuji, Takayuki

写真a

Affiliation

Faculty of Economics (Hiyoshi)

Position

Professor
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Career 【 Display / hide 】

  • 1998.04
    -
    2001.03

    JSPS Research Fellowships for Young Scientists, PD

  • 2001.04
    -
    2003.02

    Tokyo University of Agriculture & Technology, Faculty of Engineering, Senior Assistant Professor

  • 2003.03
    -
    2012.03

    Tokyo University of Agriculture & Technology, Faculty of Engineering, Associate Professor

  • 2012.04
    -
    Present

    Keio University, Faculty of Economics, Professor

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Academic Background 【 Display / hide 】

  • 1993.03

    Keio University, Faculty of Science and Technology

    University, Graduated

  • 1995.03

    Tokyo Institute of Technology, Graduate School of Science and Technology

    Graduate School, Completed, Master's course

  • 1998.03

    The University of Tokyo, Graduate School of Mathematical Sciences

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 博士（数理科学）, The University of Tokyo, Coursework, 1998.03

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Research Areas 【 Display / hide 】

  • Natural Science / Geometry

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Books 【 Display / hide 】

  • Handbook of Group Actions (Vol. I) ALM 31

    MORIFUJI Takayuki, Higher Education Press and International Press, 2015.03

    Scope: 527-576

  • Twisted Alexander invariants

    Kitano Teruaki, Goda Hiroshi, MORIFUJI Takayuki, The Mathematical Society of Japan, 2006.07

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Papers 【 Display / hide 】

  • TWISTED ALEXANDER POLYNOMIALS ON MANGUM-SHANAHAN CURVES

    Morifuji T., Tran A.T.

    Osaka Journal of Mathematics 61 ( 4 ) 591 - 600 2024.10

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  00306126

    　View Summary

    Mangum and Shanahan construct a complex curve of irreducible SL3 (C)-representations of the fundamental group of a once-punctured torus bundle over the circle. In this paper, we provide an explicit formula for the twisted Alexander polynomial of a once-punctured torus bundle with tunnel number one associated with the Mangum-Shanahan representations. As a corollary, we exhibit the interesting phenomenon that the Reidemeister torsion of the complement of the figure-eight knot is constant on the curve.

  • A VOLUME PRESENTATION OF A FIBERED KNOT

    Goda H., Morifuji T.

    Tohoku Mathematical Journal 76 ( 3 ) 423 - 443 2024.09

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  00408735

    　View Summary

    In this paper, we provide a volume presentation of a hyperbolic fibered knot using the Bell polynomials. More precisely, we show that the hyperbolic volume of a fibered knot can be expressed in terms of the traces of powers of a monodromy matrix. We also show that the hyperbolic volume of the figure-eight knot is obtained by the asymptotics of a positive integer sequence consisting of the special values of the twisted Alexander invariants.

  • Simple Hurwitz groups and eta invariant

    Morifuji T.

    Journal of the Mathematical Society of Japan (Journal of the Mathematical Society of Japan)  76 ( 1 ) 217 - 228 2024

    Research paper (scientific journal), Single Work, Accepted,  ISSN  00255645

    　View Summary

    A Hurwitz group is a conformal automorphism group of a compact Riemann surface with precisely 84(g − 1) automorphisms, where g is the genus of the surface. Our starting point is a result on the smallest Hurwitz group PSL(2, F7) which is the automorphism group of the Klein surface. In this paper, we generalize it to various classes of simple Hurwitz groups and discuss a relationship between the surface symmetry and spectral asymmetry for compact Riemann surfaces. To be more precise, we show that the reducibility of an element of a simple Hurwitz group is equivalent to the vanishing of the η-invariant of the corresponding mapping torus. Several wide classes of simple Hurwitz groups which include the alternating group, the Chevalley group and the Monster, which is the largest sporadic simple group, satisfy our main theorem.

  • Twisted Alexander polynomials, chirality, and local deformations of hyperbolic 3-cone-manifolds

    Hiroshi Goda, Takayuki Morifuji

    Annales Mathématiques Blaise Pascal (The Laboratoire de Mathématiques Blaise Pascal (UMR 6620-CNRS) of the Université Clermont Auvergne)  30 ( 1 ) 75 - 95 2023

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  12591734

    　View Summary

    In this paper, we discuss a relationship between the chirality of knots and higher-dimensional twisted Alexander polynomials associated with holonomy representations of hyperbolic 3-cone-manifolds. In particular, we provide a new necessary condition for a knot, that appears in a hyperbolic 3-cone-manifold of finite volume as a singular set, to be amphicheiral. Moreover, we can detect the chirality of hyperbolic twist knots, according to our criterion, using low-dimensional irreducible representations.

  • On a theorem of Friedl and Vidussi

    Morifuji T., Suzuki M.

    International Journal of Mathematics (International Journal of Mathematics)  33 ( 13 )  2022.11

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  0129167X

    　View Summary

    A theorem of Friedl and Vidussi says that any 3-manifold N and any non-fibered class in H1(N;Z) there exists a representation such that the corresponding twisted Alexander polynomial is zero. However, it seems that no concrete example of such a representation is known so far. In this paper, we provide several explicit examples of non-fibered knots and their representations with zero twisted Alexander polynomial.

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 双曲絡み目のパラボリック表現とねじれアレキサンダー多項式に関する研究

    2021.04
    -
    2025.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  • 双曲的トーション多項式と絡み目のDFJ予想に関する研究

    2017.04
    -
    2023.03

    Grant-in-Aid for Scientific Research, Research grant, Principal investigator

  • 双曲結び目のDunfield-Friedl-Jackson予想に関する研究

    2014.04
    -
    2018.03

    Grant-in-Aid for Scientific Research, Takayuki Morifuji, Research grant, Principal investigator

  • 結び目群の指標代数多様体を用いたファイバー性と種数の研究

    2011.04
    -
    2015.03

    Grant-in-Aid for Scientific Research, Research grant, Principal investigator

  • A study on the moduli space of representations and the twisted Alexander invariant

    2008.04
    -
    2011.03

    Grant-in-Aid for Scientific Research, Research grant, Principal investigator

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Awards 【 Display / hide 】

  • Takebe Prize

    MORIFUJI Takayuki, 2000.09, The Mathematical Society of Japan, A study of secondary characteristic classes of the mapping class group

    Type of Award： Award from Japanese society, conference, symposium, etc.

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Memberships in Academic Societies 【 Display / hide 】

  • The Mathematical Society of Japan

    　
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