Hayano, Kenta

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics ( Yagami )

Position

Associate Professor

E-mail Address

E-mail address

Related Websites

External Links
Scopus Paper Info  
Paper Count: 19 Citation Count: 85 h-index: 6

Click to view the Scopus page. The data was downloaded from Scopus API in April 26, 2026, via http://api.elsevier.com and http://www.scopus.com .

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Career 【 Display / hide 】

  • 2013.11
    -
    2016.03

    Hokkaido University, 理学研究院, 助教

  • 2016.04
    -
    2020.03

    Keio University, 理工学部, 専任講師

  • 2020.04
    -
    Present

    Keio University, 理工学部, 准教授

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Academic Background 【 Display / hide 】

  • 2006.04
    -
    2010.03

    Osaka University, 理学部, 数学科

    University, Graduated

  • 2010.04
    -
    2012.03

    Osaka University, 理学研究科, 数学専攻

    Graduate School, Completed, Master's course

  • 2012.04
    -
    2013.03

    Osaka University, 理学研究科, 数学専攻

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 博士（理学）, Osaka University, Coursework, 2013.03

    Complete classification of genus-1 simplified broken Lefschetz fibrations

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Research Areas 【 Display / hide 】

  • Natural Science / Geometry (Low-dimensional topology, Singularity theory)

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Research Keywords 【 Display / hide 】

  • Lefschetz fibration

  • Stable mapping

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Books 【 Display / hide 】

  • 4次元多様体とファイバー構造 ―レフシェッツ束のトポロジー―

    遠藤　久顕，早野　健太, 共立出版, 2024.06,  Page： 226

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Papers 【 Display / hide 】

  • Constraint Qualification for Generic Parameter Families of Constraints in Optimization

    N Hamada, K Hayano, H Teramoto

    arXiv preprint arXiv:2510.02381  2025.09

    　View Summary

    Constraint qualifications (CQs) are central to the local analysis of constrained optimization. In this paper, we completely determine the validity of the four classical CQs -- LICQ, MFCQ, ACQ, and GCQ -- for constraint map-germs that arise in generic four-parameter families. Our approach begins by proving that all four CQs are invariant under the action of the group $\mathcal{K}[G]$ and under the operation of reduction. As a consequence, the verification of CQ-validity for a generic constraint reduces to checking CQ-validity on the $\mathcal{K}[G]$-normal forms of fully reduced map-germs. Such normal forms have been classified in our recent work. In the present paper, we verify which CQs hold in each germ appearing in the classification tables from that work. This analysis provides a complete picture of the generic landscape of the four classical CQs. Most notably, we find that there exist numerous generic map-germs for which GCQ holds while all stronger CQs fail, showing that the gap between GCQ and the other qualifications is not an exceptional phenomenon but arises generically.

  • Combinatorial construction of symplectic 6-manifolds via bifibration structures

    K Hayano

    arXiv preprint arXiv:2501.04282  2025.01

    　View Summary

    A bifibration structure on a $6$-manifold is a map to either the complex projective plane $\mathbb{P}^2$ or a $\mathbb{P}^1$-bundle over $\mathbb{P}^1$, such that its composition with the projection to $\mathbb{P}^1$ is a ($6$-dimensional) Lefschetz fibration/pencil, and its restriction to the preimage of a generic $\mathbb{P}^1$-fiber is also a ($4$-dimensional) Lefschetz fibration/pencil. This object has been studied by Auroux, Katzarkov, Seidel, among others. From a pair consisting of a monodromy representation of a Lefschetz fibration/pencil on a $4$-manifold and a relation in a braid group, which are mutually compatible in an appropriate sense, we construct a bifibration structure on a closed symplectic $6$-manifold, producing the given compatible pair as its monodromies. We further establish methods for computing topological invariants of symplectic $6$-manifolds, including Chern numbers, from compatible pairs. Additionally, we provide an explicit example of a compatible pair, conjectured to correspond to a bifibration structure derived from the degree-$2$ Veronese embedding of the $3$-dimensional complex projective space. This example can be viewed as a higher-dimensional analogue of the lantern relation in the mapping class group of the four-punctured sphere. Our results not only extend the applicability of combinatorial techniques to higher-dimensional symplectic geometry but also offer a unified framework for systematically exploring symplectic $6$-manifolds.

  • Characterization of generic parameter families of constraint mappings in optimization

    N Hamada, K Hayano, H Teramoto

    arXiv preprint arXiv:2407.12333 28   104 - 147 2025.01

    ISSN  19492006

    　View Summary

    The purpose of this paper is to understand generic behavior of constraint functions in optimization problems relying on singularity theory of smooth mappings. To this end, we will focus on a subgroup of the Mather’s contact group, whose action to constraint map-germs preserves the corresponding feasible set-germs (i.e. the set consisting of points satisfying the constraints). We will classify map-germs with small stratum extended-codimensions with respect to the subgroup we introduce, and calculate the codimensions of the orbits by the subgroup of jets represented by germs in the classification lists and those of the complements of these orbits. Applying these results and a variant of the transversality theorem, we will show that families of constraint mappings whose germ at any point in the corresponding feasible set is equivalent to one of the normal forms in the classification list compose a residual set in the entire space of constraint mappings with at most four parameters. These results enable us to quantify genericity of given constraint mappings, and thus evaluate to what extent known test suites are generic.

  • Stability of non-proper functions

    K Hayano

    Mathematica Scandinavica 128 ( 2 ) 317 - 353 2022.06

    Accepted,  ISSN  00255521

    　View Summary

    The purpose of this paper is to give a sufficient condition for (strong)
    stability of non-proper smooth functions (with respect to the Whitney
    $C^\infty$-topology). We show that a Morse function is stable if it is
    end-trivial at any point in its discriminant, where end-triviality (which is
    also called local triviality at infinity) is a property concerning behavior of
    functions around the ends of the source manifolds. We further show that a Morse
    function $f:N\to \mathbb{R}$ is strongly stable (i.e. there exists a continuous
    mapping $g\mapsto (\Phi_g,\phi_g)\in\operatorname{Diff}(N)\times
    \operatorname{Diff}(\mathbb{R})$ such that $\phi_g\circ g\circ \Phi_g =f$ for
    any $g$ close to $f$) if (and only if) $f$ is quasi-proper. This result yields
    existence of a strongly stable but not infinitesimally stable function.
    Applying our result on stability, we give a reasonable sufficient condition for
    stability of Nash functions, and show that any Nash function becomes stable
    after a generic linear perturbation.

  • Classification of genus-1 holomorphic Lefschetz pencils

    Noriyuki Hamada, Kenta Hayano

    Turkish Journal of Mathematics 45 (3), 1079-1119 45 ( 3 ) 1079 - 1119 2021.01

    Accepted,  ISSN  13000098

    　View Summary

    In this paper, we classify relatively minimal genus-1 holomorphic Lefschetz pencils up to smooth isomorphism. We first show that such a pencil is isomorphic to either the pencil on P1× P1of bidegree (2, 2) or a blow-up of the pencil on P2of degree 3, provided that no fiber of a pencil contains an embedded sphere (note that one can easily classify genus-1 Lefschetz pencils with an embedded sphere in a fiber). We further determine the monodromy factorizations of these pencils and show that the isomorphism class of a blow-up of the pencil on P2of degree 3 does not depend on the choice of blown-up base points. We also show that the genus-1 Lefschetz pencils constructed by Korkmaz-Ozbagci (with nine base points) and Tanaka (with eight base points) are respectively isomorphic to the pencils on P2and P1× P1above, in particular these are both holomorphic.

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

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

  • 曲面の写像類群による高次元シンプレクティック多様体の組み合わせ的研究手法の確立

    2022.04
    -
    Present

    No Setting, Principal investigator

  • 組み合わせ的手法による低次元シンプレクティック多様体の研究

    2017.04
    -
    Present

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Principal investigator

  • Topology of stable mappings and diagrams of four-manifolds

    2014.04
    -
    2018.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Principal investigator

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Courses Taught 【 Display / hide 】

  • MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY D

    2026

  • GEOMETRY 1 AND ITS EXERCISE

    2026

  • DOCTORAL RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES

    2026

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 1

    2026

  • GRADUATE RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES 2

    2026

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    2011.04
    -
    Present
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