Hayano, Kenta

写真a

Affiliation

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

Position

Associate Professor

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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 】

  • 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.

  • On diagrams of simplified trisections and mapping class groups

    K Hayano

    Osaka Journal of Mathematics 57 (1), 17-37 (Osaka Journal of Mathematics)  57 ( 1 ) 17 - 37 2020.01

    ISSN  00306126

    　View Summary

    A simplified trisection is a trisection map on a 4–manifold such that, in its critical value set, there is no double point and cusps only appear in triples on innermost fold circles. We give a necessary and sufficient condition for a 3–tuple of systems of simple closed curves in a surface to be a diagram of a simplified trisection in terms of mapping class groups. As an application of this criterion, we show that trisections of spun 4–manifolds due to Meier are diffeomorphic (as trisections) to simplified ones. Baykur and Saeki recently gave an algorithmic construction of a simplified trisection from a directed broken Lefschetz fibration. We also give an algorithm to obtain a diagram of a simplified trisection derived from their construction.

  • Topology of Pareto sets of strongly convex problems

    N Hamada, K Hayano, S Ichiki, Y Kabata, H Teramoto

    SIAM Journal on Optimization 30 (3), 2659-2686 (SIAM Journal on Optimization)  30 ( 3 ) 2659 - 2686 2020

    ISSN  10526234

    　View Summary

    A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to the Pareto set and front of a subproblem that treats a subset of objective functions. In this paper, we show that strongly convex problems are simplicial under a mild assumption on the ranks of the differentials of the objective mappings. We further prove that one can make any strongly convex problem satisfy the assumption by a generic linear perturbation, provided that the dimension of the source is sufficiently larger than that of the target. We demonstrate that the location problems, a biological modeling, and the ridge regression can be reduced to multiobjective strongly convex problems via appropriate transformations preserving the Pareto ordering and the topology.

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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 】

  • BACHELOR'S THESIS

    2025

  • FOUNDATION FOR MATHEMATICAL SCIENCE 1 AND EXERCISE

    2025

  • MATHEMATICS 1B

    2025

  • MATHEMATICS 1A

    2025

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2025

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    2011.04
    -
    Present
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