Hayano, Kenta

写真a

Affiliation

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

Position

Associate Professor

Related Websites

External Links

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

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

Academic Degrees 【 Display / hide

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

    Complete classification of genus-1 simplified broken Lefschetz fibrations

 

Research Areas 【 Display / hide

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

Research Keywords 【 Display / hide

  • Lefschetz fibration

  • Stable mapping

 

Papers 【 Display / hide

  • Stability of non-proper functions

    K Hayano

    Mathematica Scandinavica 128 ( 2 )  2022.06

    Accepted

     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  2021.01

    Accepted

  • 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.

  • Unchaining surgery and topology of symplectic 4-manifolds

    R. Inanc Baykur, Kenta Hayano, Naoyuki Monden

     2019.03

     View Summary

    We study a symplectic surgery operation we call unchaining, which effectively
    reduces the second Betti number and the symplectic Kodaira dimension at the
    same time. Using unchaining, we give novel constructions of symplectic
    Calabi-Yau surfaces from complex surfaces of general type, as well as from
    rational and ruled surfaces via the natural inverse of this operation.
    Combining the unchaining surgery with others, which all correspond to certain
    monodromy substitutions for Lefschetz pencils, we provide further applications,
    such as a complete resolution of a conjecture of Stipsicz on the existence of
    exceptional sections in Lefschetz fibrations, new constructions of exotic
    symplectic 4-manifolds, and inequivalent pencils of the same genera and the
    same number of base points on families of symplectic 4-manifolds. Meanwhile, we
    give a handy criterion for determining from the monodromy of a pencil whether
    its total space is spin or not.

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

Presentations 【 Display / hide

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

 

Courses Taught 【 Display / hide

  • TOPICS IN GEOMETRY A

    2022

  • MATHEMATICS 1B

    2022

  • MATHEMATICS 1A

    2022

  • INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

    2022

  • GRADUATE RESEARCH ON FUNDAMENTAL SCIENCE AND TECHNOLOGY 2

    2022

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Memberships in Academic Societies 【 Display / hide

  • 日本数学会, 

    2011.04
    -
    Present