KEIO RESEARCHERS INFORMATION SYSTEM

Career 【 Display / hide 】

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 】

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 】

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 】

Research Areas 【 Display / hide 】

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

Research Keywords 【 Display / hide 】

Research Keywords 【 Display / hide 】

• Lefschetz fibration

• Stable mapping

Books 【 Display / hide 】

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

Papers 【 Display / hide 】

Papers 【 Display / hide 】

• Realizing crosscap transpositions as monodromies of singular fibrations

  Kenta Hayano

   2026.05

  　View Summary

  We introduce a new type of singularity for smooth maps from $4$-manifolds to surfaces, called an $M$-singularity, whose critical locus is a circle contained in a single fiber. We show that the monodromy around an $M$-singularity is a crosscap transposition in the mapping class group of a non-orientable surface. We also introduce $M$-fibrations, namely smooth maps whose singularities consist only of $M$-singularities, and prove that relations among crosscap transpositions give rise to such fibrations on non-orientable $4$-manifolds. We then study handle decompositions associated with $M$-fibrations and their orientation double coverings. In particular, we describe the attaching circles and framings of the two $2$-handles arising from the orientation double cover of an $M$-singularity. Using this description, we construct a closed non-orientable $4$-manifold which admits an $M$-fibration but admits no Lefschetz fibration. We further discuss singularity-theoretic properties of the local model of an $M$-singularity, namely its infinite $\mathcal{A}_e$-codimension and an explicit stable perturbation.

• 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.

  • Access to Document (DOI)

• 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.
  

  • Access to Document (DOI)

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

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

• 数学の論文が出版されるまで

  Hayano, Kenta

  新版 窮理図解 (慶應義塾大学理工学部)   ( 35 )  2022.11

• Getting a math paper published

  Hayano, Kenta

  New Kyurizukai (Faculty of Science and Technology, Keio University)   ( 35 )  2022.11

• Study of low-dimensional symplectic manifolds in combinatorial ways

  Hayano, Kenta

  科学研究費補助金研究成果報告書 2022

• Topology of stable mappings and diagrams of four-manifolds

  Hayano, Kenta

  科学研究費補助金研究成果報告書 2017

Presentations 【 Display / hide 】

Presentations 【 Display / hide 】

• Combinatorial construction of symplectic 6-manifolds via bifibration structures

  早野　健太

  [Domestic presentation]  接触構造、特異点、微分方程式及びその周辺, 

  2026.01

  , 

  Oral presentation (invited, special)

• Constraint qualification for generic constraint map-germs in optimization problems

  早野　健太

  [Domestic presentation]  可微分写像の特異点論とその応用, 

  2025.11

  , 

  Oral presentation (general)

• Constraint qualification for generic parameter families of constraints in optimization

  早野　健太

  九州大学トポロジーセミナー, 

  2025.11

  , 

  Oral presentation (invited, special)

• Combinatorial construction of symplectic 6-manifolds via bifibration structures

  早野　健太

  [Domestic presentation]  北海道大学幾何学コロキウム, 

  2025.10

  , 

  Oral presentation (invited, special)

• Combinatorial construction of symplectic 6-manifolds via bifibration structures

  早野　健太

  [Domestic presentation]  東京科学大学トポロジーセミナー, 

  2025.07

  , 

  Oral presentation (invited, special)

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Research Projects of Competitive Funds, etc. 【 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 】

Courses Taught 【 Display / hide 】

• MATHEMATICS 1B

  2026

• INDEPENDENT STUDY ON FUNDAMENTAL SCIENCE AND TECHNOLOGY

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY F

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY C

  2026

• MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY E

  2026

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Memberships in Academic Societies 【 Display / hide 】

Memberships in Academic Societies 【 Display / hide 】

• 日本数学会, 

  2011.04

  -

  Present