Hayano, Kenta

 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

• 2010.04
-
2012.03

Osaka University, 理学研究科, 数学専攻

• 2012.04
-
2013.03

Osaka University, 理学研究科, 数学専攻

### 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

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

Accepted

• 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.

• 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.

• 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.

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

• Hayano, Kenta

科学研究費補助金研究成果報告書 2017

### Presentations 【 Display / hide 】

• HAYANO Kenta

Local and global study of singularity theory of differentiable maps (Kyoto University(RIMS)) ,

2017.11

Oral presentation (general)

• HAYANO Kenta

Four Dimensional Topology (大阪市立大学) ,

2017.11

Oral presentation (general)

• HAYANO Kenta

Boston University/Keio University workshop 2017 (Boston University) ,

2017.06

Oral presentation (general)

• Topology of holomorphic Lefschetz pencils on the four-torus

HAYANO Kenta

Branched Coverings, Degenerations, and Related Topics 2017 (Tohoku Gakuin University) ,

2017.03

Oral presentation (invited, special)

• Topology of Lefschetz pencils on symplectic Calabi-Yau 4-manifolds with positive b_1

HAYANO Kenta

リーマン面に関連する位相幾何学 (The University of Tokyo) ,

2016.09

Oral presentation (invited, special)

### 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

• 日本数学会,

2011.04
-
Present