Updated on 2026/03/10
I am interested in Singularity Theory of differentiable mappings.
Moreover, for the purpose of applications of mathematics to industry, I am also studying Multiobjective optimization from the viewpoint of Topology and Singularity Theory.
Doctor of Philosophy ( 2018.3 Yokohama National University )
可微分写像の特異点論
Mather theory
multiobjective optimization
distance-squared mapping
transversality theorem
ジェネリックな写像
stable mapping
structural stability problem
Singularity Theory of differentiable mappings
Natural Science / Geometry
Yokohama National University Graduate School of Environment and Information Sciences (Doctor course)
2016.4 - 2018.3
Yokohama National University Graduate School of Environment and Information Sciences (Master course)
2012.4 - 2014.3
Yokohama National University College of Engineering
2008.4 - 2012.3
Institute of Science Tokyo Department of Mathematical and Computing Science, School of Computing Assistant Professor
2024.10
Tokyo Institute of Technology Department of Mathematical and Computing Science, School of Computing Assistant Professor
2020.4 - 2024.9
Kyushu University Institute of Mathematics for Industry Research Fellow CPD of Japan Society for the Promotion of Science
2019.10 - 2020.3
Kyushu University Institute of Mathematics for Industry Research Fellow PD of Japan Society for the Promotion of Science
2019.4 - 2019.9
Yokohama National University Faculty of Environment and Information Sciences Research Fellow PD of Japan Society for the Promotion of Science
2018.4 - 2019.3
Yokohama National University Graduate School of Environment and Information Sciences Research Fellow DC1 of Japan Society for the Promotion of Science
2016.4 - 2018.3
Dai Nippon Printing Co., Ltd.
2014.4 - 2016.3
THE MATHEMATICAL SOCIETY OF JAPAN
Non-density of $C^0$-stable mappings on non-compact manifolds Reviewed
Shunsuke Ichiki
International Mathematics Research Notices ( 11 ) 9044 - 9053 2024
A refined transversality theorem on linear perturbations and its applications Reviewed
Shunsuke Ichiki
Journal of the Mathematical Society of Japan 76 ( 3 ) 739 - 754 2024
Non-density of stable mappings on non-compact manifolds Reviewed
Shunsuke Ichiki
Pure and Applied Mathematics Quarterly 19 ( 2 ) 515 - 527 2023
A Refined Version of Parametric Transversality Theorems Reviewed
Shunsuke Ichiki
The Journal of Geometric Analysis 32 ( 9 ) 2022
Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency Reviewed
Naoki Hamada, Shunsuke Ichiki
Journal of Optimization Theory and Applications 192 ( 1 ) 248 - 270 2022
Simpliciality of strongly convex problems Reviewed
Naoki HAMADA, Shunsuke ICHIKI
Journal of the Mathematical Society of Japan 73 ( 3 ) 965 - 982 2021
Generic distance-squared mappings on plane curves Reviewed
Shunsuke Ichiki
Hiroshima Mathematical Journal 51 ( 1 ) 65 - 76 2021
All unconstrained strongly convex problems are weakly simplicial.
Yusuke Mizota, Naoki Hamada, Shunsuke Ichiki
CoRR abs/2106.12704 2021
Topology of Pareto Sets of Strongly Convex Problems Reviewed
Naoki Hamada, Kenta Hayano, Shunsuke Ichiki, Yutaro Kabata, Hiroshi Teramoto
SIAM Journal on Optimization 30 ( 3 ) 2659 - 2686 2020
Characterization of generic transversality Reviewed
Shunsuke Ichiki
Bulletin of the London Mathematical Society 51 978 - 988 2019
Preservation of immersed or injective properties by composing generic generalized distance-squared mappings Reviewed
Shunsuke Ichiki, Takashi Nishimura
Springer Proceedings in Mathematics and Statistics 222 537 - 547 2018
Transversality theorems on generic linearly perturbed mappings Reviewed
Shunsuke Ichiki
Methods and Applications of Analysis 25 ( 4 ) 323 - 336 2018
Generic linear perturbations Reviewed
Shunsuke Ichiki
Proceedings of the American Mathematical Society 146 4981 - 4991 2018
Composing generic linearly perturbed mappings and immersions/injections Reviewed
Shunsuke Ichiki
Journal of the Mathematical Society of Japan 70 ( 3 ) 1165 - 1184 2018
Generalized distance-squared mappings of $\mathbb{R}^{n+1}$ into $\mathbb{R}^{2n+1}$ Reviewed
S. Ichiki, T. Nishimura
REAL AND COMPLEX SINGULARITIES 675 121 - 132 2016
Generalized distance-squared mappings of the plane into the plane Reviewed
S. Ichiki, T. Nishimura, R. Oset Sinha, M. A. S. Ruas
ADVANCES IN GEOMETRY 16 ( 2 ) 189 - 198 2016
Recognizable classification of Lorentzian distance-squared mappings Reviewed
Shunsuke Ichiki, Takashi Nishimura
JOURNAL OF GEOMETRY AND PHYSICS 81 62 - 71 2014
Distance-squared mappings Reviewed
Shunsuke Ichiki, Takashi Nishimura
TOPOLOGY AND ITS APPLICATIONS 160 ( 8 ) 1005 - 1016 2013
これからの集合と位相
梅原 雅顕, 一木 俊助
裳華房, 330頁, 2022.11 （ ISBN:9784785315962 ）
Singularity theory and its applications to strongly convex multiobjective optimization problems
Shunsuke Ichiki
MI Lecture Note 95, Institute of Mathematics for Industry, Kyushu University, ISSN 2188-1200, 103 - 107 2024
Around generic linear perturbations
Shunsuke Ichiki
RIMS Kokyuroku 2085 36 - 42 2018
Non-injectivity of generalized distance-squared mappings of equidimensional cases
Shunsuke Ichiki
RIMS Kokyuroku 2049 173 - 175 2017
AROUND DISTANCE-SQUARED MAPPINGS (Singularity theory of differential maps and its applications)
Shunsuke Ichiki, Takashi Nishimura
RIMS Kokyuroku 1948 28 - 37 2015
Singularity theory and its applications to strongly convex multiobjective optimization problems (Mini-course, 45min×3) Invited International conference
Shunsuke Ichiki
WORKSHOP ON MATHEMATICS FOR INDUSTRY, Warsaw, September, 25, 27 and 29, 2023
やわらかい図形の観点から見る多目的最適化（40分講演を2回）
一木 俊助
東京科学大学理工学系オープンキャンパス2025，東京科学大学 大岡山キャンパス (ライブ配信あり), 2025.8
Characterization of generic transversality International conference
Shunsuke Ichiki
6th International Workshop on Singularities in Generic Geometry and Applications, València VI 2019.10
On strongly convex multi-objective optimization problems of class C^1
Shunsuke Ichiki
MSJ Autumn Meeting 2019 2019.9
強凸多目的最適化問題への特異点論の応用 Invited
一木 俊助
九州大学マス・フォア・インダストリ研究所共同利用・共同研究 一般研究-研究集会(I) 令和2年度採択分「進化計算の数理」, Zoom, 2021.9
横断性定理の精密化とその応用 Invited
一木 俊助
埼玉大学木曜セミナー（幾何）, Zoom, 2020.11
A refinement of transversality theorems
Shunsuke Ichiki
16th International Workshop on Real and Complex Singularities - celebrating 30 years, by recorded videos 2020.11
横断性定理の精密化とその応用 Invited
一木 俊助
東工大幾何セミナー（東工大トポロジーセミナーと合同), Zoom 2020.7
Generalized distance-squared mappings of the plane into the plane and of $\mathbb{R}^{n+1}$ into $\mathbb{R}^{2n+1}$ International conference
S. Ichiki, T. Nishimura, R. Oset Sinha, M. A. S. Ruas
14th International Workshop on Real and Complex Singularities（Sao Carlos, Brazil） 2016.7
Generalized distance-squared mappings of the plane into the plane International conference
Shunsuke Ichiki
Workshop on Singularity Theory（Universidade Federal Fluminense – Niteroi, Brazil） 2014.1
Distance-squared mappings
Shunsuke Ichiki
2013.3
An application of singularity theory to strongly convex multiobjective optimization problems Invited
Shunsuke Ichiki
Differential Geometry with Udo, Tokyo Institute of Technology, 2023.5
Non-density of stable mappings on non-compact manifolds Invited
The 15th Mathematical Society of Japan - Seasonal Institute "Deepening and Evolution of Applied Singularity Theory", Zoom, 2022.11
Generalized Thom's jet transversality theorem applicable to subspaces and its applications
Shunsuke Ichiki
Singularity Theory and its related fields 2024.6
An improvement of the fundamental transversality lemma
Shunsuke Ichiki
2017.11
Generic linear perturbations
Shunsuke Ichiki
2017.9
Generic linear perturbations
Shunsuke Ichiki
2017.8
Preservation of immersed or injective properties by composing generic generalized distance-squared mappings
Shunsuke Ichiki
2016.12
Generalized distance-squared mappings of $\mathbb{R}^{n+1}$ into $\mathbb{R}^{2n+1}$
2016.9
Generalized distance-squared mappings and the future projects
Shunsuke Ichiki
2016.8
Generic linear perturbations International conference
Shunsuke Ichiki
SINGULARITIES IN GENERIC GEOMETRY AND ITS APPLICATIONS: VALENCIA V（Facultad de Ciencias UNAM, Mexico City） 2017.8
An improvement of the fundamental transversality lemma and its applications
Shunsuke Ichiki
2017.6
Composing generic linearly perturbed mappings and immersions/injections
Shunsuke Ichiki
2017.3
Generic linear perturbations
Shunsuke Ichiki
2017.1
$C^1$級強凸多⽬的最適化問題と特異点論
一木 俊助
One day workshop リーマン幾何学，粗幾何学，特異点 2019.11
Strongly convex multi-objective optimization problems and Singularity Theory
Shunsuke Ichiki
Kyushu University Topology Seminar 2019.5
$C^1$級強凸写像のパレート解集合のトポロジー
一木 俊助
東京学芸大学小研究集会 幾何学と特異点 ２０１９ 2019.3
On transversality lemmas
Shunsuke Ichiki
2018.1
Generic linear perturbations International conference
Shunsuke Ichiki
International Conference on Singularity Theory and Dynamical Systems – in Memory of John Mather（Tsinghua Sanya International Mathematics Forum (TSIMF), Sanya, China） 2017.12
On transversality lemmas
Shunsuke Ichiki
2017.11
An improvement of the fundamental transversality lemma
Shunsuke Ichiki
2017.11
一木 俊助
進化計算シンポジウム2018（※特別企画第２部の後半にて講演），休暇村志賀島 （福岡市） 2018.12
多目的最適化におけるパレート集合と弱パレート集合の一致条件（※一木の担当箇所は「ある凸的な条件をもつ問題での一致性：凸解析によるアプローチ」）
一木 俊助, 濱田 直希氏, 早野 健太
理研AIPセミナー 2018.11
Characterization of generic transversality
Shunsuke Ichiki
2018.9
Generic distance-squared mappings on plane curves
Shunsuke Ichiki
2018.2
Transversality results and their applications Invited
Workshop on Surface Theory —UY60—, アットビジネスセンター横浜西口駅前, 2022.3
Global properties of differentiable mappings from the viewpoint of object recognition
Shunsuke Ichiki
Development of a mathematical theory on methods for recognizing contours and its applications to engineering 2019.8
Characterization of generic transversality International conference
Shunsuke Ichiki
Hyperplane arrangements and Japanese Australian workshop on Real and Complex Singularities, Memorial conference for Professor Stefan Papadima 2019.12
第３６回井上研究奨励賞
2019.12 公益財団法人井上科学振興財団
一木 俊助
Award for students in Graduate School of Environment and Information Sciences
2018.3 Yokohama National University
Shunsuke Ichiki
写像の特異点論における，ジェネリシティーの先駆的研究
Grant number：21K13786 2021.4 - 2025.3
日本学術振興会 科学研究費助成事業 若手研究 若手研究
一木 俊助
Authorship：Principal investigator
Grant amount：\2990000 （ Direct Cost: \2300000 、 Indirect Cost：\690000 ）
20世紀半ばに提出された「安定写像は写像空間内に稠密に存在するだろうか」という特異点論における一つの重要問題は，1970年代前半にジョン・マザー（1942-2017）の安定写像の一連の理論により，定義域多様体がコンパクトな場合においては，その稠密性の特徴づけが与えられた．定義域多様体がコンパクトでない場合については，その数年後の1979年にA. Dimcaが，終域が直線という特別な場合において調べ，その場合は安定写像は稠密には存在しないという結果を与えた．そして本年度申請者は，定義域多様体がコンパクトではない場合は，いつでも安定写像は非稠密になることを証明した．この結果と，上述のマザーの結果を合わせることによって，安定写像の稠密性問題は完全に特徴づけられたことになる．本結果についての論文は現在査読中である．
また，産学連携に関連する最適化の研究として，濱田直希氏（KLab株式会社），溝田裕介氏（九州産業大学）と共同で，可微分性を仮定しない強凸多目的最適化問題の最適解集合の位相的性質に関する研究を行った．本結果についての論文も現在査読中である．
安定写像の一般論の構築
Grant number：19J00650 2019.4 - 2020.3
日本学術振興会 科学研究費助成事業 特別研究員奨励費 特別研究員奨励費
一木 俊助
Authorship：Principal investigator
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
ルネ・トム（1923-2002）は，（弱）構造安定性問題という「（位相的）安定写像は写像空間内でいつ稠密に存在するか」という問題を提出し，いずれも1970年代前半にジョン・マザー（1942-2017）によって，定義域多様体がコンパクトの場合においては解決された．その数年後の1979年，A. Dimcaによって，定義域多様体がコンパクトでなく値域が直線という特殊な場合においては，安定写像は稠密には存在しないという結果が得られている．そして本年度私は，コンパクトでないn次元多様体からp次元ユークリッド空間（n<p）への写像全体の空間の中での位相的安定写像の非稠密性に関する結果を得た．
更には特異点論の，（産業との親和性の高い）多目的最適化理論への応用として，以前より研究していた強凸多目的最適化問題の最適解集合の位相的性質に関する共同研究が2019年度に一段落し，現在２本の論文（arXiv:1904.03615 及び arXiv:1912.09328）を査読付きジャーナルに投稿中である．
2019
九州大学マス・フォア・インダストリ研究所 若手研究_短期共同研究
一木 俊助
Authorship：Principal investigator Grant type：Competitive
JSPS KAKENHI Grant Number 16J06911
2016.4 - 2019.3
Shunsuke Ichiki
Authorship：Principal investigator Grant type：Competitive
Exercises in Set and Topology II
2022 Institution：Tokyo Institute of Technology
Linear Algebra I (Exercise part)
2022 Institution：Tokyo Institute of Technology
Algebra (Exercise part)
2022 Institution：Tokyo Institute of Technology
Linear Algebra I (Exercise part)
2021 Institution：Tokyo Institute of Technology
Algebra (Exercise part)
2021 Institution：Tokyo Institute of Technology
Exercises in Set and Topology II
2021 Institution：Tokyo Institute of Technology
Exercises in Set and Topology I
2020 Institution：Tokyo Institute of Technology
Algebra (Exercise part)
2020 Institution：Tokyo Institute of Technology
Exercises in Set and Topology II
2020 Institution：Tokyo Institute of Technology
研究集会「特異点論及びその周辺分野の深化と異分野への応用」，福岡工業大学FITホール (Zoomを利用したハイブリッド形式)
Role(s)： Planning, management, etc.
一木 俊助 (代表者)，福永 知則，本多 俊一， 2023.6
研究集会「位相幾何・微分幾何及びその周辺分野への特異点論の応用」(Zoomによるオンライン開催)
Role(s)： Planning, management, etc.
福永 知則 (代表者)，寺本 圭佑，一木 俊助， 2022.6
