Updated on 2024/07/28

Information

 

写真a

 
KUSAKABE YUTA
 
Organization
Faculty of Mathematics Division of Analysis Associate Professor
School of Sciences Department of Mathematics(Concurrent)
Graduate School of Mathematics Department of Mathematics(Concurrent)
Joint Graduate School of Mathematics for Innovation (Concurrent)
Title
Associate Professor
Contact information
メールアドレス
Profile
I am studying complex analysis and complex geometry, especially around the Oka principle, the homotopy principle in complex analysis, and Gromov ellipticity, the opposite of Kobayashi hyperbolicity. The Oka principle is a heuristic principle that analytic problems on Stein manifolds have only topological obstructions, which was extolled by Thom as “the most beautiful principle in analysis” when he visited Kyushu University. I have clarified the relationship between this analytic principle and ellipticity in complex geometry, and am currently studying the Oka principle from a broader perspective, including algebraic geometry and differential geometry.
External link

Degree

  • Doctor of Philosophy (Science)

Research History

  • 2020年12月 - 2024年3月 京都大学, 大学院理学研究科, 助教 2020年10月 - 2020年11月 大阪大学, 大学院理学研究科, 日本学術振興会特別研究員 (PD) 2018年4月 - 2020年9月 大阪大学, 大学院理学研究科, 日本学術振興会特別研究員 (DC1) 2017年4月 - 2018年3月 大阪大学, 大学院理学研究科, リサーチ・アシスタント

Research Interests・Research Keywords

  • Research theme:Complex Analysis, Complex Geometry

    Keyword:Oka principle, Oka manifold, Stein space, Gromov ellipticity

    Research period: 2024.4

Awards

  • 日本数学会賞建部賢弘奨励賞

    2020.9   日本数学会   岡多様体および楕円性に関する研究

Papers

  • Oka properties of complements of holomorphically convex sets Reviewed

    Yuta Kusakabe

    Annals of Mathematics   199 ( 2 )   899 - 917   2024.3

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.4007/annals.2024.199.2.7

  • Elliptic characterization and unification of Oka maps Reviewed

    Yuta Kusakabe

    Mathematische Zeitschrift   298 ( 3-4 )   1735 - 1750   2021.8

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00209-020-02661-y

  • Elliptic characterization and localization of Oka manifolds Reviewed

    Yuta Kusakabe

    Indiana University Mathematics Journal   70 ( 3 )   1039 - 1054   2021.7

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1512/iumj.2021.70.8454

  • Thom's jet transversality theorem for regular maps Reviewed

    Yuta Kusakabe

    The Journal of Geometric Analysis   31   6031 - 6041   2021.6

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s12220-020-00515-x

  • An implicit function theorem for sprays and applications to Oka theory Reviewed

    Yuta Kusakabe

    International Journal of Mathematics   31 ( 9 )   2050071-1 - 2050071-9   2020.8

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1142/s0129167x20500718

  • Oka complements of countable sets and nonelliptic Oka manifolds Reviewed

    Yuta Kusakabe

    Proceedings of the American Mathematical Society   148 ( 3 )   1233 - 1238   2020.3

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1090/proc/14832

  • Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps Reviewed

    Yuta Kusakabe

    International Journal of Mathematics   28 ( 4 )   1750028-1 - 1750028-15   2017.4

     More details

    Language:Others   Publishing type:Research paper (scientific journal)  

    DOI: 10.1142/s0129167x17500288

▼display all

Presentations

  • 岡領域と双対Levi問題 Invited

    日下部 佑太

    第11回福岡複素解析シンポジウム  2024.3 

     More details

    Event date: 2024.3

    Language:Japanese  

    Venue:九州大学   Country:Other  

  • Dynamical methods in Gromov's elliptic geometry Invited

    Workshop on Dynamics in Arithmetic and Complex Geometry and its Applications  2024.1 

     More details

    Event date: 2024.1

    Language:English  

    Country:Other  

  • Oka tubes in holomorphic line bundles Invited

    2023.12 

     More details

    Event date: 2023.12

    Language:Japanese  

    Country:Other  

  • Gromov's elliptic geometry from the viewpoints of foliations and dynamics Invited

    2023.11 

     More details

    Event date: 2023.11

    Language:English  

    Country:Other  

  • Gromov ellipticity in complex analytic geometry and algebraic geometry Invited

    Young Mathematicians Workshop on Several Complex Variables 2023  2023.8 

     More details

    Event date: 2023.8

    Language:English  

    Country:Other  

  • Surjective morphisms onto Gromov elliptic varieties Invited

    Oka Theory and Complex Geometry Conference, Summer 2023  2023.6 

     More details

    Event date: 2023.6

    Language:English  

    Country:Other  

  • Gromov ellipticity in complex analytic geometry and algebraic geometry Invited

    2023.6 

     More details

    Event date: 2023.6

    Language:English  

    Country:Other  

  • Surjective morphisms onto subelliptic varieties Invited

    Workshop on Complex Geometry in Osaka 2023  2023.3 

     More details

    Event date: 2023.3

    Language:Japanese  

    Country:Other  

  • 岡多様体と楕円性 Invited

    日下部 佑太

    第17回代数・解析・幾何学セミナー  2022.2 

     More details

    Event date: 2022.2

    Language:Japanese  

    Venue:オンライン   Country:Other  

  • Oka manifolds and ellipticity Invited

    The 7th KTGU Mathematics Workshop for Young Researchers  2022.2 

     More details

    Event date: 2022.2

    Language:English  

    Country:Other  

  • Elliptic characterization and unification of Oka maps Invited

    2021.12 

     More details

    Event date: 2021.12

    Language:Japanese  

    Country:Other  

  • Oka theory for algebraic manifolds Invited

    2021.8 

     More details

    Event date: 2021.8

    Language:Japanese  

    Country:Other  

  • Oka manifolds and the dual Levi problem Invited

    HAYAMA Symposium on Complex Analysis in Several Variables XXII  2021.7 

     More details

    Event date: 2021.7

    Language:English  

    Country:Other  

  • 岡多様体と楕円性 Invited

    日下部 佑太

    日本数学会2021年度年会  2021.3 

     More details

    Event date: 2021.3

    Language:Japanese  

    Venue:慶應義塾大学 (オンライン)   Country:Other  

  • The Oka principle and the dual Levi problem Invited

    Grauert theory and recent complex geometry  2021.2 

     More details

    Event date: 2021.2

    Language:English  

    Country:Other  

  • 岡多様体と楕円性 Invited

    日下部 佑太

    多変数関数論若手オンライン勉強会  2020.12 

     More details

    Event date: 2020.11 - 2020.12

    Language:Japanese  

    Venue:大阪市立大学 (オンライン)   Country:Other  

  • 多項式凸集合の補空間の岡性

    日下部 佑太

    日本数学会2020年度秋季総合分科会  2020.9 

     More details

    Event date: 2020.9

    Language:Japanese  

    Venue:熊本大学 (オンライン)   Country:Other  

  • Elliptic characterization of the Oka principle Invited

    Virtual Conference on Complex Analysis and Complex Geometry  2020.5 

     More details

    Event date: 2020.5 - 2020.6

    Language:English  

    Country:Other  

  • Oka complements of countable sets and non-elliptic Oka manifolds Invited

    2019.12 

     More details

    Event date: 2019.12

    Language:Japanese  

    Country:Other  

  • 柏原の定理とddbar-lemma Invited

    日下部 佑太

    複素多様体の小平理論とその進展  2019.12 

     More details

    Event date: 2019.12

    Language:Japanese  

    Venue:大阪市立大学   Country:Other  

  • Dense entire curves and Oka manifolds Invited

    Rational Points on Higher Dimensional Varieties  2019.12 

     More details

    Event date: 2019.12

    Language:English  

    Country:Other  

  • 岡の原理と楕円性 Invited

    日下部 佑太

    第62回函数論シンポジウム  2019.11 

     More details

    Event date: 2019.11

    Language:Japanese  

    Venue:大同大学   Country:Other  

  • 岡多様体と楕円性

    日下部 佑太

    第54回函数論サマーセミナー  2019.8 

     More details

    Event date: 2019.8

    Language:Japanese  

    Venue:伊豆長岡温泉 おおとり荘   Country:Other  

  • Oka principle and relative ellipticity Invited

    Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry  2019.3 

     More details

    Event date: 2019.3

    Language:English  

    Country:Other  

  • 岡の原理と楕円性 Invited

    日下部 佑太

    接触構造、特異点、微分方程式及びその周辺  2019.1 

     More details

    Event date: 2019.1

    Language:Japanese  

    Venue:静岡県男女共同参画センター「あざれあ」   Country:Other  

  • Elliptic characterization and localization of Oka manifolds Invited

    2018.11 

     More details

    Event date: 2018.11

    Language:English  

    Country:Other  

  • Elliptic characterization and localization of Oka manifolds Invited

    Stein Manifolds and Holomorphic Mappings 2018  2018.9 

     More details

    Event date: 2018.9

    Language:English  

    Country:Other  

  • Elliptic characterization and localization of Oka manifolds

    2018.8 

     More details

    Event date: 2018.8

    Language:Japanese  

    Country:Other  

  • Holomorphic flexibility properties of mapping spaces Invited

    HAYAMA Symposium on Complex Analysis in Several Variables XX & Pacific Rim Complex-Symplectic Geometry Conference  2018.7 

     More details

    Event date: 2018.7

    Language:English  

    Country:Other  

  • Holomorphic maps with dense images Invited

    2017.12 

     More details

    Event date: 2017.12

    Language:Japanese  

    Country:Other  

  • Dense holomorphic curves in spaces of holomorphic maps Invited

    Young Mathematicians Workshop on Several Complex Variables and Complex Geometry 2017  2017.12 

     More details

    Event date: 2017.12

    Language:English  

    Country:Other  

  • Characterizations of Oka manifolds by entire curves Invited

    Topology of pseudoconvex domains and analysis of reproducing kernels  2017.11 

     More details

    Event date: 2017.11

    Language:English  

    Country:Other  

  • Dense holomorphic curves and universal holomorphic maps

    2017.9 

     More details

    Event date: 2017.9

    Language:Japanese  

    Country:Other  

  • Dense holomorphic curves in spaces of holomorphic maps Invited

    2017.3 

     More details

    Event date: 2017.3

    Language:Japanese  

    Country:Other  

  • Holomorphic flexibility properties of configuration spaces, symmetric products and Douady spaces

    2016.9 

     More details

    Event date: 2016.9

    Language:Japanese  

    Country:Other  

  • Dense holomorphic curves in spaces of holomorphic maps Invited

    2017.4 

     More details

    Language:Japanese  

    Country:Other  

  • Dense holomorphic curves in spaces of holomorphic maps Invited

    2017.4 

     More details

    Language:Japanese  

    Country:Other  

  • Dense holomorphic curves in spaces of holomorphic maps Invited

    2017.5 

     More details

    Language:Japanese  

    Country:Other  

  • Elliptic characterization and localization of Oka manifolds Invited

    2019.10 

     More details

    Language:Japanese  

    Country:Other  

  • Oka properties of complements of holomorphically convex sets Invited

    2020.6 

     More details

    Language:Japanese  

    Country:Other  

  • 多項式凸集合の補空間の岡性 Invited

    日下部 佑太

    幾何セミナー  2020.11 

     More details

    Language:Japanese  

    Venue:大阪大学 (オンライン)   Country:Other  

  • Oka manifolds and the dual Levi problem Invited

    2021.5 

     More details

    Language:Japanese  

    Country:Other  

  • 複素解析学における剛性と柔軟性 Invited

    日下部 佑太

    2021年度ガロア祭  2021.6 

     More details

    Language:Japanese  

    Venue:京都大学 (オンライン)   Country:Other  

  • Oka theory for algebraic manifolds

    2021.11 

     More details

    Language:Japanese  

    Country:Other  

  • 岡多様体と双対Levi問題 Invited

    日下部 佑太

    京都大学数学談話会  2022.4 

     More details

    Language:Japanese  

    Venue:京都大学   Country:Other  

  • Oka theory for algebraic manifolds Invited

    2022.6 

     More details

    Language:Japanese  

    Country:Other  

  • 複素解析幾何と代数幾何における楕円性について Invited

    日下部 佑太

    OCAMI複素解析セミナー  2023.2 

     More details

    Language:Japanese  

    Venue:大阪公立大学   Country:Other  

  • Toward Gromov's Oka principle with growth conditions Invited

    Complex Analysis Seminar  2023.10 

     More details

    Language:English  

    Country:Other  

    Toward Gromov's Oka principle with growth conditions

  • Oka tubes in holomorphic line bundles Invited

    Online Differential Geometry Seminar  2023.12 

     More details

    Language:English  

    Country:Other  

▼display all

MISC

  • Gromov の楕円幾何学から岡の原理へ(連載)

    日下部 佑太

    現代数学   2024.3

     More details

    Language:Japanese  

  • Oka theory for algebraic manifolds

    2022.1

     More details

    Language:Japanese  

  • 岡多様体と楕円性 Reviewed

    日下部 佑太

    日本数学会2021年度年会函数論分科会講演アブストラクト   2021.3

     More details

    Language:Japanese  

  • Characterizations of Oka manifolds by holomorphic flexibilities

    2021.2

     More details

    Language:Japanese  

  • 岡の原理と楕円性

    日下部 佑太

    第62回函数論シンポジウム講演アブストラクト   2019.11

     More details

    Language:Japanese  

Professional Memberships

  • The Mathematical Society of Japan

Academic Activities

  • 主催者

    ( 大阪公立大学 ) 2024.8

     More details

    Type:Competition, symposium, etc. 

  • 主催者

    福岡複素解析セミナー  2024.4 - Present

     More details

    Type:Competition, symposium, etc. 

  • 主催者

    代数幾何学セミナー  ( 京都大学数学教室 ) 2021.10 - 2024.3

     More details

    Type:Competition, symposium, etc. 

Research Projects

  • 代数的楕円幾何学と岡の原理の新展開

    Grant number:24K16919  2024 - 2026

    日本学術振興会  科学研究費助成事業  若手研究

      More details

    Grant type:Scientific research funding

  • 岡の原理の幾何学的側面

    Grant number:21K20324  2021 - 2024

    日本学術振興会  科学研究費助成事業  研究活動スタート支援

      More details

    Grant type:Scientific research funding

  • 正則写像の空間の幾何と岡多様体

    Grant number:18J20418  2018 - 2020

    日本学術振興会  科学研究費助成事業  特別研究員奨励費

      More details

    Grant type:Scientific research funding

  • 正則写像の空間の幾何と岡多様体

    2018 - 2020

    日本学術振興会  特別研究員

      More details

    Grant type:Joint research

Class subject

  • 数学概論Ⅳ・演習

    2024.10 - 2025.3   Second semester

  • 数学概論Ⅱ・演習

    2024.4 - 2024.9   First semester

  • 数学展望Ⅰ

    2024.4 - 2024.9   First semester

FD Participation

  • 2024.4   Role:Participation   Title:令和6年度 第1回全学FD(新任教員の研修)The 1st All-University FD (training for new faculty members) in FY2024

  • 2024.4   Role:Participation   Title:数理学府FD

Media Coverage

  • 「Gromovの楕円幾何学から岡の原理へ」の連載(2024年4月号〜) Newspaper, magazine

    現代数学  2024.3

     More details

    「Gromovの楕円幾何学から岡の原理へ」の連載(2024年4月号〜)