Faculty Profiles - MORITA Yosuke

Information

写真a

MORITA Yosuke

Organization

Faculty of Mathematics Division of Algebra and Geometry Associate Professor
Joint Graduate School of Mathematics for Innovation （Concurrent）
School of Sciences Department of Mathematics（Concurrent）
Graduate School of Mathematics Department of Mathematics（Concurrent）

Profile

様々な幾何学の話題に興味があります。これまでは次のようなことを研究してきました： 1) 等質空間 G/H に、G の離散部分群が固有かつ自由に作用するとき、商空間は G/H を局所的なモデルとする多様体になり、Clifford−Klein 形と呼ばれています。私は「非 Riemann な等質空間が、コンパクトな Clifford-Klein 形をいつ持つか？」という問題を、主にコホモロジー的な手法を用いて探究してきました。 2) 位相力学系の研究に現れる Conley 指数と呼ばれるホモトピー的な不変量の、より簡明な定式化を提案しました。大まかには「ホモトピー論の枠組みを使って、Lie 群論・微分幾何・力学系など、狭義の代数トポロジーからは少し離れたところにある問題に取り組む」というのが私の数学上の好みです。

Homepage

https://www2.math.kyushu-u.ac.jp/~y-morita/

External link

Research Areas

Natural Science / Geometry

Degree

Ph.D. (Mathematical Sciences) （ 2017.3 The University of Tokyo ）

Research History

2017年4月〜 2023年3月：京都大学大学院理学研究科数学教室助教

Education

The University of Tokyo Graduate School of Mathematical Sciences

2014.4 - 2017.3

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Notes：Ph.D.

Research Interests・Research Keywords

Research theme： A new framework for Conley index theory

Keyword： Conley index, topological dynamics, Morse theory, condensed set

Research period： 2019.2
Research theme： Clifford-Klein forms of non-Riemannian homogeneous spaces

Keyword： Lie groups, homogeneous space, Clifford-Klein form, proper action

Research period： 2013.6

Papers

Exotic proper actions on homogeneous spaces via convex cocompact representations International coauthorship

Maciej Bocheński;Yosuke Morita

arXiv:2501.14274 2025.1

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Language：English

DOI： 10.48550/arXiv.2501.14274
Cartan projections of some non-reductive subgroups and proper actions on homogeneous spaces Reviewed International journal

Yosuke Morita

Transformation Groups 29 ( 2 ) 823 - 845 2024.6 （ ISSN:1083-4362 eISSN:1531-586X ）

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Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Science and Business Media LLC

Kobayashi (Duke Math. J. 67:653–664, 1992) gave a necessary condition for the existence of compact Clifford–Klein forms in terms of Cartan projections and non-compact dimensions of reductive subgroups. We extend his method to non-reductive subgroups and give some examples of homogeneous spaces of reductive type that do not admit compact Clifford–Klein forms by comparing Cartan projections and non-compact dimensions of reductive subgroups with those of non-reductive subgroups.

DOI： 10.1007/s00031-022-09736-6

DOI： 10.48550/arXiv.2106.07848

Scopus

researchmap

Other Link： https://link.springer.com/article/10.1007/s00031-022-09736-6/fulltext.html
Conley index theory without index pairs. I: The point-set level theory Reviewed International journal

Yosuke Morita

Journal of Fixed Point Theory and Applications 25 ( 1 ) Paper No. 15 2023.2 （ ISSN:1661-7738 eISSN:1661-7746 ）

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Language：English Publishing type：Research paper (scientific journal) Publisher：Springer Science and Business Media LLC

We propose a new framework for Conley index theory. The main feature of our approach is that we do not use the notion of index pairs. We introduce, instead, the notions of compactifiable subsets and index neighbourhoods and formulate and prove basic results in Conley index theory using these notions. We treat both the discrete time case and the continuous time case.

DOI： 10.1007/s11784-022-01037-5

DOI： 10.1007/s11784-023-01094-4 (correction)

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Other Link： https://link.springer.com/article/10.1007/s11784-022-01037-5/fulltext.html
A cohomological obstruction to the existence of compact Clifford–Klein forms Reviewed International journal

Yosuke Morita

Selecta Mathematica 23 ( 3 ) 1931 - 1953 2017.7

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

DOI： 10.1007/s00029-016-0295-1, 10.48550/arXiv.1601.07359
A topological necessary condition for the existence of compace Clifford-Klein forms Reviewed International journal

Yosuke Morita

Journal of Differential Geometry 100 ( 3 ) 533 - 545 2015.7

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

DOI： 10.4310/jdg/1432842364, 10.48550/arXiv.1310.7096
Proof of Kobayashi's rank conjecture on Clifford–Klein forms Reviewed International journal

Yosuke Morita

Journal of the Mathematical Society of Japan 71 ( 4 ) 1153 - 1171 2019.10

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

DOI： 10.2969/jmsj/78007800, 10.48550/arXiv.1705.06544
Semisimple symmetric spaces that do not model any compact manifold Reviewed International journal

Yosuke Morita

Journal of Lie Theory 29 ( 2 ) 493 - 510 2019.5

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

DOI： 10.48550/arXiv.1811.01495
Homogeneous spaces of nonreductive type that do not model any compact manifold Reviewed International journal

Yosuke Morita

Publications of the Research Institute for Mathematical Sciences 53 ( 2 ) 287 - 298 2017.5

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

DOI： 10.4171/PRIMS/53-2-3
Semisimple symmetric spaces without compact manifolds locally modelled thereon Reviewed International journal

Yosuke Morita

Proceedings of the Japan Academy, Series A, Mathematical Sciences 91 ( 2 ) 29 - 33 2015.2

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

DOI： 10.3792/pjaa.91.29

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Presentations

Conley index theory and condensed sets Invited International conference

Yosuke Morita

Arbeitstagung 2023 on Condensed Mathematics 2023.6

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Event date： 2023.6

Language：English Presentation type：Oral presentation (general)

Venue：Max Planck Institute for Mathematics Country：Germany

Other Link： https://www.mpim-bonn.mpg.de/node/11707
非 Riemann 等質空間のコンパクト商の存在問題 Invited

森田陽介

第68回幾何学シンポジウム（基調講演） 2021.9

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Event date： 2021.9

Language：Japanese

Venue：北海道大学（オンライン） Country：Japan

The existence problem of compact quotients of non-Riemannian homogeneous spaces
非 Riemann 等質空間のコンパクト商のコホモロジー Invited

森田陽介

日本数学会2018年度秋季総合分科会（幾何学分科会、特別講演） 2018.9

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Event date： 2018.9

Language：Japanese

Venue：岡山大学 Country：Other

On the cohomology of compact quotients of non-Riemannian homogeneous spaces
The existence problem of compact Clifford-Klein forms Invited International conference

森田陽介

Rigidity School, Nagoya 2017（全4回、11月23日-26日） 2017.11

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Event date： 2017.11

Language：English

Venue：名古屋大学 Country：Other

The existence problem of compact Clifford-Klein forms
Around proper actions on homogeneous spaces Invited International conference

Morita Yosuke, Maciej Bocheński

Higher Rank Geometric Structures (Mini-course, 28-30 April, 6 hours in total) 2025.4

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Event date： 2025.4

Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：Institut Henri Poincaré Country：France

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Exotic proper actions on reductive homogeneous spaces via convex cocompact representations Invited International conference

Yosuke Morita

Teichmüller Theory and Beyond 2025.2

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Event date： 2025.2

Language：English Presentation type：Oral presentation (general)

Venue：Seoul Nataional University Country：Korea, Republic of

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An easy formulation of Conley indices Invited International conference

Yosuke Morita

Workshop on geometry of foliations and its applications 2024.12

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Event date： 2024.12

Language：Japanese Presentation type：Oral presentation (general)

Venue：Kyoto University of Education Country：Japan

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Compact quotients of homogeneous spaces and sphere bundles Invited International conference

Yosuke Morita

International Workshop on Higher Teichmüller theory 2024.5

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Event date： 2024.5

Language：English Presentation type：Oral presentation (general)

Venue：Chern Institute of Mathematics, Nankai University Country：China

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The existence problem of compact quotients of pseudo-Riemannian homogeneous spaces Invited International conference

Yosuke Morita

Zariski dense subgroups, number theory and geometric applications 2024.1

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Event date： 2024.1

Language：English Presentation type：Oral presentation (general)

Venue：International Centre for Theoretical Sciences Country：India

Other Link： https://www.icts.res.in/program/ZDSG
The existence problem of compact quotients of homogeneous spaces Invited International conference

Yosuke Morita

Séminaire Géométrie et applications (Université de Strasbourg) 2023.11

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Event date： 2023.11

Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：Université de Strasbourg Country：France

Other Link： https://irma.math.unistra.fr/seminaires/seminaire-geometrie-et-applications.html
The existence problem of compact Clifford-Klein forms of pseudo-Riemannian homogeneous spaces Invited International conference

Yosuke Morita

7th Tunisian-Japanese Conference "Geometric and Harmonic Analysis on Homogeneous Spaces and Applications" in Honor of Professor Toshiyuki Kobayashi 2023.11

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Event date： 2023.11

Language：English Presentation type：Oral presentation (general)

Venue：Iberostar Selection Kuriat Palace Country：Tunisia

Other Link： https://sites.google.com/view/tunisian-japanese-conference/home/2023-7th
The existence problem of compact quotients of homogeneous spaces Invited International conference

Yosuke Morita

Séminaire Géométrie Topologie Dynamique (Université Paris-Saclay) 2023.11

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Event date： 2023.11

Language：English Presentation type：Public lecture, seminar, tutorial, course, or other speech

Venue：Université Paris-Saclay Country：France

Other Link： https://www.imo.universite-paris-saclay.fr/en/events/7171
コンパクト商を持たない非 Riemann 等質空間について Invited

森田陽介

第62回実函数論・函数解析学合同シンポジウム 2023.8

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Event date： 2023.8

Language：Japanese Presentation type：Oral presentation (general)

Venue：千葉大学 Country：Japan
Sphere bundles, KO-theory, and vector fields on spheres (after Adams)

森田陽介

Workshop on "Actions of Reductive Groups and Global Analysis" 2023.8

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Event date： 2023.8

Language：Japanese Presentation type：Oral presentation (general)

Venue：Zoom Country：Japan
Conley 指数の定義について Invited

森田陽介

Geometry and Topology 2023.6

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Event date： 2023.6

Language：Japanese Presentation type：Oral presentation (general)

Venue：九州大学 Country：Japan

Other Link： https://sites.google.com/view/geometry-and-topology/
非 Riemann 等質空間の Clifford-Klein 形の幾何学 Invited

森田陽介

九州大学数理談話会 2023.5

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Event date： 2023.5

Language：Japanese

Venue：九州大学 Country：Japan

Geometry of Clifford-Klein forms of non-Riemannian homogeneous spaces
Conley 指数理論の新しい定式化について Invited

森田陽介

幾何学・トポロジー合同セミナー（九州大学） 2023.4

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Event date： 2023.4

Language：Japanese

Venue：九州大学 Country：Japan

On a new formulation of Conley index theory
A new framework for Conley index theory Invited International conference

Yosuke Morita

Low dimensional topology and number theory XIV 2023.3

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Event date： 2023.3

Language：English

Venue：九州大学 Country：Japan

A new framework for Conley index theory
Morse theory on the loop spaces of Lie groups and manifolds with hyperpolar actions (after Bott, Bott-Samelson, Conlon)

森田陽介

Workshop on "Actions of Reductive Groups and Global Analysis" 2022.8

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Event date： 2022.8

Language：Japanese

Venue：玉原国際セミナーハウス（オンライン） Country：Japan

Morse theory on the loop spaces of Lie groups and manifolds with hyperpolar actions (after Bott, Bott-Samelson, Conlon)
The Conley index of topological dynamical systems

Yosuke Morita

iTHEMS 数学セミナー 2021.12

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Event date： 2021.12

Language：English

Venue：理化学研究所 iTHEMS（オンライン） Country：Japan

The Conley index of topological dynamical systems
Conley 指数の定義について Invited

森田陽介

リー群論・表現論セミナー（東京大学） 2021.12

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Event date： 2021.12

Language：Japanese

Venue：東京大学（オンライン） Country：Japan

On the definition of Conley indices
指数対を使わない Conley 指数理論 Invited

森田陽介

京都力学系セミナー 2021.11

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Event date： 2021.11

Language：Japanese

Venue：京都大学（オンライン） Country：Japan

Conley index theory without index pairs
Conley 指数について

森田陽介

Workshop on "Actions of Reductive Groups and Global Analysis" 2021.8

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Event date： 2021.8

Language：Japanese

Venue：玉原国際セミナーハウス（オンライン） Country：Japan

On Conley indices
非簡約な閉部分群の Cartan 射影と等質空間のコンパクト商 Invited

森田陽介

リー群論、表現論およびその周辺分野 2021.8

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Event date： 2021.8

Language：Japanese

Venue：京都大学数理解析研究所（オンライン） Country：Other

Cartan projections of some nonreductive closed subgroups and compact quotients of homogeneous spaces
非簡約な部分群の Cartan 射影とコンパクト Clifford–Klein 形の存在問題 Invited

森田陽介

リー群論・表現論セミナー（東京大学） 2021.6

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Event date： 2021.6

Language：Japanese

Venue：東京大学（オンライン） Country：Other

Cartan projections of some nonreductive subgroups and the existence problem of compact Clifford–Klein forms
コンパクト Clifford–Klein 形と球面束

森田陽介

Workshop on "Actions of Reductive Groups and Global Analysis" 2020.8

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Event date： 2020.8

Language：Japanese

Venue：玉原国際セミナーハウス（オンライン） Country：Other

Compact Clifford–Klein forms and sphere bundles
Cartan projections of some nonreductive subgroups Invited International conference

Yosuke Morita

Séminaire de Mathématique (Institut des Hautes Études Scientifiques) 2020.1

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Event date： 2020.1

Language：English

Venue：Institut des Hautes Études Scientifiques Country：France
A generalization of the ping-pong lemma

森田陽介

リー群の群作用と大域解析に関するセミナー2019 2019.8

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Event date： 2019.8

Language：Japanese

Venue：玉原国際セミナーハウス Country：Other

A generalization of the ping-pong lemma
Cartan projections of abelian horospherical subgroups and proper actions on homogeneous spaces Invited

森田陽介

表現論とその周辺分野の進展 2019.7

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Event date： 2019.7

Language：Japanese

Venue：京都大学数理解析研究所 Country：Other

Cartan projections of abelian horospherical subgroups and proper actions on homogeneous spaces
等質空間の Clifford-Klein 形の幾何学 Invited

森田陽介

幾何学特別講義2/先端幾何学特別講義2（集中講義、全10回、10月8日-12日） 2018.10

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Event date： 2018.10

Language：Japanese

Venue：首都大学東京 Country：Other

Geometry of Clifford-Klein forms of homogeneous spaces
Cohomological obstructions to the existence of compact Clifford-Klein forms Invited International conference

森田陽介

Seminar（Korea Institute of Advanced Study、全2回、7月24日-25日） 2018.7

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Event date： 2018.7

Language：English

Country：Korea, Republic of

Cohomological obstructions to the existence of compact Clifford-Klein forms
等質空間の Clifford-Klein 形のコホモロジーについて Invited

森田陽介

ワークショップ：幾何学的群論の新展開 2018.2

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Event date： 2018.2

Language：Japanese

Venue：ルネッサ赤沢 Country：Other

Cohomology of Clifford-Klein forms of homogeneous spaces
簡約型等質空間のコンパクト商と不変式

森田陽介

2017年度表現論シンポジウム 2017.11

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Event date： 2017.11

Language：Japanese

Venue：かんぽの宿石和 Country：Other

Compact quotients of homogeneous spaces of reductive type and invariants
等質空間の Clifford-Klein 形のコホモロジーについて

森田陽介

広島幾何学研究集会 2017 2017.10

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Event date： 2017.10

Language：Japanese

Venue：広島大学 Country：Other

Cohomology of Clifford-Klein forms of homogeneous spaces
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited International conference

Yosuke Morita

The Third Japanese-Spanish Workshop on Differential Geometry 2017.9

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Event date： 2017.9

Language：English

Venue：Instituto de Ciencias Matemáticas Country：Spain
Real cohomology of compact homogeneous spaces (after Cartan-Chevalley-Koszul-Weil)

森田陽介

リー群の群作用と大域解析に関するセミナー（全3回、8月16日-18日） 2017.8

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Event date： 2017.8

Language：Japanese

Venue：玉原国際セミナーハウス Country：Other

Real cohomology of compact homogeneous spaces (after Cartan-Chevalley-Koszul-Weil)
等質空間上の固有な作用 Invited

森田陽介

談話会（京都大学） 2017.6

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Event date： 2017.6

Language：Japanese

Venue：京都大学数理解析研究所 Country：Other

Proper actions on homogeneous spaces
等質空間の Clifford-Klein 形のコホモロジーについて Invited

森田陽介

幾何学セミナー（名古屋大学） 2017.5

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Event date： 2017.5

Language：Japanese

Venue：名古屋大学 Country：Other

Cohomology of Clifford-Klein forms of homogeneous spaces
等質空間のコンパクト Clifford-Klein 形の存在に対するコホモロジー的障害 Invited

森田陽介

微分トポロジーセミナー（京都大学） 2017.5

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Event date： 2017.5

Language：Japanese

Venue：京都大学 Country：Other

A cohomological obstruction to the existence of compact Clifford-Klein forms of homogeneous spaces
Homogeneous spaces that do not model any compact manifold Invited

森田陽介

表現論セミナー（京都大学） 2017.4

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Event date： 2017.4

Language：Japanese

Venue：京都大学数理解析研究所 Country：Other

Homogeneous spaces that do not model any compact manifold
A cohomological obstruction to the existence of compact Clifford-Klein forms and ε-family of semisimple symmetric spaces

森田陽介

2016年度表現論シンポジウム 2016.11

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Event date： 2016.11

Language：Japanese

Venue：オキナワグランメールリゾート Country：Other

A cohomological obstruction to the existence of compact Clifford-Klein forms and ε-family of semisimple symmetric spaces
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited International conference

Yosuke Morita

International Conference for the 70th Anniversary of Korean Mathematical Society (session: Geometric Group Theory and Dynamics of Group Actions) 2016.10

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Event date： 2016.10

Language：English

Venue：Seoul National University Country：Korea, Republic of
A cohomological obstruction to the existence of compact Clifford-Klein forms International conference

Yosuke Morita

Group Actions and Dynamics Seminar (Yale University) 2016.9

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Event date： 2016.9

Language：English

Venue：Yale University Country：United States
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited

森田陽介

第63回幾何学シンポジウム 2016.8

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Event date： 2016.8

Language：Japanese

Venue：岡山大学 Country：Other

A cohomological obstruction to the existence of compact Clifford-Klein forms
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited International conference

森田陽介

Rigidity School, Nagoya 2016 2016.7

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Event date： 2016.7

Language：English

Venue：名古屋大学 Country：Other

A cohomological obstruction to the existence of compact Clifford-Klein forms
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited International conference

Yosuke Morita

Geometry and Topology Seminar (University of Luxembourg) 2016.6

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Event date： 2016.6

Language：English

Venue：University of Luxembourg Country：Luxembourg
A cohomological obstruction to the existence of compact Clifford-Klein forms Invited International conference

森田陽介

Geometric Analysis on Discrete Groups 2016.5

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Event date： 2016.5

Language：English

Venue：京都大学数理解析研究所 Country：Other

A cohomological obstruction to the existence of compact Clifford-Klein forms
等質空間を局所モデルとするコンパクト多様体が存在するための障害

森田陽介

日本数学会2016年度年会（幾何学分科会、一般講演） 2016.3

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Event date： 2016.3

Language：Japanese

Venue：筑波大学 Country：Other

Obstructions to the existence of compact manifolds locally modelled on homogeneous spaces
Cohomological obstructions to the existence of compact Clifford–Klein forms International conference

Yosuke Morita

Berkeley–Tokyo Winter School "Geometry, Topology and Representation Theory" (student session) 2016.2

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Event date： 2016.2

Language：English

Venue：University of California, Berkeley（アメリカ合衆国、バークレー） Country：United States
コンパクト Clifford-Klein 形の存在問題について

森田陽介

2015年度表現論シンポジウム 2015.11

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Event date： 2015.11

Language：English

Venue：公共の宿おおとり荘 Country：Other

On the existence problem of compact Clifford-Klein forms
Homogeneous spaces locally modelling no compact manifold Invited

森田陽介

第15回関東若手幾何セミナー 2015.10

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Event date： 2015.10

Language：Japanese

Venue：慶應義塾大学 Country：Other

Homogeneous spaces locally modelling no compact manifold
A new cohomological obstruction to the existence of compact Clifford-Klein forms

森田陽介

リー群の群作用と大域解析セミナー 2015.8

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Event date： 2015.8

Language：Japanese

Venue：玉原国際セミナーハウス Country：Other

A new cohomological obstruction to the existence of compact Clifford-Klein forms
Proper actions on corank-one reductive homogeneous spaces (after Kassel)

森田陽介

リー群の群作用と大域解析セミナー（全2回、8月4日-5日） 2015.8

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Event date： 2015.8

Language：Japanese

Venue：玉原国際セミナーハウス Country：Other

Proper actions on corank-one reductive homogeneous spaces (after Kassel)
Cohomological obstructions to the existence of compact Clifford–Klein forms International conference

Yosuke Morita

Mathematical Symposium ENS Lyon–Todai (poster session) 2015.6

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Event date： 2015.6

Language：English

Venue：ENS de Lyon（フランス、リヨン） Country：France

Cohomological obstructions to the existence of compact Clifford–Klein forms
等質空間がコンパクト商を持つための位相的制約

森田陽介

日本数学会2015年度年会（函数解析学分科会、一般講演） 2015.3

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Event date： 2015.3

Language：Japanese

Venue：明治大学 Country：Other

A topological obstruction to the existence of compact quotients of homogeneous spaces
Volume forms and compact Clifford-Klein forms Invited International conference

森田陽介

ワークショップ「不連続群の変形とその周辺」 2015.2

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Event date： 2015.2

Language：English

Venue：名古屋大学 Country：Other

Volume forms and compact Clifford-Klein forms
A necessary condition for the existence of compact manifolds locally modelled on homogeneous spaces Invited International conference

Yosuke Morita

2015 East Asian Core Doctorial Forum on Mathematics 2015.1

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Event date： 2015.1

Language：English

Venue：National Taiwan University Country：Taiwan, Province of China
等質空間を局所モデルとするコンパクト多様体が存在するための障害 Invited

森田陽介

広島大学トポロジー・幾何セミナー 2014.12

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Event date： 2014.12

Language：Japanese

Venue：広島大学 Country：Other

An obstruction for the existence of compact manifolds locally modelled on homogeneous spaces
A necessary condition for the existence of compact manifolds locally modelled on homogeneous spaces Invited International conference

森田陽介

Rigidity School, Tokyo 2014 (2nd) 2014.11

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Event date： 2014.11

Language：English

Venue：東京大学 Country：Other

A necessary condition for the existence of compact manifolds locally modelled on homogeneous spaces
A necessary condition for the existence of compact manifolds locally modelled on homogeneous spaces Invited

森田陽介

第61回幾何学シンポジウム 2014.8

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Event date： 2014.8

Language：Japanese

Venue：名城大学 Country：Other

A necessary condition for the existence of compact manifolds locally modelled on homogeneous spaces
Y. Benoist "Actions propres sur les espaces homogènes réductifs" Chapitre 4 の解説

森田陽介

リー群の表現論と群作用についての研究会 2014.8

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Event date： 2014.8

Language：Japanese

Venue：玉原国際セミナーハウス Country：Other

A survey on Y. Benoist "Actions propres sur les espaces homogènes réductifs", Chapitre 4
等質空間がコンパクト商を持つための位相的制約

森田陽介

表現論と調和解析の新たな進展 2014.6

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Event date： 2014.6

Language：Japanese

Venue：京都大学数理解析研究所 Country：Other

A topological obstruction for the existence of compact quotients of homogeneous spaces of reductive type
簡約型等質空間がコンパクト商を持つための位相的制約

森田陽介

2013年度表現論シンポジウム 2013.11

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Event date： 2013.11

Language：Japanese

Venue：マホロバ・マインズ三浦 Country：Other

A topological obstruction for the existence of compact quotients of homogeneous spaces of reductive type

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Professional Memberships

THE MATHEMATICAL SOCIETY OF JAPAN

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Academic Activities

Screening of academic papers

Role(s)： Peer review

2023

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Type：Peer review

Number of peer-reviewed articles in foreign language journals：0

Number of peer-reviewed articles in Japanese journals：0

Proceedings of International Conference Number of peer-reviewed papers：1

Proceedings of domestic conference Number of peer-reviewed papers：0
世話人 International contribution

The 7th KTGU Mathematics Workshop for Young Researchers （ Japan ） 2022.2

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Type：Competition, symposium, etc.

Research Projects

等質空間のコンパクト商とファイブレーション

Grant number：24K16922 2024 - 2027

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Early-Career Scientists

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Authorship：Principal investigator Grant type：Scientific research funding
Clifford-Klein forms and Dolbeault cohomology

Grant number：19K14529 2019 - 2023

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Early-Career Scientists

Morita Yosuke

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Authorship：Principal investigator Grant type：Scientific research funding

1) In joint work with Fanny Kassel and Nicolas Tholozan, we prove that a (non-Riemannian) reductive homogeneous space can admit a compact quotient only when a certain sphere bundle on the homogeneous space is fibrewise homotopy equivalent to the trivial sphere bundle. Using the Adams operations on KO-theory, we obtained many examples of homogeneous spaces for which our necessary condition is not satisfied (and hence, compact quotients do not exist).
2) The Conley index is an invariant for isolated invariant subsets in topological dynamical systems. Usually, it is formulated using an index pair (N, L). I gave a new, simpler formulation of the Conley index, based on an observation that only the difference set N - L is important in Conlye index theory. I also observed that one can naturally define Conly indices in the point-set level if one uses condensed sets, a generalization of topological spaces.

CiNii Research
簡約型等質空間と非簡約型等質空間のコンパクトClifford-Klein形

Grant number：17H06784 2017 - 2018

Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Research Activity start-up

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Authorship：Principal investigator Grant type：Scientific research funding
指数定理と余随伴軌道に関する研究

2014 - 2016

Japan Society for the Promotion of Science Research Fellowships for Young Scientists

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Authorship：Principal investigator Grant type：Joint research

Class subject

数学特論B4

2025.12 - 2026.2 Winter quarter
入門微分積分Ⅱ

2025.12 - 2026.2 Winter quarter
表現論大意

2025.10 - 2026.3 Second semester
数学特論８

2025.10 - 2026.3 Second semester
幾何学Ⅲ

2025.10 - 2026.3 Second semester
コアセミナーⅡ

2025.10 - 2026.3 Second semester
Representation Theory

2025.10 - 2026.3 Second semester
入門微分積分Ⅰ

2025.10 - 2025.12 Fall quarter
入門微分積分Ⅱ

2024.12 - 2025.2 Winter quarter
入門微分積分Ⅱ

2024.12 - 2025.2 Winter quarter
幾何学Ⅲ

2024.10 - 2025.3 Second semester
数理科学特論７

2024.10 - 2025.3 Second semester
数理科学特別講義Ⅶ

2024.10 - 2025.3 Second semester
入門微分積分Ⅰ

2024.10 - 2024.12 Fall quarter
入門微分積分Ⅰ

2024.10 - 2024.12 Fall quarter
表現論大意

2024.4 - 2024.9 First semester
数学特論８

2024.4 - 2024.9 First semester

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FD Participation

2025.2 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2024.7 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2024.4 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2023.8 Role：Participation Title：数理学府FD

Organizer：[Undergraduate school/graduate school/graduate faculty]
2023.4 Role：Participation Title：令和5年度第1回全学FD（新任教員の研修）

Organizer：University-wide

Media Coverage

記事名：『京都大学ガロア祭／問題と解説』 Newspaper, magazine

『数学セミナー』（日本評論社）2021年12月号 2021.11

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記事名：『京都大学ガロア祭／問題と解説』