Abe Hiraku 阿部拓

Researcher Number	00736499
Other IDs
Affiliation (Current)	2025: 岡山理科大学, 理学部, 准教授
Affiliation (based on the past Project Information) *help	2020 – 2023: 岡山理科大学, 理学部, 講師 2018 – 2019: 大阪府立大学, 高等教育推進機構, 教育拠点形成教員 2015 – 2017: 大阪市立大学, 大学院理学研究科, 数学研究所専任研究所員
Review Section/Research Field	Principal Investigator Basic Section 11020:Geometry-related / Geometry
Keywords	Principal Investigator コホモロジー環 / 旗多様体 / Peterson多様体 / ヘッセンバーグ多様体 / トーリック多様体 / Hessenberg多様体 / toric orbifold / 可積分系 / 戸田格子 / Mishchenko-Fomenko多項式 … More / Fano多様体 / 正値性 / 基底 / Schubert多様体 / 基本関係式 / 正規性 / 特異点 / 弱Fano多様体 / 完全可積分系 / regular nilpotent / regular semisimple / ポアンカレ双対代数 / 対称群の表現 Less

ヘッセンバーグ多様体とトーリック幾何の繋がりPrincipal Investigator
- Principal Investigator
  
  阿部拓
- Project Period (FY)
  2023 – 2027
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Okayama University of Science
The family of Hessenberg varieties and integrable systemsPrincipal Investigator
- Principal Investigator
  
  ABE Hiraku
- Project Period (FY)
  2018 – 2022
- Research Category
  
  Grant-in-Aid for Early-Career Scientists
- Review Section
  
  Basic Section 11020:Geometry-related
- Research Institution
  Okayama University of Science
  Osaka Prefecture University
Topology of Hessenberg varieties and representations of symmetric groupsPrincipal Investigator
- Principal Investigator
  
  Abe Hiraku
- Project Period (FY)
  2015 – 2017
- Research Category
  
  Grant-in-Aid for Young Scientists (B)
- Research Field
  
  Geometry
- Research Institution
  Osaka City University

All 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 Other

All Journal Article Presentation Other

[Journal Article] Geometry of Peterson Schubert calculus in type A and left-right diagrams2024
- Author(s)
  Abe Hiraku、Horiguchi Tatsuya、Kuwata Hideya、Zeng Haozhi
- Journal Title
  
  Algebraic Combinatorics
  
  Volume: 7 Issue: 2 Pages: 383-412
- DOI
  10.5802/alco.342
- Peer Reviewed / Open Access / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-19K14508, KAKENHI-PROJECT-23K03102
[Journal Article] On singularity and normality of regular nilpotent Hessenberg varieties2024
- Author(s)
  Abe Hiraku、Insko Erik
- Journal Title
  
  Journal of Algebra
  
  Volume: 651 Pages: 70-110
- DOI
  10.1016/j.jalgebra.2024.02.042
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K03102
[Journal Article] Fano and weak Fano Hessenberg varieties2021
- Author(s)
  Hiraku Abe, Naoki Fujita, and Haozhi Zeng
- Journal Title
  
  Michigan Math. J.
  
  Volume: -
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Journal Article] Geometry of regular Hessenberg varieties2020
- Author(s)
  Hiraku Abe, Naoki Fujita, and Haozhi Zeng
- Journal Title
  
  Transform. Groups
  
  Volume: -
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Journal Article] A survey of recent developments on Hessenberg varieties2020
- Author(s)
  Hiraku Abe and Tatsuya Horiguchi
- Journal Title
  
  Adv. Stud. Pure Math.
  
  Volume: -
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-18K13413
[Journal Article] Hessenberg varieties, Slodowy slices, and integrable systems2019
- Author(s)
  H. Abe and P. Crooks
- Journal Title
  
  Math. Z.
  
  Volume: 291(3) Pages: 1093-1132
- Peer Reviewed / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Journal Article] The cohomology rings of regular semisimple Hessenberg varieties for h=(h(1),n,...,n)2018
- Author(s)
  Hiraku Abe, Tatsuya Horiguchi, Mikiya Masuda
- Journal Title
  
  Journal of Combinatorics
  
  Volume: 印刷中
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-15K17544
[Journal Article] Hessenberg varieties for the minimal nilpotent orbit2017
- Author(s)
  Hiraku Abe and Peter Crooks
- Journal Title
  
  Pure Appl. Math. Q.
  
  Volume: 印刷中
- Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Line bundles over regular semisimple Hessenberg variety for h=(2,3,4,...,n,n)2024
- Author(s)
  Hiraku Abe
- Organizer
  Topology and Geometry of Torus actions and related Combinatorics Workshop 2024 in Himeji
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Hessenberg varieties and toric geometry2024
- Author(s)
  阿部拓
- Organizer
  第8回代数幾何学研究集会 ‐宇部‐
- Invited
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Peterson varieties and toric orbifolds associated to Cartan matrices2023
- Author(s)
  Hiraku Abe
- Organizer
  2023 KMS Annual Meeting
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Peterson varieties and Cartan toric orbifolds2023
- Author(s)
  阿部拓
- Organizer
  Toric topology 2023
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Peterson多様体の非負部分とトーリック幾何2023
- Author(s)
  阿部拓
- Organizer
  南大阪代数セミナー
- Invited
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Peterson varietyの多面体について2023
- Author(s)
  阿部拓
- Organizer
  第5回ヘッセンバーグ勉強会
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Peterson多様体とトーリック幾何2023
- Author(s)
  阿部拓
- Organizer
  第49回変換群論シンホジウム
- Invited
- Data Source
  KAKENHI-PROJECT-23K03102
[Presentation] Hessenberg多様体2023
- Author(s)
  阿部拓
- Organizer
  AGU表現論セミナー：幾何学と表現論を巡って
- Invited
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Peterson Schubert calculus2022
- Author(s)
  阿部拓
- Organizer
  第24回代数曲面ワークショップ at 半田山
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] A型Peterson-Schubert calculusの幾何と計算2022
- Author(s)
  阿部拓
- Organizer
  変換群論の新潮流
- Invited
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Peterson多様体とトーリック軌道体2022
- Author(s)
  阿部拓
- Organizer
  阿部拓第4回ヘッセンバーグ勉強会2022
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Some computations in the cohomology of Peterson varieties2022
- Author(s)
  阿部拓
- Organizer
  第3回ヘッセンバーグ勉強会
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] On the integral cohomology ring of the Peterson variety2021
- Author(s)
  Hiraku Abe
- Organizer
  Toric topology in Osaka 2021
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Geometry of Peterson Schubert calculus2021
- Author(s)
  阿部拓
- Organizer
  ヘッセンバーグ勉強会
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Geometry of Peterson Schubert calculus and its computations2021
- Author(s)
  Hiraku Abe
- Organizer
  Hessenberg seminars 2021-2022 in Osaka by Zoom
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Peterson 多様体の整係数コホモロジー2021
- Author(s)
  阿部拓
- Organizer
  第2回ヘッセンバーグ勉強会
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Geometry of Hessenberg varieties2020
- Author(s)
  Hiraku Abe
- Organizer
  Geometry and Topology Seminar
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Toric topology of Peterson varieties2020
- Author(s)
  Hiraku Abe
- Organizer
  Washington University weekend workshop on geometry and combinatorics
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] The integral cohomology rings of Peterson varieties2020
- Author(s)
  Hiraku Abe
- Organizer
  Washington University weekend workshop on geometry and combinatorics
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Hessenberg varieties2019
- Author(s)
  Hiraku Abe
- Organizer
  Hamiltonian systems and Lie groups
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] 旗多様体上のあるベクトル束に現れる正則 Poisson 構造と完全可積分系について2018
- Author(s)
  阿部拓
- Organizer
  変換群論における幾何・代数・組み合わせ論
- Invited
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] 正則半単純なヘッセンバーグ多様体のコホモロジー環について2018
- Author(s)
  阿部拓
- Organizer
  日本数学会2018年度年会
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] An introduction to Hessenberg varieties2018
- Author(s)
  Hiraku Abe
- Organizer
  Hessenberg varieties 2018 in Osaka
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] An introduction to Hessenberg varieties2018
- Author(s)
  Hiraku Abe
- Organizer
  Hessenberg Varieties in Combinatorics, Geometry and Representation Theory
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-18K13413
[Presentation] Hessenberg varieties I2017
- Author(s)
  Hiraku Abe
- Organizer
  Toric topology in Osaka 2017
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Flat families of Hessenberg varieties with an application to Newton-Okounkov bodies2017
- Author(s)
  Hiraku Abe
- Organizer
  AMS special session
- Place of Presentation
  Atlanta (United States of America)
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Extensions of pavings by affines of Peterson varieties2017
- Author(s)
  Hiraku Abe
- Organizer
  Young Researchers in Homotopy Theory and Topic Topology
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Cohomology of Hessenberg varieties and representations of symmetric groups2017
- Author(s)
  Hiraku Abe
- Organizer
  International Festival in Schubert Calculus
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Flat families of Hessenberg varieties with an application to Newton-Okounkov bodies2017
- Author(s)
  Hiraku Abe
- Organizer
  Geometry and Topology seminar
- Place of Presentation
  The University of Western Ontario (Canada)
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] The cohomology of Hessenberg varieties and representations of symmetric groups2016
- Author(s)
  Hiraku Abe
- Organizer
  Geometry & Topology seminar
- Place of Presentation
  Hamilton (Canada)
- Year and Date
  2016-02-25
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] On flat degenerations of regular semisimple Hessenberg varieties2016
- Author(s)
  Hiraku Abe
- Organizer
  Mini-Workshop on Toric Topology in Okayama
- Place of Presentation
  岡山理科大学（岡山県岡山市北区理大町）
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] On the flatness of certain families of Hessenberg varieties2016
- Author(s)
  Hiraku Abe
- Organizer
  Toric Topology 2016 in Kagoshima
- Place of Presentation
  鹿児島大学（鹿児島県鹿児島市郡元）
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Flat families of Hessenberg varieties with an application to Newton-Okounkov bodies2016
- Author(s)
  Hiraku Abe
- Organizer
  algebra/combinatorics/geometry research seminar
- Place of Presentation
  Smith college (United States of America)
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Nilpotent vs. semisimple via representations of symmetric groups2015
- Author(s)
  Hiraku Abe
- Organizer
  Workshop on Recent Developments in the Geometry and Combinatorics of Hessenberg Varieties
- Place of Presentation
  Toronto (Canada)
- Year and Date
  2015-07-23
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] The cohomology of Hessenberg varieties and representations of symmetric groups2015
- Author(s)
  Hiraku Abe
- Organizer
  Topology and Geometric Group Theory Seminar
- Place of Presentation
  Ithaca (United States of America)
- Year and Date
  2015-04-28
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] ヘッセンバーグ多様体のコホモロジー環と対称群の表現2015
- Author(s)
  阿部拓
- Organizer
  幾何学・組合せ論に現れる環と代数構造
- Place of Presentation
  京都大学数理解析研究所（京都市左京区北白川追分町）
- Year and Date
  2015-06-11
- Invited
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] The cohomology of regular Hessenberg varieties and representations of symmetric groups2015
- Author(s)
  Hiraku Abe
- Organizer
  A special session on Algebraic Geometry and Combinatorics at the AMS Sectional Meeting
- Place of Presentation
  New Brunswick (United States of America)
- Year and Date
  2015-11-14
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] Representations of symmetric groups on the cohomology of Hessenberg varieties2015
- Author(s)
  Hiraku Abe
- Organizer
  Toric Topology 2015 in Osaka
- Place of Presentation
  大阪市立大学（大阪市住吉区杉本）
- Year and Date
  2015-06-18
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[Presentation] The cohomology of Hessenberg varieties and representations of symmetric group2015
- Author(s)
  Hiraku Abe
- Organizer
  Symplectic Geometry Seminar
- Place of Presentation
  Toronto (Canada)
- Year and Date
  2015-06-01
- Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-15K17544
[]

1. 堀口達也

# of Collaborated Projects: 0 results

# of Collaborated Products: 1 results

Abe Hiraku 阿部 拓

Research Projects

Research Products

Co-Researchers

ヘッセンバーグ多様体とトーリック幾何の繋がりPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

The family of Hessenberg varieties and integrable systemsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Topology of Hessenberg varieties and representations of symmetric groupsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] Geometry of Peterson Schubert calculus in type A and left-right diagrams2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] On singularity and normality of regular nilpotent Hessenberg varieties2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Fano and weak Fano Hessenberg varieties2021

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[Journal Article] Geometry of regular Hessenberg varieties2020

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[Journal Article] A survey of recent developments on Hessenberg varieties2020

Author(s)

Journal Title

Data Source

[Journal Article] Hessenberg varieties, Slodowy slices, and integrable systems2019

Author(s)

Journal Title

Data Source

[Journal Article] The cohomology rings of regular semisimple Hessenberg varieties for h=(h(1),n,...,n)2018

Author(s)

Journal Title

Data Source

[Journal Article] Hessenberg varieties for the minimal nilpotent orbit2017

Author(s)

Journal Title

Data Source

[Presentation] Line bundles over regular semisimple Hessenberg variety for h=(2,3,4,...,n,n)2024

Author(s)

Organizer

Data Source

[Presentation] Hessenberg varieties and toric geometry2024

Author(s)

Organizer

Data Source

[Presentation] Peterson varieties and toric orbifolds associated to Cartan matrices2023

Author(s)

Organizer

Data Source

[Presentation] Peterson varieties and Cartan toric orbifolds2023

Author(s)

Organizer

Data Source

[Presentation] Peterson多様体の非負部分とトーリック幾何2023

Author(s)

Organizer

Data Source

[Presentation] Peterson varietyの多面体について2023

Author(s)

Organizer

Data Source

Abe Hiraku 阿部拓

[Presentation] 旗多様体上のあるベクトル束に現れる正則 Poisson 構造と完全可積分系について2018