Abe Hiraku

アベヒラク | Abe Hiraku

Affiliation and department：

Research field (1)： Geometry

Research keywords (7)： Hessenberg varieties , Transformation groups , Schubert calculus , Toric varieties , Algebraic geometry , Algebraic topology , Combinatorics

Research theme for competitive and other funds (8)：

2023 - 2028 ヘッセンバーグ多様体とトーリック幾何の繋がり
2022 - 2023 Hessenberg多様体の幾何学と組み合わせ論
2020 - 2022 Hessenberg多様体のトポロジーと組合せ論
2018 - 2022 ヘッセンバーグ多様体の族と可積分系
2019 - 2020 トーラス群作用の幾何とトポロジー

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Papers (16)：

Hiraku Abe, Erik Insko. On singularity and normality of regular nilpotent Hessenberg varieties. Journal of Algebra. 2024. 651. 70-110
Hiraku Abe, Tatsuya Horiguchi, Hideya Kuwata, Haozhi Zeng. Geometry of Peterson Schubert calculus in type A and left-right diagrams. To appear in Algebraic Combinatorics. 2024
Hiraku Abe, Naoki Fujita, Haozhi Zeng. Fano and Weak Fano Hessenberg Varieties. Michigan Math. J. 2022. 73. 3. 511-555
Hiraku Abe, Tatsuya Horiguchi. A survey of recent developments on Hessenberg varieties. Schubert calculus and its applications in combinatorics and representation theory. 2020. 251-279
Hiraku Abe, Naoki Fujita, Haozhi Zeng. Geometry of regular Hessenberg varieties. Transform. Groups. 2020. 25. 305-333

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MISC (7)：

Hiraku Abe, Haozhi Zeng. Totally nonnegative part of the Peterson variety in Lie type A. 2023
Hiraku Abe, Haozhi Zeng. Peterson varieties and toric orbifolds associated to Cartan matrices. 2023
Hiraku Abe, Haozhi Zeng. The integral cohomology rings of Peterson varieties in type A. arXiv:2203.02629. 2022
阿部拓. 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. 数理解析研究所講究録. 2018. 76-82
阿部拓. ルート系から定まるトーリック多様体上の交叉数とヤング図 (変換群の位相幾何と代数構造). 数理解析研究所講究録. 2014. 1922. 78-83

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Books (1)：

トゥー多様体
裳華房 2019 ISBN:9784785315863

Lectures and oral presentations (23)：

Line bundles over regular semisimple Hessenberg variety for h=(2,3,4,...,n,n)
(TGTC workshop 2024 in Himeji 2024)
Hessenberg varieties and toric geometry
(第8回代数幾何学研究集会 -宇部- 2024)
Peterson多様体とトーリック幾何
(第49回変換群論シンポジウム (長崎商工会議所) 2023)
Peterson多様体の非負部分とトーリック幾何
(南大阪代数セミナー (i-Siteなんば) 2023)
Peterson varieties and toric orbifolds associated to Cartan matrices
(2023 KMS Annual Meeting (Seoul National University) 2023)

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Association Membership(s) (1)：

THE MATHEMATICAL SOCIETY OF JAPAN

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