Updated on 2026/03/22

写真a

 
ISHIDA HIROAKI
 
Organization
Graduate School of Science Department of Mathematics Associate Professor
School of Science Department of Mathematics
Title
Associate Professor
Affiliation
Institute of Science
Contact information
メールアドレス
Homepage
https://researchmap.jp/hiroaki.ishida?lang=en
Affiliation campus
Sugimoto Campus

Position

  • Graduate School of Science Department of Mathematics 

    Associate Professor  2023.04 - Now

  • School of Science Department of Mathematics 

    Associate Professor  2023.04 - Now

Degree

  • 博士（理学） （ Osaka City University ）

  • 修士（理学） （ Osaka City University ）

  • 学士（理学） （ Osaka City University ）

Papers

  • Double-sided torus actions and complex geometry on $SU(3)$ Reviewed

    Hiroaki Ishida, Hisashi Kasuya

    Journal of Symplectic Geometry   23 ( 4 )   751 - 777   2025.09（ ISSN:1527-5256 ） （ eISSN:1540-2347 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.4310/jsg.250820105435

  • Strong cohomological rigidity of Hirzebruch surface bundles in Bott towers Reviewed

    Hiroaki ISHIDA

    Journal of the Mathematical Society of Japan   -1 ( -1 )   2024.01（ ISSN:0025-5645 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.2969/jmsj/88718871

  • Non-invariant deformations of left-invariant complex structures on compact Lie groups Reviewed

    Hiroaki Ishida, Hisashi Kasuya

    Forum Mathematicum   2022.04（ ISSN:0933-7741 ） （ eISSN:1435-5337 ）

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    Publishing type：Research paper (scientific journal)  

    Abstract

    We give small deformations of a left-invariant complex structure on each simply connected semisimple compact Lie group of even dimension which are not biholomorphic to any left-invariant (right-invariant) complex structure by using the Kuranishi space.On such deformed complex manifolds, we prove the Borel–Weil–Bott type theorem, and we compute the cohomology of holomorphic tangent bundles.

    DOI： 10.1515/forum-2021-0133

    Other URL： https://www.degruyter.com/document/doi/10.1515/forum-2021-0133/pdf

  • Basic Cohomology of Canonical Holomorphic Foliations on Complex Moment-Angle Manifolds Reviewed

    Hiroaki Ishida, Roman Krutowski, Taras Panov

    International Mathematics Research Notices   2022 ( 7 )   5541 - 5563   2022.03（ ISSN:1073-7928 ） （ eISSN:1687-0247 ）

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    Publishing type：Research paper (scientific journal)  

    Abstract

    We describe the basic cohomology ring of the canonical holomorphic foliation on a moment-angle manifold, LVMB-manifold, or any complex manifold with a maximal holomorphic torus action. Namely, we show that the basic cohomology has a description similar to the cohomology ring of a complete simplicial toric variety due to Danilov and Jurkiewicz. This settles a question of Battaglia and Zaffran, who previously computed the basic Betti numbers for the canonical holomorphic foliation in the case of a shellable fan. Our proof uses an Eilenberg–Moore spectral sequence argument; the key ingredient is the formality of the Cartan model for the torus action on a moment-angle manifold. We develop the concept of transverse equivalence as an important tool for studying smooth and holomorphic foliated manifolds. For an arbitrary complex manifold with a maximal torus action, we show that it is transverse equivalent to a moment-angle manifold and therefore has the same basic cohomology.

    DOI： 10.1093/imrn/rnaa252

  • Complex manifolds with maximal torus actions Reviewed

    Hiroaki Ishida

    Journal für die reine und angewandte Mathematik (Crelles Journal)   2019 ( 751 )   121 - 184   2019.06（ ISSN:0075-4102 ） （ eISSN:1435-5345 ）

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    Publishing type：Research paper (scientific journal)  

    <title>Abstract</title>In this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds, in terms of combinatorial objects, which are triples <inline-formula id="j_crelle-2016-0023_ineq_9999_w2aab3b7b1b1b6b1aab1c14b1b1Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2016-0023_eq_0410.png" /><tex-math>{(\Delta,\mathfrak{h},G)}</tex-math></alternatives></inline-formula> of nonsingular complete fan Δ in <inline-formula id="j_crelle-2016-0023_ineq_9998_w2aab3b7b1b1b6b1aab1c14b1b3Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2016-0023_eq_1084.png" /><tex-math>{\mathfrak{g } }</tex-math></alternatives></inline-formula>, complex vector subspace <inline-formula id="j_crelle-2016-0023_ineq_9997_w2aab3b7b1b1b6b1aab1c14b1b5Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2016-0023_eq_1090.png" /><tex-math>{\mathfrak{h } }</tex-math></alternatives></inline-formula> of <inline-formula id="j_crelle-2016-0023_ineq_9996_w2aab3b7b1b1b6b1aab1c14b1b7Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2016-0023_eq_1080.png" /><tex-math>{\mathfrak{g}^{\mathbb{C } } }</tex-math></alternatives></inline-formula> and compact torus <italic>G</italic> satisfying certain conditions. We also give an equivalence of categories with suitable definitions of morphisms in these families, like toric geometry. We obtain several results as applications of our equivalence of categories; complex structures on moment-angle manifolds, classification of holomorphic nondegenerate <inline-formula id="j_crelle-2016-0023_ineq_9995_w2aab3b7b1b1b6b1aab1c14b1c11Aa"><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_crelle-2016-0023_eq_0986.png" /><tex-math>{\mathbb{C}^{n } }</tex-math></alternatives></inline-formula>-actions on compact connected complex manifolds of complex dimension <italic>n</italic>, and construction of concrete examples of non-Kähler manifolds.

    DOI： 10.1515/crelle-2016-0023

    Other URL： https://www.degruyter.com/document/doi/10.1515/crelle-2016-0023/pdf

  • Transverse Kähler structures on central foliations of complex manifolds Reviewed

    Hiroaki Ishida, Hisashi Kasuya

    Annali di Matematica Pura ed Applicata (1923 -)   198 ( 1 )   61 - 81   2019.02（ ISSN:0373-3114 ） （ eISSN:1618-1891 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s10231-018-0762-8

    Other URL： http://link.springer.com/article/10.1007/s10231-018-0762-8/fulltext.html

  • Torus invariant transverse Kähler foliations Reviewed

    Hiroaki Ishida

    Transactions of the American Mathematical Society   369 ( 7 )   5137 - 5155   2017.03（ ISSN:0002-9947 ） （ eISSN:1088-6850 ）

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    Publishing type：Research paper (scientific journal)  

    <p>In this paper, we show the convexity of the image of a moment map on a transverse symplectic manifold equipped with a torus action under a certain condition. We also study properties of moment maps in the case of transverse Kähler manifolds. As an application, we give a positive answer to the conjecture posed by Cupit-Foutou and Zaffran.</p>

    DOI： 10.1090/tran/7070

  • The cohomology ring of the GKM graph of a flag manifold of classical type Reviewed

    Yukiko Fukukawa, Hiroaki Ishida, Mikiya Masuda

    Kyoto Journal of Mathematics   54 ( 3 )   2014（ ISSN:2156-2261 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.1215/21562261-2693478

  • Invariant stably complex structures on topological toric manifolds Reviewed

    Hiroaki Ishida

    Osaka Journal of Mathematics   50 ( 3 )   795 - 806   2013.09（ ISSN:0030-6126 ）

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    Publishing type：Research paper (scientific journal)  

    CiNii Research

    Other URL： http://hdl.handle.net/11094/26017

  • Completely integrable torus actions on complex manifolds with fixed points Reviewed

    Hiroaki Ishida, Yael Karshon

    Mathematical Research Letters   19 ( 6 )   1283 - 1295   2013.07（ ISSN:1073-2780 ） （ eISSN:1945-001X ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.4310/mrl.2012.v19.n6.a9

  • Topological Toric Manifolds Reviewed

    Hiroaki Ishida, Yukiko Fukukawa, Mikiya Masuda

    Moscow Mathematical Journal   13 ( 1 )   57 - 98   2013（ ISSN:1609-3321 ） （ eISSN:1609-4514 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.17323/1609-4514-2013-13-1-57-98

  • Todd genera of complex torus manifolds Reviewed

    Hiroaki Ishida, Mikiya Masuda

    Algebraic & Geometric Topology   12 ( 3 )   1777 - 1788   2012.08（ ISSN:1472-2747 ） （ eISSN:1472-2739 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.2140/agt.2012.12.1777

  • Filtered cohomological rigidity of Bott towers Reviewed

    Hiroaki Ishida

    Osaka Journal of Mathematics   49 ( 2 )   515 - 522   2012.07

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    Publishing type：Research paper (scientific journal)  

  • Symplectic real Bott manifolds Reviewed

    Hiroaki Ishida

    Proceedings of the American Mathematical Society   139 ( 8 )   3009 - 3014   2011.01（ ISSN:0002-9939 ） （ eISSN:1088-6826 ）

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    Publishing type：Research paper (scientific journal)  

    <p>A real Bott manifold is the total space of an iterated <inline-formula content-type="math/mathml">
    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R upper P Superscript 1">
    <mml:semantics>
    <mml:mrow>
    <mml:mrow class="MJX-TeXAtom-ORD">
    <mml:mi mathvariant="double-struck">R</mml:mi>
    </mml:mrow>
    <mml:msup>
    <mml:mi>P</mml:mi>
    <mml:mn>1</mml:mn>
    </mml:msup>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\mathbb {R}P^1</mml:annotation>
    </mml:semantics>
    </mml:math>
    </inline-formula>-bundle over a point, where each <inline-formula content-type="math/mathml">
    <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R upper P Superscript 1">
    <mml:semantics>
    <mml:mrow>
    <mml:mrow class="MJX-TeXAtom-ORD">
    <mml:mi mathvariant="double-struck">R</mml:mi>
    </mml:mrow>
    <mml:msup>
    <mml:mi>P</mml:mi>
    <mml:mn>1</mml:mn>
    </mml:msup>
    </mml:mrow>
    <mml:annotation encoding="application/x-tex">\mathbb {R}P^1</mml:annotation>
    </mml:semantics>
    </mml:math>
    </inline-formula>-bundle is the projectivization of a Whitney sum of two real line bundles. In this paper, we characterize real Bott manifolds which admit a symplectic form. In particular, it turns out that a real Bott manifold admits a symplectic form if and only if it is cohomologically symplectic. In this case, it admits even a Kähler structure. We also prove that any symplectic cohomology class of a real Bott manifold can be represented by a symplectic form. Finally, we study the flux of a symplectic real Bott manifold.</p>

    DOI： 10.1090/s0002-9939-2011-10729-9

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Presentations

  • トーラス作用で不変な横断ケーラー構造

    石田 裕昭

    葉層構造論シンポジウム（2024年）：特に複素解析的ベクトル場・葉層構造とその周辺について  2024.10 

  • Complex manifolds with maximal torus actions International conference

    Hiroaki Ishida

    IMVAST-OCAMI Joint Conference on Selected Areas in Mathematics  2024.05  Doan Trung Cuong, Phng Ho Hai, Doan Thai Son (IMVAST), Hirotaka Akiyoshi, Mitsuyasu Hashimoto, Futoshi Takahashi, Hiroshi Tamaru (OCAMI)

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    Presentation type：Oral presentation (invited, special)  

    Venue：10th Floor, Sugimoto Library, Osaka Metropolitan University  

Grant-in-Aid for Scientific Research

  • リー群上の両側トーラス作用の幾何とトポロジー

    Grant-in-Aid for Scientific Research(C)  2028

  • リー群上の両側トーラス作用の幾何とトポロジー

    Grant-in-Aid for Scientific Research(C)  2027

  • リー群上の両側トーラス作用の幾何とトポロジー

    Grant-in-Aid for Scientific Research(C)  2026

  • リー群上の両側トーラス作用の幾何とトポロジー

    Grant-in-Aid for Scientific Research(C)  2025

  • リー群上の両側トーラス作用の幾何とトポロジー

    Grant-in-Aid for Scientific Research(C)  2024

Charge of on-campus class subject

  • 海外特別研究3

    2025   Intensive lecture   Graduate school

  • 海外特別研究3

    2025   Intensive lecture   Graduate school

  • 海外特別研究4

    2025   Intensive lecture   Graduate school

  • 海外特別研究5

    2025   Intensive lecture   Graduate school

  • 数学特別研究3B

    2025   Intensive lecture   Graduate school

  • 数学特別研究4B

    2025   Intensive lecture   Graduate school

  • 数学特別研究5B

    2025   Intensive lecture   Graduate school

  • 幾何構造論ゼミナール

    2025   Intensive lecture   Graduate school

  • 幾何構造論ゼミナール

    2025   Intensive lecture   Graduate school

  • 幾何学特論B

    2025   Weekly class   Graduate school

  • 幾何構造論演習1

    2025   Intensive lecture   Graduate school

  • 幾何構造論演習2

    2025   Intensive lecture   Graduate school

  • 海外特別研究1

    2025   Intensive lecture   Graduate school

  • 海外特別研究2

    2025   Intensive lecture   Graduate school

  • 数学特別研究1B

    2025   Intensive lecture   Graduate school

  • 数学特別研究2B

    2025   Intensive lecture   Graduate school

  • 特別研究

    2025   Intensive lecture   Undergraduate

  • 幾何学講義Ⅲ

    2025   Weekly class   Undergraduate

  • 海外特別研究

    2025   Intensive lecture   Undergraduate

  • 数学卒業研究B

    2025   Intensive lecture   Undergraduate

  • 数学特別研究3A

    2025   Intensive lecture   Graduate school

  • 数学特別研究4A

    2025   Intensive lecture   Graduate school

  • 数学特別研究5A

    2025   Intensive lecture   Graduate school

  • 数学概論A

    2025   Weekly class   Graduate school

  • 海外特別研究2

    2025   Intensive lecture   Graduate school

  • 数学特別研究1A

    2025   Intensive lecture   Graduate school

  • 数学特別研究2A

    2025   Intensive lecture   Graduate school

  • 微分幾何学1

    2025   Weekly class   Undergraduate

  • 微分幾何学1演習

    2025   Weekly class   Undergraduate

  • 数学卒業研究A

    2025   Intensive lecture   Undergraduate

  • 海外特別研究

    2024   Intensive lecture   Undergraduate

  • 特別研究

    2024   Intensive lecture   Undergraduate

  • 幾何構造論ゼミナールA

    2024   Intensive lecture   Graduate school

  • 海外特別研究3

    2024   Intensive lecture   Graduate school

  • 海外特別研究4

    2024   Intensive lecture   Graduate school

  • 海外特別研究5

    2024   Intensive lecture   Graduate school

  • 数学特別研究3B

    2024   Intensive lecture   Graduate school

  • 数学特別研究4B

    2024   Intensive lecture   Graduate school

  • 数学特別研究5B

    2024   Intensive lecture   Graduate school

  • 幾何構造論演習1

    2024   Intensive lecture   Graduate school

  • 海外特別研究1

    2024   Intensive lecture   Graduate school

  • 海外特別研究2

    2024   Intensive lecture   Graduate school

  • 海外特別研究2

    2024   Intensive lecture   Graduate school

  • 数学特別研究1B

    2024   Intensive lecture   Graduate school

  • 数学特別研究2B

    2024   Intensive lecture   Graduate school

  • 位相数学2

    2024   Weekly class   Undergraduate

  • 位相数学2演習

    2024   Weekly class   Undergraduate

  • 数学特別研究3A

    2024   Intensive lecture   Graduate school

  • 数学特別研究4A

    2024   Intensive lecture   Graduate school

  • 数学特別研究5A

    2024   Intensive lecture   Graduate school

  • 幾何構造論特別講義A

    2024   Intensive lecture   Graduate school

  • 数学特別研究1A

    2024   Intensive lecture   Graduate school

  • 数学特別研究2A

    2024   Intensive lecture   Graduate school

  • 微分幾何学1

    2024   Weekly class   Undergraduate

  • 微分幾何学1演習

    2024   Weekly class   Undergraduate

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Faculty development activities

  • 2025年度前期数学FDミーティング  2025

  • 2025年度後期数学FDミーティング  2025

  • 2024年度FD研修会「科学計算と数学」  2024

  • 2024年度後期数学FDミーティング  2024

  • 2024年度前期数学FDミーティング  2024