Updated on 2024/10/29

Information

 

写真a

 
SASAHIRA HIROFUMI
 
Organization
Faculty of Mathematics Division of Algebra and Geometry 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
Professor
Profile
I study 4-dimensional manifolds, using gauge theory.
External link

Degree

  • Ph.D (mathematical science)

Research History

  • ２０１０年名古屋大学　多元数理科学研究科　助教   

Research Interests・Research Keywords

  • Research theme： I study 3 and 4-dimensional topology using gauge theory.

    Keyword： Geometry, Topology, Gauge theory

    Research period： 2007.4

Papers

  • Unfolded Seiberg-Witten Floer spectra II, Relative invariants and the gluing theorem. Reviewed International journal

    Tirasan Khandhawit, Jianfeng Lin, Hirofumi Sasahira

    Journal of Differential Geometry   124 ( 2 )   231 - 316   2023.6   （ ISSN:0022040X ）

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    Language：Japanese   Publishing type：Research paper (scientific journal)   Publisher：Journal of Differential Geometry  

    We use the construction of unfolded Seiberg–Witten Floer spectra of general 3-manifolds defined in our previous paper to extend the notion of relative Bauer–Furuta invariants to general 4-manifolds with boundary. One of the main purposes of this paper is to give a detailed proof of the gluing theorem for the relative invariants.

    DOI： 10.4310/jdg/1686931602

    Scopus

  • UNFOLDED SEIBERG-WITTEN FLOER SPECTRA, II: RELATIVE INVARIANTS AND THE GLUING THEOREM

    Khandhawit, T; Lin, JF; Sasahira, H

    JOURNAL OF DIFFERENTIAL GEOMETRY   124 ( 2 )   231 - 316   2023.6   （ ISSN:0022-040X eISSN:1945-743X ）

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  • Seiberg-Witten Floer stable homotopy type and its applications to corks and the intersection forms of 4-manifolds (New trends of transformation groups)

    Sasahira Hirofumi

    RIMS Kokyuroku   2231   64 - 69   2022.11   （ ISSN:18802818 ）

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    Language：Japanese   Publisher：京都大学数理解析研究所  

    CiNii Research

  • Twisted Donaldson invariants Reviewed International journal

    Tsuyoshi Kato, Hirofumi Sasahira, Hang Wang

    Mathematical Proceeding of the Cambridge Philosophical Society   2021.2

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

    DOI： https://doi.org/10.1017/S0305004121000013

  • Unfolded Seiberg–Witten Floer spectra, I : Definition and invariance Reviewed International journal

    Tirasan Khandhawit, Jianfeng Lin, Hirofumi Sasahira

    Geometry and Topology   22 ( 4 )   2027 - 2114   2018.4

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

    DOI： 10.2140/gt.2018.22.2027

    Repository Public URL： http://hdl.handle.net/2324/4771849

  • Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number II: Applications. Reviewed International journal

    Masashi Ishida, Hirofumi Sasahira

    Communications in Analysis and Geometry   2017.1

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

  • Stable cohomotopy Seiberg-Witten invariants of connected sums of four-manifolds with positive first Betti number, I: non-vanishing theorem. Reviewed International journal

    Masashi Ishida, Hirofumi Sasahira

    International Journal of Mathematics   2015.4

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

  • Floer homology for 2-torsion instanton invariants Invited Reviewed International journal

    Hirofumi Sasahira

    Asian Journal of Mathematics   2013.9

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

  • Instanton Floer homology for lens spaces. Invited Reviewed International journal

    Hirofumi Sasahira

    Mathematische Zeitschrift   2012.3

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

  • An SO(3)-version of 2-torsion instanton invariants. Invited Reviewed International journal

    Hirofumi Sasahira

    The University of Tokyo. Journal of Mathematical Sciences   2008.1

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

  • Spin structures on Seiberg-Witten moduli spaces. Reviewed International journal

    Hirofumi Sasahira

    The University of Tokyo. Journal of Mathematical Sciences   2006.1

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

▼display all

Books

Presentations

  • Surgery exact triangle for Seiberg-Witten Floer stable homotopy type International conference

    笹平　裕史

    Gauge theory in Kyoto  2023.3 

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    Event date： 2023.3

    Language：Japanese  

    Venue：京都大学   Country：Japan  

  • Seiberg-Witten Floer stable homotopy type and its applications to corks and the intersection forms of 4-manifolds

    笹平 裕史

    変換群論の新潮流  2022.5 

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    Event date： 2022.5

    Language：Japanese  

    Venue：京都大学   Country：Japan  

  • 第一Betti数が正の３次元多様体のSeiberg-Witten-Floer安定ホモトピー型とトポロジーへの応用

    笹平　裕史

    研究集会"４次元トポロジー"  2020.11 

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    Event date： 2020.11

    Language：Japanese  

    Venue：オンライン   Country：Japan  

  • Seiberg-Witten-Floer安定ホモトピー型 Invited

    笹平 裕史

    幾何学シンポジウム  2019.8 

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    Event date： 2020.8

    Language：Japanese   Presentation type：Oral presentation (general)  

    Venue：名古屋大学   Country：Japan  

  • Seiberg-Witten-Floer stable homotopy type for 3-manifolds with positive first Betti number Invited International conference

    笹平 裕史

    第1回日独友好幾何学研究集会  2019.9 

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    Event date： 2020.1

    Language：English   Presentation type：Oral presentation (general)  

    Venue：中央大学   Country：Japan  

  • Seiberg-Witten equations and topology Invited International conference

    笹平　裕史

    Geometry, Topology and Dynamics seminar  2019.1 

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    Event date： 2019.1

    Language：English   Presentation type：Oral presentation (general)  

    Venue：OIST   Country：Japan  

  • Twisted Donaldson invariants International conference

    笹平　裕史

    Spring operator algebra program  2018.4 

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    Event date： 2018.4

    Language：English  

    Venue：East China Normal University   Country：China  

  • Seiberg-Witten方程式とその応用 Invited

    笹平　裕史

    日本数学会　幾何学分科会特別講演  2018.3 

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    Event date： 2018.3

    Language：Japanese   Presentation type：Oral presentation (invited, special)  

    Venue：東京大学   Country：Japan  

  • Analytic construction of spectral section International conference

    笹平　裕史

    Gauge theory in Fukuoka  2018.2 

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    Event date： 2018.2

    Language：English  

    Country：Japan  

  • ゲージ理論の低次元トポロジーへの応用

    笹平　裕史

    京都大学　談話会  2017.12 

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    Event date： 2017.12

    Language：Japanese  

    Country：Japan  

  • Twisted Donaldson invariants International conference

    笹平　裕史

    Advances in non commutative geometry  2017.5 

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    Event date： 2017.5

    Language：English  

    Country：Japan  

  • Unfolded Seiberg-Witten stable homotopy type International conference

    笹平　裕史

    Australia-Japan Geometry, Analysis and their applications  2017.1 

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    Event date： 2017.1

    Language：English  

    Venue：京都大学   Country：Japan  

  • Seiberg-Witten-Floer 安定ホモトピー型

    笹平　裕史

    関西ゲージ理論セミナー  2016.3 

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    Event date： 2016.3

    Language：Japanese  

    Venue：京都大学   Country：Japan  

  • Spin structures on Seiberg-Witten moduli spaces International conference

    笹平　裕史

    The joint Los Angeles topology seminar  2015.4 

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    Event date： 2015.4

    Language：English  

    Venue：UCLA   Country：United States  

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Professional Memberships

  • 日本数学会

Academic Activities

  • 組織委員 International contribution

    East Asia conference on gauge theory and related topics  （ Japan ） 2018.9

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    Type：Competition, symposium, etc. 

  • 組織委員 International contribution

    Gauge theory in Fukuoka  （ Japan ） 2018.2

    　More details

    Type：Competition, symposium, etc. 

Research Projects

  • Computations and applications of Seiberg-Witten Floer stable homotopy type

    Grant number：23K03115  2023 - 2027

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    笹平 裕史

    　 More details

    Authorship：Principal investigator  Grant type：Scientific research funding

    Seiberg-Witten Floer安定ホモトピー型という３次元多様体の不変量の計算手法を開発し、低次元トポロジーや結び目理論への応用を行う予定である。応用として、境界付き４次元多様体のトポロジーへの応用や、Seiberg-Witten Floer安定ホモトピー型と結目理論の不変量であるKhovanovホモトピーとの関連を研究していく予定である。

    CiNii Research

  • ゲージ理論からの無限次元力学系とホモトピー論による低次元多様体の不変量

    Grant number：19K03493  2019 - 2022

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

    笹平 裕史

    　 More details

    Authorship：Principal investigator  Grant type：Scientific research funding

    本研究は３次元多様体、４次元多様体と呼ばれる図形の分類や性質を調べることを目的としている。その方法として、ゲージ理論とよばれる理論に由来する偏微分方程式を用いる。その偏微分方程式からうまく３次元、４次元多様体の情報を取り出すことが重要である。本研究では、Floer理論やホモトピー論というものを用いて情報を取り出す。

    CiNii Research

  • Floer 理論のホモトピー論的研究とその応用

    2016 - 2019

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Young Scientists(A)or(B)

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    Authorship：Principal investigator  Grant type：Scientific research funding

  • 精密化されたゲージ理論的不変量の研究

    2013 - 2015

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Young Scientists(A)or(B)

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    Authorship：Principal investigator  Grant type：Scientific research funding

Educational Activities

  • I have lectures and seminars on geometry.

Class subject

  • 微分積分学Ⅱ

    2023.10 - 2024.3   Second semester

  • 幾何学Ⅲ

    2023.10 - 2024.3   Second semester

  • コアセミナーⅡ

    2023.10 - 2024.3   Second semester

  • 数学入門

    2023.10 - 2024.3   Second semester

  • 微分積分学Ⅰ

    2023.4 - 2023.9   First semester

  • 数理科学特別講義XⅢ

    2022.10 - 2023.3   Second semester

  • 微分幾何学基礎・演習

    2022.10 - 2023.3   Second semester

  • 数理科学特論１３

    2022.10 - 2023.3   Second semester

  • コアセミナーⅡ

    2022.10 - 2023.3   Second semester

  • 数学入門

    2022.10 - 2023.3   Second semester

  • 応用複素関数論

    2022.4 - 2022.9   First semester

  • 入門線形代数Ⅱ

    2021.6 - 2021.8   Summer quarter

  • 入門線形代数Ⅱ

    2021.6 - 2021.8   Summer quarter

  • 応用複素関数論

    2021.4 - 2021.9   First semester

  • 入門線形代数Ⅰ

    2021.4 - 2021.6   Spring quarter

  • 入門線形代数Ⅰ

    2021.4 - 2021.6   Spring quarter

  • 微分積分学・同演習Ｂ

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習Ｂ

    2020.10 - 2021.3   Second semester

  • 線形代数学・同演習Ａ

    2020.4 - 2020.9   First semester

  • 微分積分学・同演習Ａ

    2020.4 - 2020.9   First semester

  • 応用複素関数論

    2020.4 - 2020.9   First semester

  • 線形代数学・同演習Ｂ

    2019.10 - 2020.3   Second semester

  • 位相幾何学基礎・演習

    2019.10 - 2020.3   Second semester

  • 幾何学Ⅰ・演習

    2019.4 - 2019.9   First semester

  • 微分幾何学大意

    2019.4 - 2019.9   First semester

  • 微分幾何学大意

    2019.4 - 2019.9   First semester

  • 線形代数学・同演習Ａ

    2019.4 - 2019.9   First semester

  • 数学特論４

    2019.4 - 2019.9   First semester

  • 微分積分学・同演習Ⅱ

    2018.10 - 2019.3   Second semester

  • 位相幾何学基礎・演習

    2018.10 - 2019.3   Second semester

  • 線形代数学・同演習Ｂ

    2018.10 - 2019.3   Second semester

  • 数学特論４

    2018.4 - 2018.9   First semester

  • 微分幾何学大意

    2018.4 - 2018.9   First semester

  • 微分幾何学大意

    2018.4 - 2018.9   First semester

  • 線形代数学・同演習Ａ

    2018.4 - 2018.9   First semester

  • 微分積分学・同演習Ⅰ

    2018.4 - 2018.9   First semester

  • 幾何学Ⅰ・演習

    2018.4 - 2018.9   First semester

  • 線形代数学･同演習B

    2017.10 - 2018.3   Second semester

  • 数理科学特別講義Ⅶ

    2017.10 - 2018.3   Second semester

  • 線形代数学･同演習B

    2017.10 - 2018.3   Second semester

  • 微分積分学･同演習Ⅱ

    2017.10 - 2018.3   Second semester

  • 微分積分学･同演習Ⅰ

    2017.4 - 2017.9   First semester

  • 線形代数学･同演習A

    2017.4 - 2017.9   First semester

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Visiting, concurrent, or part-time lecturers at other universities, institutions, etc.

  • 2017  京都大学  Classification:Intensive course 

Outline of Social Contribution and International Cooperation activities

  • I gave public lectures on geometry. And I organized international conferences on gauge theory.

Social Activities

  • オープンキャンパスで模擬講義を行なった

    九州大学オープンキャンパス  2019.8

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    Audience：General,　Scientific,　Company,　Civic organization,　Governmental agency

    Type：Lecture

  • オイラー数とトポロジーという題目で講義した.

    九州大学  九州大学 西新プラザ  2017.8

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    Audience：General,　Scientific,　Company,　Civic organization,　Governmental agency

    Type：Lecture

Travel Abroad

  • 2014.11 - 2014.12

    Staying countory name 1：Germany   Staying institution name 1：マックスプランク研究所

  • 2012.8 - 2013.7

    Staying countory name 1：United States   Staying institution name 1：ハーバード大学