Updated on 2025/04/12

写真a

 
MATSUO Shinichiroh
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Associate Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate Professor
External link

Degree 1

  1. Doctor (Mathematical Sciences) ( 2010.3   The University of Tokyo ) 

Research Interests 11

  1. scalar curvature

  2. Gauge theory

  3. Differential geometry

  4. Geometric analysis

  5. lattice gauge theory

  6. index theorem

  7. Nevanlinna theory

  8. Gauge theory

  9. dynamical system

  10. Geometric analysis

  11. Differential geometry

Research Areas 2

  1. Natural Science / Geometry

  2. Natural Science / Geometry

Research History 9

  1. Nagoya University   Associate Professor

    2016.4

      More details

  2. Osaka University   Graduate School of Mathematics   Associate Professor

    2012.4 - 2016.3

      More details

    Country:Japan

  3. Osaka University   Assistant Professor

    2012.4 - 2016.3

      More details

  4. Kyoto University   Department of Mathematics, Graduate School of Science   JSPS PD

    2011.4 - 2012.3

      More details

    Country:Japan

  5. Kyoto University   JSPS PD

    2011.4 - 2012.3

      More details

▼display all

Education 4

  1. The University of Tokyo   Graduate School, Division of Mathematical Sciences   Mathematical sciences

    2007.4 - 2010.3

      More details

    Country: Japan

  2. University of Tokyo

    2005.4 - 2010.3

      More details

  3. The University of Tokyo   Graduate School, Division of Mathematical Sciences   Mathematical sciences

    2005.4 - 2007.3

      More details

    Country: Japan

  4. The University of Tokyo   Faculty of Science

    2001.4 - 2005.3

      More details

    Country: Japan

Professional Memberships 1

  1. Mathematical Society of Japan

 

Papers 9

  1. The Atiyah–Patodi–Singer Index and Domain-Wall Fermion Dirac Operators Reviewed

    Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi, Mayuko Yamashita

    Communications in Mathematical Physics   Vol. 380 ( 3 ) page: 1295 - 1311   2020.8

     More details

    Authorship:Corresponding author   Publishing type:Research paper (scientific journal)   Publisher:Springer Science and Business Media LLC  

    DOI: 10.1007/s00220-020-03806-0

    Web of Science

    researchmap

    Other Link: http://link.springer.com/article/10.1007/s00220-020-03806-0/fulltext.html

  2. The prescribed scalar curvature problem for metrics with unit total volume Reviewed

    Shinichiroh Matsuo

    MATHEMATISCHE ANNALEN   Vol. 360 ( 3-4 ) page: 675 - 680   2014.12

     More details

    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER HEIDELBERG  

    We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.

    DOI: 10.1007/s00208-014-1052-4

    Web of Science

    arXiv

    researchmap

  3. Brody curves and mean dimension Reviewed

    Shinichiroh Matsuo, Masaki Tsukamoto

    Journal of the American Mathematical Society   Vol. 28 ( 1 ) page: 159 - 182   2014.5

     More details

    Publishing type:Research paper (scientific journal)   Publisher:American Mathematical Society (AMS)  

    DOI: 10.1090/s0894-0347-2014-00798-0

    researchmap

  4. The index of lattice Dirac operators and K-theory Invited

    Shoto Aoki, Hidenori Fukaya, Mikio Furuta, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi

    arXiv     2024.7

     More details

    Authorship:Corresponding author   Language:English  

  5. Mod-two APS index and domain-wall fermion Reviewed

    Hidenori Fukaya, Mikio Furuta, Yoshiyuki Matsuki, Shinichiroh Matsuo, Tetsuya Onogi, Satoshi Yamaguchi, and Mayuko Yamashita

    Letters in Mathematical Physics   Vol. 112 ( 16 )   2022.2

     More details

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

    DOI: https://doi.org/10.1007/s11005-022-01509-2

▼display all

Books 5

  1. h同境定理

    松尾 信一郎( Role: Supervisor (editorial) ,  監訳者)

    岩波書店  2024.11  ( ISBN:9784000050975

     More details

    Total pages:132   Language:Japanese Book type:Scholarly book

  2. Bott周期性と族の指数

    松尾 信一郎( Role: Sole author)

    2024.8 

     More details

    Language:Japanese

  3. 位相的K理論をめぐって

    ( Role: Supervisor (editorial))

    サイエンス社  2024.8 

     More details

    Language:Japanese

  4. 巻頭言

    松尾 信一郎( Role: Sole author)

    2024.8 

     More details

    Language:Japanese Book type:Scholarly book

  5. K理論

    松尾 信一郎( Role: Supervisor (editorial) ,  監訳者)

    岩波書店  2022.7  ( ISBN:9784000053310

     More details

    Total pages:214   Language:Japanese Book type:Scholarly book

    Other Link: https://www.iwanami.co.jp/moreinfo/tachiyomi/0053310.pdf

Presentations 4

  1. Lattice gauge theory and the discretization of Dirac operators Invited International conference

    Shenzhen-Nagoya Workshop on Quantum Science  2023.9.6 

     More details

    Event date: 2023.9

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

  2. Lattice gauge theory and the discretization of Dirac operators Invited International conference

    Joint Japan/US Collaborative Workshop on Geometric Analysis  2023.8.8 

     More details

    Event date: 2023.8

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

    Venue:Stanford  

  3. Lattice gauge theory and the discretization of Dirac operators Invited International conference

    Geometric Analysis in Regensburg  2023.3.8 

     More details

    Event date: 2023.3

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

    Venue:Regensburg  

  4. The prescribed scalar curvature problem for metrics with unit total volume Invited International conference

    Workshop on Variational Methods and Functional Inequalities  2023.2.15 

     More details

    Event date: 2023.2

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

    Venue:Osaka  

KAKENHI (Grants-in-Aid for Scientific Research) 11

  1. 格子ゲージ理論の四次元多様体論への応用とザイバーグ=ウィッテン理論の差分化

    Grant number:21K03222  2021.4 - 2026.3

    科学研究費助成事業  基盤研究(C)

    松尾 信一郎

      More details

    Authorship:Principal investigator 

    Grant amount:\3900000 ( Direct Cost: \3000000 、 Indirect Cost:\900000 )

    1. 平坦とは限らないトーラスにおいてWD作用素を定式化して,トーラスに正スカラー曲率計量が存在しないことを組み合わせ論的に証明すること.
    2. 一般のリーマン多様体でWD作用素を定式化して,特に四次元多様体のとき,ロホリンの定理を組み合わせ論的に証明すること.
    3. 一般の四次元リーマン多様体でWD作用素を用いて,非線型方程式のザイバーグ=ウィッテン方程式を組み合わせ論的に再定式化すること.
    今年度も,前年度までに引き続き,境界付き多様体の指数とドメインウォールフェルミオンとの関係について考察した.物理的にはアノマリーの考察に相当する.最初に得られたのはAPS指数のときで,次が mod 2指数のときで,現在は複素フェルミオンのときを引き続き考えている.しかし,めざましい進展は得られなかったので,前年度に引き続き,物理的応用も研究することにした.そちらではGelfand-Yaglom理論についての結果が出た.論文準備中である.
    また,格子指数の連続極限の存在について証明を大幅に簡略化した.自明なベクトル束に非自明な接続を入れたときに帰着することができた.証明の大幅な簡略化である.結果としてウィルソン項の数学的位置付けがさらに明確になった.
    さらに,派生研究として,反自己双対計量のモジュライ空間の向き付けについてさらに考察した.K3曲面のとき,反自己双対計量のモジュライ空間が向き付け可能ではないという大変興味深い結果を得ていたが,その証明をさらに見直し,現在も引き続き一般の多様体の向き付けの条件を求めるために,KR指数を計算している.
    当初の計画通りにおおむね順調に進展しており,さらに派生研究もある.
    今後は,複素フェルミオンを引き続き考えるとともに,格子指数の応用を探っていきたい.また,ウィルソン項の役割をさらに突き詰めることによって,格子指数への透明な理解を目指す.おそらくそれはザイバーグーウィッテン理論への応用もあると考えている.

  2. Does a compact hyperbolic 4-manifold have a symplectic structure?

    Grant number:17K14186  2017.4 - 2022.3

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

    Matsuo Shinichiroh

      More details

    Authorship:Principal investigator 

    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    We have investigated the scope of Witten localisation techniques:
    First, we studied the relation between the index on manifolds with boundary and domain wall fermions, inspired by lattice gauge theory; and we derived a formula expressing the Atiyah-Patodi-Singer index interms of the eta invariants of domain wall fermion Dirac operators. We also studied mod 2 extensions.
    Second, we have studied the orientation of moduli spaces of anti-self-dual metrics.

    researchmap

  3. Moduli theory of non linear elliptic operators over non compact manifolds

    Grant number:25287009  2013.4 - 2017.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)

    Kato Tsuyoshi, Kida Yoshikata, Oguni Shin-ichi, Fukaya Tomohiro, Tsukamoto Masaki, Matsuo Shinichiroh

      More details

    Authorship:Collaborating Investigator(s) (not designated on Grant-in-Aid) 

    I have constructed a monopole map over the universal covering space of a compact oriented smooth four manifold. We apply the infinite dimensional Bott periodicity by Higson-Kasparov-Trout. In particular its degree was given when the linearized map is isomorphic, as an element in the equivariant E theory. It produces a homomorphism between K group of C* algebras related to the group ring. It corresponds to a covering version of the Bauer-Furuta degree.
    As an application, we proposed an aspherical 10/8 inequality for spin classifying 4 manifolds. We have also verified that it certainly holds for large class of 4 manifolds which includes complex minimal surfaces of general type.

  4. Moduli spaces of instantons from a metric point of view

    Grant number:25800045  2013.4 - 2017.3

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

    Matsuo Shinichiroh

      More details

    Authorship:Principal investigator 

    Grant amount:\3770000 ( Direct Cost: \2900000 、 Indirect Cost:\870000 )

    My mathematical interests include Donaldson theory and Seiberg-Witten theroy in four-manifold topology. Especially, I am interested in non-compactness phenomena of the moduli spaces of instantons.
    I proved an optimal asymptotic growth of the diameters of the moduli spaces of instantons with respect to the instanton number for the standard 4-sphere.

    researchmap

  5. 非コンパクト四次元多様体のドナルドソン理論におけるモジュライ空間の幾何解析的研究

    Grant number:23740044  2011.4 - 2012.3

    日本学術振興会  科学研究費助成事業  若手研究(B)

    松尾 信一郎

      More details

    Authorship:Principal investigator 

    Grant amount:\2600000 ( Direct Cost: \2000000 、 Indirect Cost:\600000 )

    researchmap

▼display all

 

Social Contribution 2

  1. NHKカルチャー

    Role(s):Lecturer

    NHK文化センター  秋の数学散策  2016.10

     More details

    Audience: General

    Type:Lecture

    ガウスの愛した算術幾何平均

  2. 2016年度名古屋大学数学公開講座

    Role(s):Lecturer

    名古屋大学大学院多元数理科学研究科  2016.10

     More details

    Audience: High school students, Teachers, General

    Type:Lecture