Moduli spaces of instantons from a metric point of view

• Project/Area Number: 25800045
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Nagoya University (2016); Osaka University (2013-2015)
• Principal Investigator: Matsuo Shinichiroh 名古屋大学, 多元数理科学研究科, 准教授 (40599487)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: Donaldson理論 / 四次元多様体 / 幾何解析 / ゲージ理論 / ドナルドソン理論 / ザイバーグ＝ウィッテン理論 / モジュライ空間 / 微分幾何 / スカラー曲率 / サイバーグ=ウィッテン方程式 / 山辺不変量 / トポロジカル絶縁体 / トポロジカル超伝導体 / バルクエッジ対応 / インスタントン / モジュライの計量幾何

Outline of Final Research Achievements

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.

Research Products

• [Journal Article] Yamabe Invariants and the Pin2-monopole Equations (2016)
  • Author(s): Masashi Ishida, Shinichiroh Matsuo, and Nobuhiro Nakamura
  • Journal Title: Mathematical Research Letters Volume: 23 Issue: 4 Pages: 1049-1069
  • DOI: 10.4310/mrl.2016.v23.n4.a4
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The perturbation of the Seiberg–Witten equations revisited (2016)
  • Author(s): Mikio Furuta and Shinichiroh Matsuo
  • Journal Title: Journal of the Mathematical Society of Japan Volume: 68 Issue: 4 Pages: 1655-1668
  • DOI: 10.2969/jmsj/06841655
  • NAID: 130005433270
  • ISSN: 0025-5645, 1881-1167, 1881-2333
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Brody curves and mean dimension (2015)
  • Author(s): Shinichiroh Matsuo and Masaki Tsukamoto
  • Journal Title: the Journal of the American Mathematical Society Volume: 28 Issue: 1 Pages: 159-182
  • DOI: 10.1090/s0894-0347-2014-00798-0
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Local mean dimension of ASD moduli spaces over the cylinder (2015)
  • Author(s): Shinichiroh Matsuo and Masaki Tsukamoto
  • Journal Title: Israel Journal of Mathematics Volume: 207 Issue: 2 Pages: 793-834
  • DOI: 10.1007/s11856-015-1162-z
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The prescribed scalar curvature problem for metrics with total unit volume (2014)
  • Author(s): Shinichiroh Matsuo
  • Journal Title: Mathematische Annalen Volume: 360 Issue: 3-4 Pages: 675-680
  • DOI: 10.1007/s00208-014-1052-4
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] ASD connections and mean dimension (2016)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Recent Developments in the Mathematical study of Gauge Theory
  • Place of Presentation: Simons Center for Geometry and Physics
  • Year and Date: 2016-10-17
  • Int'l Joint Research / Invited
• [Presentation] Brody curves and mean dimension (2016)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Modern Interactions between Algebra, Geometry and Physics
  • Place of Presentation: Tohoku Forum for Creativity
  • Year and Date: 2016-07-13
  • Int'l Joint Research / Invited
• [Presentation] The perturbation of the Seiberg-Witten equations (2016)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Modern Interactions between Algebra, Geometry and Physics
  • Place of Presentation: Tohoku Forum for Creativity
  • Year and Date: 2016-06-28
  • Int'l Joint Research / Invited
• [Presentation] トポロジカル相とK理論 (2016)
  • Author(s): Shinichiroh Matsuo
  • Organizer: 理研 iTHES・東北大 AIMR・東大 生産研 合同シンポジューム 数理科学の新しい地平
  • Place of Presentation: 理化学研究所
  • Year and Date: 2016-04-28
  • Int'l Joint Research / Invited
• [Presentation] Gysin maps and bulk-edge correspondence (2016)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Spectral Theory of Novel Materials
  • Place of Presentation: CIRM
  • Year and Date: 2016-04-21
  • Int'l Joint Research / Invited
• [Presentation] The twisted Seiberg-Witten equations and the Yamabe invariant (2016)
  • Author(s): 松尾信一郎
  • Organizer: The 4th Workshop "Complex Geometry and Lie Groups
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2016-03-22
  • Int'l Joint Research / Invited
• [Presentation] Seiberg-Witten方程式の摂動 (2015)
  • Author(s): 松尾信一郎
  • Organizer: 京都大学 微分トポロジーセミナー
  • Place of Presentation: 京都大学
  • Year and Date: 2015-11-24
  • Invited
• [Presentation] 摂動Seiberg-Witten方程式再訪 (2015)
  • Author(s): 松尾信一郎
  • Organizer: 慶応大学 幾何セミナー
  • Place of Presentation: 慶応大学
  • Year and Date: 2015-05-11
  • Invited
• [Presentation] Bulk-edge correspondence and the Gysin map in K-theory (2015)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Mini-workshop on Topological States and Non-commutative Geometry
  • Place of Presentation: AIMR
  • Year and Date: 2015-03-23 – 2015-03-25
  • Invited
• [Presentation] The pertubation of the Seiberg-Witten equations revisited (2015)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Princeton-Tokyo workshop on Geometric Analysis
  • Place of Presentation: University of Tokyo
  • Year and Date: 2015-03-17
  • Invited
• [Presentation] The bulk-edge correspondence for topological insulators and the Gysin map in K-theory (2014)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Kavli IPMU - RIKEN iTHES - Osaka TSRP Symposium "Frontiers of Theoretical Science --MATTER, LIFE and COSMOS--
  • Place of Presentation: Kavli IPMU
  • Year and Date: 2014-11-06
  • Invited
• [Presentation] Seiberg-Witten方程式の新しい摂動とLeBrunの曲率不等式 (2014)
  • Author(s): 松尾信一郎
  • Organizer: 東京工業大学 幾何セミナー
  • Place of Presentation: 東京工業大学
  • Year and Date: 2014-05-08
  • Invited
• [Presentation] Brody curves and mean dimension (2013)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Geometry and Analysis on Manifolds: A Memorial Symposium for Professor Shoshichi Kobayashi
  • Place of Presentation: University of Tokyo
  • Invited
• [Presentation] The Cauchy-Riemann equations, the ASD equations, and mean dimension (2013)
  • Author(s): Shinichiroh Matsuo
  • Organizer: Dynamics, Entropy and Semialgebraic Sets
  • Place of Presentation: Research Institute for Mathematical Sciences, Kyoto University
  • Invited
• [Presentation] 四次元開多様体と反自己双対接続と局所平均次元 (2013)
  • Author(s): 松尾 信一郎
  • Organizer: 第60回幾何学シンポジウム
  • Place of Presentation: 東京工業大学
  • Invited
• [Presentation] The prescribed scalar curvature problem for metrics with total unit volume (2013)
  • Author(s): Shinichiroh Matuso
  • Organizer: 第19回複素幾何シンポジウム
  • Place of Presentation: 信州菅平高原 プチホテル ゾンタック
  • Invited
• [Remarks] 松尾信一郎
  • URL: https://www.math.nagoya-u.ac.jp/~shinichiroh/