Perspectives for Quantum Differential Geometry

2015 Fiscal Year Final Research Report

• Project/Area Number: 23340018
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University (2014-2015); Keio University (2011-2013)
• Principal Investigator: Maeda Yoshiaki 東北大学, 知の創出センター, 特任教授(研究) (40101076)
• Co-Investigator(Kenkyū-buntansha): Moriyoshi Hitoshi 名古屋大学, 多元数理研究科, 教授 (00239708) ; Sako Akifumi 東京理科大学, 理学部, 准教授 (00424200) ; Kurihara Masato 慶應義塾大学, 理工学部, 教授 (40211221) ; Izeki Hiroyasu 慶應義塾大学, 理工学部, 教授 (90244409) ; Kotani Motoko 東北大学, 理学(系)研究科(研究院), 教授 (50230024) ; Watamura Satoshi 東北大学, 理学(系)研究科(研究院), 准教授 (00201252)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 非可換幾何学 / 変形量子化 / シンプレクティック幾何学 / 岩沢理論 / 非可換多様体 / 離散幾何学 / T-双対性 / 一般幾何学

Outline of Final Research Achievements

The aim is to study the non-commutative objects in Number theory, algebraic geometry, differential geometry, topology and mathematical physics including particle physics and to propose new idea in geometry. The features of this study is to hire the theory of deformation quantization and non-commutative geometry and develop them to apply several research topics. In particluar, we construct a new method of non-formal deformation quantization to cooperate with theoretical physics, including particle physics and string theory. We also establish an international research network in this research area.

Free Research Field

微分幾何学