Gauge theory with infinite group actions

具有无限群作用的规范理论

• 批准号: 22540080
• 负责人: KATO Tsuyoshi
• 金额: $ 2.66万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540080/
• 关键词: 無限群; 非コンパクト幾何解析; スケール変換; 概正則曲線; 無限次元多様体; ハミルトン関数; ゲージ理論; 力学系; 非線形偏微分方程式; 基本群; トロピカル幾何学

Tropical geometry connects discrete dynamical systems with automata. We used it to induce an analytic comparison theorem between mutually different rational dynamics or PDEs. We applied the method to theory of automata groups, particularly to Burnside groups and obtained a new example of infinitely quasi-recursive rational dynamical systems.We constructed moduli theory of holomorphic curves over infinite dimensional almost Kaehler manifolds with high symmetry. As an application, we constructed Hamiltonian deformation of groups acting on trees, and verified that for some class of Hamiltonians, they must be always uniformly infinite in ours sense.

热带几何将离散动力系统与自动机联系起来。我们用它来推导出相互不同的理性动力学之间的一个解析比较定理。将该方法应用于自动机群理论，特别是Burnside群，得到了无穷拟递归有理动力系统的一个新例子，构造了具有高度对称性的无限维几乎Kaehler流形上全纯曲线的模理论。作为应用，我们构造了作用在树上的群的哈密顿变形，并证明了对于某类哈密顿量，它们在我们的意义下总是一致无限的。

项目成果

Infinite sequences of almostKaehler manifolds with high symmetry

高对称性almostKaehler流形的无限序列

• 发表时间: 2012
• 期刊: their perturbations and pseudoholomorphic curves
• 作者: Vitalij Chatyrko;Yasunao Hattori(発表者:服部泰直);Yasunao Hattori;Yasunao Hattori;Nakamoto Kazunori and Torii Takeshi;Daniel G Davis and Torii Takeshi;Kazunori Nakamoto and Takeshi Torii;Daniel G Davis and Takeshi Torii;Nakamoto Kazunori and Torii Takeshi;Torii Takeshi;Torii Takeshi;Torii Takeshi;Torii Takeshi;Tori i Takeshi;Torii Takeshi;Torii Takeshi;Torii Takeshi;Tori i Takeshi;鳥居 猛;鳥居 猛;Torii Takeshi;Torii Takeshi;Tori i Takeshi;鳥居 猛;鳥居 猛;Adam Clay and Masakazu Teragaito;Masakazu Teragaito;寺垣内 政一;寺垣内 政一;寺垣内 政一;寺垣内政一;勝田 篤;A. Katsuda;寺垣内 政一;勝田 篤;寺垣内政一;寺垣内 政一;Atsushi Katsuda;寺垣内 政一;勝田篤;T.Kato
• 通讯作者: T.Kato

Automata groups, tropicalgeometry and dynamical Burnsideproblem

自动机群、热带几何和动力学伯恩赛德问题

• 发表时间: 2011
• 作者: T.Kato;Seiichi Kamada;T. Kato;Seiichi Kamada;T.Kato
• 通讯作者: T.Kato

Moduli theory over infinite dimensional spaces

无限维空间上的模理论

• 发表时间: 2012
• 作者: Atsushi Ishii;Naoko Kamada;Seiichi Kamada;相馬輝彦;Shinji Fukuhara;Yasuhiko Kamiyama;宮崎直哉;D. Shakhmatov;T. Soma;Yasuhiko Kamiyama;T.Kato
• 通讯作者: T.Kato

Automata groups and tropical geometry

自动机群和热带几何

• 发表时间: 2012
• 作者: Andrew Bartholomew;Roger Fenn;Naoko Kamada;Seiichi Kamada;T.Soma;Yasuhiko Kamiyama;Naoko Kamada;D. Shakhmatov;T.Kato;相馬輝彦;Yasuhiko Kamiyama;T.Kato;Naoko Kamada;D. Shakhmatov;T.Kato
• 通讯作者: T.Kato

Dynamical Burnside Problem

动态烧边问题

• 发表时间: 2011
• 作者: T.Kato