论文标题
对无限尺寸几何和分析的贡献
Contributions to infinite dimensional geometry and analysis
论文作者
论文摘要
本文论文中提到的作品可以以六个主题收集。在隐式函数定理和数值方案的几何形状上作品。关于在无限尺寸谎言组上的指数图。拟合无限尺寸主束的拟合和安布罗斯语定理。结果基于整合理论和离散的杨利尔理论。在非正式伪差异运算符（PDOS），$ζ-$重归于地范围的痕迹，地图和相关主题的歧管上工作。在Kadomtsev-PetsviaShvili（KP）层次结构上工作。
The works prsented in this habilitation thesis can be gathered in six themes. Works on the implicit function theorem and the geometry of numerical schemes. On the existence of an exponential map on an infinite dimensioal Lie group. Holonomy and Ambrose-Singer theorem for connections on infinite dimensional principal bundles. Results on integration theory and discretized Yang-Mills theory. Works on non-formal pseudo-differential operators (PDOs), $ζ-$renormalized traces, manifolds of maps and related topics. Works on the Kadomtsev-Petsviashvili (KP) hierarchy.
