Geometry and dynamics of systems with a hyperbolic flavor

这项建议的目的是促进在动力系统、几何和低维拓扑的相交的理论数学领域的HQP的研究和培训。我的研究项目集中在两个不同的问题子族上。第一个涉及对低维流形中某些类型的动力系统的理解和拓扑分类。第二个问题是关于几何起源系统的动力学性质(最重要的是芬斯勒或黎曼流形的测地线流)与来自度规的几何或谱数据之间的相互作用的一系列问题。

The goal of this proposal is to promote research and the training of HQPs in domains of theoretical mathematics at the intersection of dynamical systems, geometry and low dimensional topology. My research program focuses on two distinct subfamilies of questions. The first involves the understanding and topological classification of certain types of dynamical systems in manifolds of low dimension. The second is concerned with a range of questions regarding the interactions between the dynamical properties of systems of geometrical origin (the geodesic flow of a Finsler or Riemannian manifold being the foremost), and geometric or spectral data coming from the metric.