Mathematical Sciences: Topics in Geometric Mechanics and Symplectic Geometry

主要研究者将使用纤维束理论系统地研究哈密顿力学和辛几何、相对平衡的分岔、沿轨道流动的线性化、可变形体的最优控制以及辛微分同态群和Teichmuller空间的几何。现代辛几何已被用来分析机械系统研究中出现的问题。首席研究员将使用这种几何学中的一种新工具，即“纤维束理论”。在手头的问题中，这些是对称群或运动的束，它们在数学上附着在曲面或超曲面的每个点上。一个基本的例子是每个平面与给定球面相切的反射。

The principal investigator will use fiber bundle theory systematically to study Hamiltonian mechanics and symplectic geometry, bifurcation of relative equilibria, linearization of flows along orbits, optimal control of deformable bodies, and the geometry of the group of symplectic diffeomorphisms and of Teichmuller space. Modern symplectic geometry has been used to analyze problems arising from the study of mechanical systems. The principal investigator will use one of the new tools from this geometry known as "fiber bundle theory." In use for the problems at hand, these are bundles of symmetric groups or movements which are mathematically attached to each point of a surface or hypersurface. An elementary example would be a reflection of each plane tangent to a given sphere.