Topological solutions

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。PI研究了拓扑动力系统和叶状中的最小集的结构，作为Seifert猜想和修正Seifert猜想的反例。这些最小集的有趣性质是拓扑维数、Hausdorff维数、孤立性和与形状理论相关的捷克同调。动力学也用于离散几何和计算几何问题的研究。动力系统影响着其他科学领域。最小集的研究是不动点和吸引子研究的推广。除了传统的科学技术、工程和数学（STEM）领域外，该理论还适用于生物学、人口研究和经济学。PI研究的几何问题在医学成像中也有应用。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The PI investigates the structure of minimal sets in topological dynamical systems and foliations that serve as counterexamples to the Seifert Conjecture and the Modified Seifert Conjecture. The interesting properties of these minimal sets are the topological dimension, the Hausdorff dimension, isolation, and Czech homology in relation to shape theory. Dynamics is also employed in work on problems in discrete and computational geometry.Dynamical systems impact other areas of science. The study of minimal sets is an extension of the study of fixed points and attractors. The theory has application to biology, population research, and economy, in addition to the traditional Science Technology Engineering and Mathematics (STEM) fields. The geometry problems studied by the PI have applications to medical imaging.