Rigidity of Negatively Curved Locally Symmetric Spaces (Mathematics)

首席研究员将研究几何或动态性质如何表征负弯曲局部对称空间的一般问题。具体来说，她将考虑单位切线束上的保时测地线流与常数曲率之间的关系。她还将致力于证明如果测地线流的度规和拓扑熵重合，并且黎曼度规是1/4压缩的，那么流形必须具有恒定的曲率。Hamenstadt博士将教授一门研究生课程，关于负曲率流形的几何；她将担任本科生荣誉数学协会Pi Mu Epsilon的顾问，并在学院研讨会上发表演讲。该项目进一步推进了VPW计划的目标，即(1)为女性提供在工程和NSF支持的科学学科中发展职业的机会；(2)通过为在工业、政府和学术机构工作的女性科学家和工程师提供更大的知名度，鼓励女性在科学和工程领域追求职业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

The principal investigator will study the general problem of how geometric or dynamic properties characterize negatively curved locally symmetric spaces. Specifically, she will consider the relationship between time-preserving geodesic flows on the unit tangent bundle, and constant curvature. She will also work toward proving that if the metric and topological entropy of a geodesic flow coincide, and the Riemannian metric is 1/4-pinched, then the manifold must have constant curvature. Dr. Hamenstadt will teach a graduate course in the geometry of manifolds of negative curvature; she will serve as an advisor for the undergraduate honors mathematics society, Pi Mu Epsilon, and lecture in departmental seminars. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.