NSF Award
1906404
Global Riemannian Geometry generalizes the classical Euclidean, Spherical, and Hyperbolic geometries. One of the major challenges in this area of study is to understand how local geometric invariants such as curvature, that is, how the space under consideration "bends", relate to global topological invariants such as fundamental group, which indicates whether or not the space has 1-dimensional "holes". Manifolds with curvature bounds have been studied intensively since the conception of global Riemannian geometry. One relatively recent approach, which is the focus of this project, to the study of manifolds with lower curvature bounds has been the introduction of symmetries. Graduate students will be trained through research.<br/><br/>The principal investigator will pursue a program in which she carefully studies and analyzes symmetries of both Riemannian manifolds with lower curvature bounds and Alexandrov spaces, considering both sectional curvature and Ricci curvature lower bounds and their corresponding generalizations to Alexandrov spaces, with an eye to gaining a deeper understanding of this largely unknown class of spaces.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
