几何暑期学校系列课程Ricci Curvature and Convergence
Professor in Department of Mathematics ,CUNY Graduate Center ,she is a Riemannian Geometer and specialize in the study of manifolds with Ricci Curvature bounds. Educations: 1996 Courant Institute of Mathematical Sciences, Ph.D., May 1996. Adviser: Professor Jeff Cheeger, Bella Manel Prize 1991 College of Arts and Science, NYU, B.A., Magna cum Laude, Majors: Mathematics and English, Minor: Physics Her homepage is http://comet.lehman.cuny.edu/sormani/
Course Overview We will cover Gromov-Hausdorff Convergence of Riemannian Manifolds and Metric Spaces, Cheeger-Colding Theory for Manifolds with Ricci Curvature bounded below and Intrinsic Flat Convergence of Oriented Riemannian manifolds and Integral Current Spaces. These techniques have beenapplied to understand singularities which develop under various flows and limits in Riemannian Geometry including work of Hamilton and Perelman on Ricci Flow, work of Chen-Donaldson-Sun and Tian on Kahler Einstein Manifolds, and the ongoing study of the stability of the Schoen-Yau/Witten Positive Mass Theorem. All course materials are available online and the course outline and detailed topics are below.