Topics in Riemannian Geometry

Prof. Ruobing Zhang
2023-06-01 6.1, 6.3, 6.4, 6.6, 6.8, 6.10, 6.11

Speaker: Prof. Ruobing Zhang (Princeton University)

Time: (Mini Course)

Lecture 1: June 1 (Thursday) 4-6pm
Lecture 2: June 3 (Saturday) 10am-12pm
Lecture 3: June 4 (Sunday) 10am-12pm
Lecture 4: June 6 (Tuesday) 4-6pm
Lecture 5: June 8 (Thursday) 4-6pm
Lecture 6: June 10 (Saturday) 10am-12pm
Lecture 7: June 11 (Sunday) 10am-12pm

Place: MCM110 & Online (Zoom ID: 616 523 0607  Password: mcm1234)

Title: Topics in Riemannian Geometry

Abstract: The main theme of this minicourse is the metric aspect of Riemannian geometry. We are interested in the quantitative behaviors of Riemannian metrics, with a focus on the metric and topological effects of curvatures. More precisely, many fundamental problems in geometry and physics naturally motivate one to study how a family of Riemannian manifolds, as metric spaces, behave in the "space of ALL metric spaces". This abstract term is in fact naturally connected to numerous more concrete problems, such as geometric flows, rigidity and quantitative rigidity problems in Riemanian geometry, existence of "canonical metrics" on a Riemannian manifold, etc. Making progress in any of those subjects demands substantial developments in appropriate Riemannian convergence theory, i.e., the Gromov-Hausdorff theory.