Introduction to convergence and collapsing theory of Riemannian manifolds
This course is an introduction to the convergence and collapsing theory of Riemannian manifolds, which is an important tool in Riemannian geometry. We shall introduce the Gromov-Hausdorff distance and study the convergence theory of Riemannian manifolds with respect to this distance. We will discuss the collapsing theory of Riemannian manifolds with bounded sectional curvatures.
Lecturer
Date
9th October ~ 25th December, 2023
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Monday | 12:45 - 16:10 | A3-3-103 | ZOOM 02 | 518 868 7656 | BIMSA |
Prerequisite
Riemannian geometry
Reference
1. Rong Xiaochun, Convergence and collapsing theorems in Riemannian geometry. Handbook of geometric analysis, No. 2, 193–299, Adv. Lect. Math. (ALM), 13, Int. Press, Somerville, MA, 2010.
2. Fukaya Kenji, Metric Riemannian geometry. Handbook of differential geometry. Vol. II, 189–313, Elsevier/North-Holland, Amsterdam, 2006.
3. Fukaya Kenji, Hausdorff convergence of Riemannian manifolds and its applications. Recent topics in differential and analytic geometry, 143–238, Adv. Stud. Pure Math., 18-I, Academic Press, Boston, MA, 1990.
2. Fukaya Kenji, Metric Riemannian geometry. Handbook of differential geometry. Vol. II, 189–313, Elsevier/North-Holland, Amsterdam, 2006.
3. Fukaya Kenji, Hausdorff convergence of Riemannian manifolds and its applications. Recent topics in differential and analytic geometry, 143–238, Adv. Stud. Pure Math., 18-I, Academic Press, Boston, MA, 1990.
Video Public
Yes
Notes Public
Yes
Lecturer Intro
Dr. Pengyu Le graduated from ETH Zürich in 2018, then became a Van Loo postdoctoral fellow in University of Michigan. He joined BIMSA as an assistant professor in 2021. His research interest lies in differential geometry and general relativity.