Quantitative Differentiation on Spaces with Lower Curvature Bounds

Speaker

Nan Li 李楠

The City University of New York

Time

Thur., Sat. & Sun., 14:00-17:00,

Dec. 11, 13, 14, 2025

Venue

B725, Shuangqing Complex Building A

Description

Quantitative differentiation is a technique initiated by Jeff Cheeger and Aaron Naber in 2013. The core idea of this technique is to establish a controlled quantitative stratification structure based on two fundamental components: a monotonic formula and an almost rigidity property. Due to the fundamental nature of its starting points, this technique has been successfully applied to many areas of geometric analysis, including spaces with bounded Ricci curvature, harmonic maps, and Ricci flow, leading to numerous deep results.

In this mini-course, we will discuss the applications of this technique to manifolds with lower sectional curvature bounds (and their generalization Alexandrov spaces). This can be viewed as a model case for understanding the method’s core mechanics.

Topics will include:

1. Starting points: The monotonic formulas on Alexandrov spaces

2. The annulus covering theorem and an application: packing estimates of singular sets

3. Another application: bounding the curvature integral

Course Schedule:

About the speaker

Nan Li is a professor at The City University of New York – Member of Graduate Center.