题目：具有曲率下界空间的定性微分

报告人：李楠，City University of New York

时间和地点：4月20日15:40-17:55，五教5406；4月21日9:45-12:00, 新楼312；4月21日15:40-17:55，二教2204；4月22日9:45-12:00，管理科研楼1308

摘要：

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 formular 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.An introduction to metric spaces and Alexandrov spaces

2.Fundamental results on Alexandrov spaces

3.Epsilon-frame and bounding the curvature integral.