Venue: Room 204, Hai Na Yuan #2, Zijingang Campus

Time: March 30, 16:15 - 17:35

Speaker: 李楠 Nan Li (City University of New York)

Pretalk:  Introduction to Alexandrov Spaces

Abstract: We will discuss some basic properties of Alexandrov spaces.

Research talk:  A Canonical Proof of Perelman's Stability Theorem

Abstract: Perelman's remarkable stability theorem states that if X is a compact n-dimensional Alexandrov space with curvature ≥ k, then for any ε >0, there exists δ = δ (X, ε)>0 such that for any n-dimensional Alexandrov space Y with curvature ≥ k, if Y is Gromov-Hausdorff close to X by a δ -approximation f: X → Y, then there is a homeomorphism g: X → Y which is ε-close to f. 

We present a canonical proof of this theorem, which is distinct from Perelman's original approach. In fact, the homeomorphism f is constructed purely in line with the metrics of X and Y.  We will discuss some basic properties of Alexandrov spaces in the introductory talk.