Differential Geometry Seminar Series : Cao, Jiang and Wu -- Introduction to Cheeger-Colding Theory about Ricci Curvature and Recent Progress

This is supposed to be a chance for the DECRAs, Wenshuai Jiang and Haotian Wu, to
introduce their research fields, mostly differential geometry and related ones, to the
local community.  

The plan is to hold it weekly, subject to travel plans.  

The first meeting will be on August 13, after Jiang’s School seminar talk on that Monday 

http://www.maths.usyd.edu.au/s/scnitm/borisl-GeometryAndTopologySemina-038 

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Time: 13 August 2019, 11AM--1PM 

Room: Access Grid Room on Level 8 in Carslaw 

Kick-off talk: 11AM--12NOON, Professor Xiaodong Cao (Cornell) 

Title: Ricci Flow, Einstein Manifolds and Ricci Solitons: A Survey 

Abstract: in this talk, we will start with a quick introduction to the Ricci flow, its
singularities, their connections to Ricci solitons and Einstein manifolds, and recent
progress in dimension 4.  We will also discuss why it is important to understand the
limits with bounded Ricci curvature.  

The Series by Jiang: 12NOON--1PM.  

Title: Introduction to Cheeger-Colding theory about Ricci curvature and recent progress 

Abstract: in these serial seminars, we will focus on manifolds with lower Ricci
curvature bounds.  By studying the structure of Gromov-Hausdorff limit of a sequence of
manifolds with lower Ricci curvature, Cheeger-Colding obtained several important and
fundamental results about Ricci curvature.  It turns out that such theory has
significant applications to the existence of Kaehler-Einstein metrics, Ricci flow,
geometric groups and other related topics.  

The aim of theses seminars is systematically introducing Cheeger-Colding theory and
discussing its related applications.  At the end we will discuss recent progress by
Cheeger-Naber and a joint work with Cheeger-Naber.  

In the first talk, we start from the basic knowledge of Gromov-Hausdorff distance.  We
will discuss Gromov’s precompactness theorem and apply it to manifolds with lower Ricci
curvature.