Venue: Carslaw AGR (829) Time: 11:30AM--12:30PM Lecturer: Wenshuai Jiang (USyd) 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. This is the fourth lecture for the series.