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 ----------------------------------------------- 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.