Introduced by Hamilton in early 1980s, Ricci flow has been successfully applied to various geometric and topological problems, most notably, the resolution of the Poincare and Thurston geometrization conjectures for three dimensional manifolds. Ricci solitons, as self-similar solutions to the Ricci flows, are of great importance in the study of Ricci flow singularities. The talk aims to provide an overview on some recent progress on the understanding of four dimensional shrinking Ricci solitons.

Wang Jiaping is a professor of mathematics at the University of Minnesota. His main research areas are differential geometry and partial differential equations. He received his Ph.D. from the University of California, Irvine in 1994, and then served as an assistant professor at Stanford University. He was a recipient of the Centennial Research Fellow in the United States from 1996 to 1997 working at The Massachusetts Institute of Technology (MIT) and then worked as an assistant professor of HC Wang at Cornell University. He has worked at the University of Minnesota since 1999. He was an associate professor and professor in 2001 and served as the deputy director of Institute of Mathematics and Its Applications of the University of Minnesota (IMA) in 2011-2015.

Professor Wang Jiaping is an international leading expert in the field of geometric analysis. He has published many papers in journals such as Annals of Mathematics, Journal of Differential Geometry, Math. Ann., and is currently the International Journal Editor of Journal of Geometric Analysis and Proceedings of the American Mathematical Society.