Apr 30

Title: Ricci solitons in low dimensions---a survey

Speaker: Ben Chow (UC San Diego)

Abstract: We will survey various works on Ricci solitons, with an emphasis on low dimensions. Ricci solitons are self-similar solutions to the Ricci flow, when we factor in the action of the diffeomorphism group of a manifold on the space of metrics on that manifold. There are three types of Ricci solitons: shrinking, steady, and expanding. The first two are related to the local geometry of solutions to the Ricci flow going into a singularity and the latter to the local geometry coming out of a singularity. In dimensions 2 and 3 there is an almost complete classification of Ricci solitons. In higher dimensions, the picture is much more unclear and thus an interesting direction for future research.