Expanding Ricci solitons asymptotic to cones with nonnegative scalar curvature

Eric Chen, University of California, Berkeley
Fine Hall 314

In dimensions four and higher, the Ricci flow may encounter singularities modelled on cones with nonnegative scalar curvature. It may be possible to resolve such singularities and continue the flow using expanding Ricci solitons asymptotic to these cones, if they exist. I will discuss joint work with Richard Bamler in which we develop a degree theory for four-dimensional asymptotically conical expanding Ricci solitons, which in particular implies the existence of expanders asymptotic to a large class of cones.