## Degenerate neckpinches in Ricci flow.

Dan Knopf,University of Texas at Austin

Abstract

I report on work with Angenent and Isenberg in which we show that for each k\geq 3, there is a codimension-k set of initial data that gives rise to solutions of Ricci flow that encounter Type-II singularities at finite time T. I describe the asymptotics of these singularities and show that they develop at the rate (T-t)^{-2+2/k}. I also describe some related results on what rates of singularity formation ("blow-up spectra") are possible for both compact and noncompact solutions.