Differential Geometry Seminar: A family of non-collapsed steady Ricci solitons

Seminar | August 28 | 1-2 p.m. | 891 Evans Hall

 Alexander Appleton, UC Berkeley

 Department of Mathematics

Non-collapsed Ricci solitons play an important role in Ricci flow as they arise as blow up limits of singularities. The classification of three dimensional Ricci solitons has largely been carried out by the work of Hamilton, Ivey, Perelman and Brendle. In four dimensions, however, only a handful of solitons are known and a complete classification remains a distant goal.

In this talk I will present a new family of four dimensional non-collapsed steady solitons that live on the complex line bundles \(O(k)\), \(k >2\) of \( \mathbb C P^1 \). If time permits I will also show some preliminary numerical results indicating that these solitons are likely to occur as Type II singularity models in Ricci flow.