Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, June 2, 2014 - 05:00

Location:

Gilkey 115

Guest Speaker:

Institution:

University of Oregon

Abstract:

In this talk we survey results on the asymptotic analysis of finite-time neckpinch singularities in Ricci flow on compact and non-compact manifolds. In particular, we describe the construction of complete rotationally symmetric solutions to Ricci flow on $\mathbb{R}^n$ which encounter a global singularity at a finite time $T$. The curvature of these solutions can blow up at an arbitrarily fast rate. Near the origin, blow-ups of such a solution converge uniformly to the Bryant soliton; near spatial infinity, blow-ups of such a solution converge uniformly to the shrinking cylinder soliton.