# Mathematics Colloquia and Seminars

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### Local singularities of Ricci flow

**Geometry/Topology**

Speaker: | Dan Knopf, University of Texas, Austin |

Location: | 2112 MSB |

Start time: | Wed, Apr 18 2007, 4:10PM |

In applications of Ricci flow, one evolves a Riemannian metric on a manifold to improve its geometry. This evolution frequently develops singularities, which may force changes in topology. The most interesting are local singularities, in which the metric remains regular on an open subset of the manifold. In these cases, and adequate understanding of the geometry in an appropriate space-time neighborhood of the developing singularity reveals how one should modify the manifold by topological-geometric surgeries. I will describe some examples of local singularity formation and show how one can derive precise asymptotic expansions at the most common local singularity, the neckpinch.