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Ricci solitons and warped product Einstein metrics

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William Wylie, U. Pennsylvania

What
  • Colloquium
  • Topology Seminar
When Tue, Mar 15, 2011
from 04:00 PM to 05:00 PM
Where RH 142
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One of  the fundamental questions in mathematics is,  what is the "best" geometry we can put on a given space? The Ricci flow is a tool that has produced a number of exciting recent breakthroughs in understanding this basic question.  Ricci solitons appear prominently in some of these developments as  singularity models, fixed points, and as natural new candidates for optimal geometries.  They  also have a  more geometric  interpretation in terms of Riemannian manifolds with measure.  In this talk we will explore this second perspective and discuss some recent classification results that have arisen from  this viewpoint.  A natural connection between gradient Ricci solitons and warped product Einstein metrics also arises and we will discuss some recent developments in understanding this connection.

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