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Ricci Flow and the Uniformization Theorem

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Chirasree Chatterjee, Saint Louis University

What
  • PhD Oral Exam
When Tue, May 16, 2017
from 11:00 AM to 01:00 PM
Where Ritter Hall 346
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Abstract: Ricci flow is a geometric evolution equation, analogous to the heat equation, that when applied on a Riemannian manifold deforms the metric smoothing out any irregularities of the metric in the process. 

Hamilton showed that Ricci flow on 3-manifolds  with positive Ricci curvature exists for all time and converges to a constant-curvature metric. This can be generalised to different dimensions and non-positive curvature. In this presentation we will use the techniques derived by Hamilton to talk about the proof of the Uniformization Theorem which states  "any closed Riemannian surface has a conformal metric of constant curvature".

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