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Texas A&M University
Mathematics

Events for 02/26/2019 from all calendars

The Foias Lectures

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Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Panagiota Daskalopoulos, Columbia University

Title: Ancient Solutions to Geometric Flows

Abstract: Some of the most important problems in geometric flows are related to the understanding of singularities. This usually happens through a blow up procedure near the potential singularity which uses the scaling properties of the partial differential equation involved. In the case of a parabolic equation the blow up analysis often leads to special solutions which are defined for all time $-infty < t leq T$ for some $T leq +infty$. We refer to them as ancient if $T < +infty$ and eternal if $T=+infty$. The classification of such solutions often sheds new insight to the singularity analysis. In some flows it is also important for performing surgery near a singularity. In this lecture we will give an overview of uniqueness theorems for ancient solutions to geometric partial differential equations such as the Mean Curvature flow, the Ricci flow and the Yamabe flow. This often involves the understanding of the geometric properties of such solutions. We will also discuss the construction of new ancient solutions from the parabolic gluing of one or more solitons.

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