Τρίτη 14 Ιανουαρίου 2020, Αίθουσα Μ2, 12.15-13.00.
Ομιλήτρια: Παναγιώτα Δασκαλόπουλος, Columbia University
Τίτλος: Ancient solutions to geometric flows
Περίληψη: Some of the most important problems in geometric time depended partial differential equations 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 equation. In the case of a parabolic equation the blow up analysis often leads to special solutions which are defined for all time −∞ < t ≤ T, for some T ≤ +∞. We refer to them as ancient solutions. 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 flows, with emphasis on recent results for the Mean curvature flow and the Ricci flow.