## Ancient solutions to geometric flows IV

Panagiota Daskalopoulos

May 24, 2019

Tatiana Toro

University of Washington

May 24, 2019

Abstract: Quantitative geometric measure theory has played a fundamental role in the development of harmonic analysis, potential theory and partial differential equations on non-smooth domains. In general the tools used in this area differ greatly from those used in geometric measure theory as it appears in the context of geometric analysis. In this course we will discuss how ideas arising when studying perimeter minimization questions yield interesting and powerful results concerning uniform rectifiability of sets. The course will be mostly self-contained.

Various Speakers

May 23, 2019

Panagiota Daskalopoulos

Columbia University

May 23, 2019

Abstract: Some of the most important problems in geometric evolution partial differential equations are related to the understanding of singularities. This usually happens through a blow up procedure near the 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 −∞

Tatiana Toro

University of Washington

May 23, 2019

Daniela de Silva

Columbia University

May 21, 2019

Tatiana Toro

University of Washington

May 21, 2019

Panagiota Daskalopoulos

Columbia University

May 21, 2019

Panagiota Daskalopoulos

Columbia University

May 20, 2019

Abstract: Some of the most important problems in geometric evolution partial differential equations are related to the understanding of singularities. This usually happens through a blow up procedure near the 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≤+∞. We refer to them as ancient solutions. The classification of such solutions often sheds new insight upon the singularity analysis.

Tatiana Toro

University of Washington

May 20, 2019