Video Lectures

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...

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...

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...

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...

We describe a recent construction of self-similar blow-up solutions of the incompressible Euler equation. A consequence of the construction is that there exist finite-energy $C^{1,a}$ solutions to the Euler equation which develop a singularity in...

The singularities in the reduction modulo $p$ of the modular curve $Y_0(p)$ are visualized by the famous picture of two curves meeting transversally at the supersingular points. It is a fundamental question to understand the singularities which...