January 11, 2022
TITLE: Progress in singularity analysis for Lagrangian mean curvature flow in Calabi-Yau 2-folds
ABSTRACT: Singularities in Lagrangian Mean Curvature flow in Calabi-Yau 2-folds are a promising tool to understand how to decompose a graded Lagrangian into a union of special Lagrangians. The bridging tool to extend infinitesimal information in the formation of singularities to macroscopic information is the classification of ancient solutions with specified asymptotics in the ancient past. We explain forthcoming work with Lotay and Szekelyhidi on proving that ancient solutions with blow-down a pair of planes meeting along a 1-dimensional subspace are translators.
June 4, 2018
TITLE: Singularity formation in Lagrangian mean curvature flow
ABSTRACT: We will survey results on singularity formation in mean curvature flow, both in codimension one and in higher codimension with a particular focus on Lagrangian mean curvature flow. We will also review different concepts of weak flows through singularities together with geometric applications.