Yu Yuan
Department of Mathematics, University of Washington

Old and new results for Special Lagrangian equations

Abstract: We survey some old and new results on a priori estimates, regularity, and global rigidity for special Lagrangian equations withv certain convexity. The gradient graphs of the solutions are minimal or maximal Lagrangian submanifolds, respectively in Euclidean or pseudo-Euclidean spaces. In the latter pseudo-Euclidean setting, these equations are just Monge-Ampere ones. Recent counterexamples for both settings without convexity will also be mentioned.

Xuan Hien Nguyen
Department of Mathematics, Kansas State University

Translating Tridents

Abstract: In this talk, I will present a construction of new examples of self-translating surfaces under mean curvature flow. The construction is inspired by work of Kapouleas on minimal surfaces and consists in desingularizing the intersection of two known examples using a Scherk minimal surface. I will also discuss the difficulties encountered when using this strategy for self-similar surfaces.