Abstract

After Ricci flow, the mean curvature flow of submanifolds in a Riemannian manifold is perhaps the most natural and famous geometric flow, describing the gradient descent for the volume functional. It was therefore an exciting discovery when Knut Smoczyk demonstrated that in an ambient Ricci-flat Kähler manifold, the class of Lagrangian submanifolds is preserved under the flow. This phenomenon is now referred to as Lagrangian mean curvature flow.

Lagrangian mean curvature flow has since been shown to have properties and behaviour distinct from that of mean curvature flow in general. In this talk I will focus on the singular behaviour of the flow, highlight the differences and similarities to the general case, and bring attention to some open conjectures in the field.