Singularities of Mean Curvature Flow

My work is on understanding the quirks of a very natural PDE – Mean Curvature flow. This is a flow of submanifolds that reduces volume in the most efficient way possible – perhaps converging to a beautiful minimal submanifold. However in the quest for perfection, things can go wrong, and a singularity may arise!

If we understand the form that singularities of the flow may take, we may know when to expect that none occur, or possibly even how to continue the flow past these singular times, a la Perelman.

This talk will be a mixture of an introduction to the subject of Mean Curvature flow, a survey of results on singularities, and an overview of my current PhD work. I look forward to seeing you there!