Ancient Solutions to Mean Curvature Flow (virtual)

Mean curvature flow (MCF) is the gradient flow of the area functional; it moves the surface in the direction of steepest decrease of area.

An important motivation for the study of MCF comes from its potential geometric applications, such as classification theorems and geometric inequalities. MCF develops "singularities" (curvature blow-up), which obstruct the flow from existing for all times and therefore understanding these high curvature regions is of great interest.

This is done by studying ancient solutions, solutions that have existed for all times in the past, and which model singularities. In this talk I will present recent developments concerning ancient solutions. Among other things we will discuss a new way of constructing and classifying collapsed solutions. This is joint work with Mat Langford, Stephen Lynch and Giuseppe Tinaglia.