Louis Yudowitz: Generic Uniqueness for Expanders to Geometric Flows Coming Out of Cones

When evolving a manifold by a geometric flow such as Ricci flow or mean curvature flow, finite time singularities are typically encountered. These in turn are usually modeled on self-similarly shrinking solutions. When such shrinkers are cylindrical then a surgery procedure can be used to continue the flow past the singular time. On the other hand, if the shrinker is asymptotic to a cone, then it is expected that continuing the flow will involve pasting in small copies of self-similarly expanding solutions which are asymptotically conical. A major open problem here is when such a forward evolution is unique. In this talk we will discuss an approach to address this problem in a "generic" fashion by using a relative entropy function to study certain subsets of the appropriate moduli space.