# Events for 02/26/2019 from all calendars

## The Foias Lectures

**Time:** 4:00PM - 5:00PM

**Location:** Blocker 117

**Speaker:** Panagiota Daskalopoulos, Columbia University

**Title:** *Ancient Solutions to Geometric Flows*

**Abstract:** Some of the most important problems in *geometric flows* are related to the understanding of *singularities*. This usually happens through a blow up procedure near the potential singularity which uses the scaling properties of the partial differential equation involved. In the case of a *parabolic* equation the blow up analysis often leads to special solutions which are defined for all time $-infty < t leq T$ for some $T leq +infty$. We refer to them as *ancient* if $T < +infty$ and *eternal* if $T=+infty$. The classification of such solutions often sheds new insight to the singularity analysis. In some flows it is also important for performing *surgery* near a singularity. In this lecture we will give an overview of *uniqueness theorems* for ancient solutions to geometric partial differential equations such as the Mean Curvature flow, the Ricci flow and the Yamabe flow. This often involves the understanding of the geometric properties of such solutions. We will also discuss the construction of new ancient solutions from the *parabolic gluing* of one or more solitons.