The Foias Lectures
The Foias Lectures honor Distinguished University Professor Ciprian Foias, who has been a member of the Department of Mathematics since 2000. Foias Lecturers are distinguished mathematicians who work in some branch of analysis. They deliver up to three lectures over the course of a week during the academic year. The series is made possible by an endowment established through generous initial gifts by Professors Ron Douglas and Carl Pearcy in 2014, augmented by contributions from friends and colleagues of Professor Foias (matched by a magnanimous anonymous donor). Initial support is also provided by the Powell Chair in Mathematics and the Mobil Chair in Computational Science.

Date Time 
Location  Speaker 
Title – click for abstract 

02/25 4:00pm 
Blocker 117 
Panagiota Daskalopoulos Columbia University 
Nonlinear Geometric Flows
We will give an overview on the development of extrinsic Nonlinear Geometric Flows, emphasizing both the analytical and geometric point of views. Special emphasis will be given to the Mean curvature flow (an example of quasilinear diffusion), the Inverse Mean curvature flow (an example of ultrafast diffusion) and to the Gauss curvature flow (an example of slowdiffusion). We will address the questions of the long time existence of the flow, regularity of solutions, asymptotic behavior and singularities. 

02/26 4:00pm 
Blocker 117 
Panagiota Daskalopoulos Columbia University 
Ancient Solutions to Geometric Flows
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. 

02/28 4:00pm 
Blocker 117 
Panagiota Daskalopoulos Columbia University 
Uniqueness of Ancient Solutions to the Mean Curvature flow and Ricci flow
This is a continuation of Lecture 2. We will discuss new results regarding the classification of ancient noncollapsed solutions to the Mean Curvature flow and the Ricci flow, answering well known conjectures in the field. 