Math 510 - Spring 2019

Instructor : Natasa Sesum

Email :  natasas@math.rutgers.edu
Office :  536 Hill Center
Office Phone : (732) 445-2390 (ext 1323)
Office Hours : by appointment
Lecture : TF noon-1:20pm  

Texts :
Introduction to Ricci flow by Topping and selected papers throughout the course.

Prerequisities: PDE. Knowing differential geometry is also recommended but not required. No knowledge on particular flows is needed, I will introduce all what I need during the course.

Description: In this course I will introduce students to the Mean Curvature Flow. It is a geometric PDE in which one evolves a hypersurface in the normal direction by a speed given by the mean curvature. I will discuss the existence of the flow, characterization of the first singular time, regularity properties of the flow. I will also discuss the monotonicity formula for the flow that was discovered by Huisken. After introducing and proving the monotonicity formula we will discuss singularity formation of the flow and singularity models that often happen to be self-shrinkers.