**Convergence of the Mean Curvature Flow**

Rory Martin-Hagemeyer

(University of Massachusetts Boston)

**Abstract:
**We will prove that the rate of convergence of the rescaled mean curvature flow to a shrinker is at most exponential. We shall motivate and present the basic elements of the theory of mean curvature flow, the geometric evolution equation which in some suitable sense holds the distinction of being the fastest way to decrease the surface area of a given surface. We shall introduce the basic notions of hypersurface geometry, shrinkers, rescaling of the mean curvature flow, and the convergence of the rescaled flow to a shrinker. Then we shall introduce a novel flow, the normal rescaled mean curvature flow, discuss its properties, and use it to establish our result.

**Biographical Sketch:**

Rory Martin-Hagemeyer grew up in the Hyde Park area of greater Boston. He attended university at UMass Boston where he developed a fondness for geometry. Afterwards he attended Rutgers University where he earned a PhD under the direction of Natasa Sesum. His work is primarily in mean curvature flow, but uses methods developed in various other areas in geometric analysis, such as the theory of Ricci flow and minimal surfaces. Since September 2022, he has been a** Robert T. Seeley Visiting Assistant Professor** in Mathematics at Umass Boston.

**Date and time: **

Saturday, February 25, 2023

12:45 PM—2:30 PM

**Zoom Meeting Link:**

https://umassboston.zoom.us/j/91225891672