**SMS scnews item created by Haotian Wu at Fri 1 Dec 2017 1746**

Type: Seminar

Distribution: World

Expiry: 2 Jun 2018

**Calendar1: 11 Dec 2017 1100-1200**

**CalLoc1: Carslaw 275**

CalTitle1: Geometry & Topology Seminar: Zhu (Harvard) -- Entropy and self-shrinkers of the mean curvature flow

Auth: haotianw@phaotianw2.pc (assumed)

### Geometry & Topology Seminar

# Entropy and self-shrinkers of the mean curvature flow

### Jonathan Zhu (Harvard)

**Monday 11 December 11:00–12:00 in Carslaw 275.**

Please join us for lunch after the talk!

**Abstract:**
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set.