Rotational symmetry of ancient solutions of Ricci flow in higher dimensions

Abstract:

In this talk, we will discuss symmetry inheritance in the Ricci flow in higher dimensions under suitable curvature positivity assumptions. After some background, we will cover the three main ingredients of the proof: a linear analysis on the cylinder, the important neck improvement theorem, and the contradiction argument for cap symmetry (closely following the argument in 3D). Time permitting, we will compare the argument to its counterpart for mean curvature flow and mention some potential applications to the mean curvature flow in higher codimension. This is joint work with Simon Brendle.