# Seminars & Colloquia Calendar

Geometric Analysis Seminar

## On uniqueness of non-uniquneness of ancient ovals

#### Wenkui Du - University of Toronto

Location:  Zoom
Date & time: Tuesday, 26 April 2022 at 10:00AM - 11:00AM

Abstract: In this talk, I will describe my recent joint work with Robert Haslhofer on uniqueness and non-uniqueness of ancient ovals under mean curvature flow.  We confirm the conjecture of Angenent-Daskalopoulos-Sesum that $$SO(k)times SO(n+1-k)$$-symmetric ancient ovals are unique up to parabolically rescaling and space-time rigid motion. On the other hand, we also construct a (k-1)-parameter family of uniformly (k+1)-convex ancient ovals that are only $$mathbb{Z}^{k}_{2}times O(n+1-k)$$-symmetric, which gives counterexamples to a conjecture of Daskalopoulos. In the end, I will also discuss a bit about related works, works in progress and future directions.