Explore ODE techniques in curvature flows through this lecture on the dynamics, symmetry, and asymmetry of ancient solutions to mean curvature flow. Delivered by Sigurd Angenent from the University of Wisconsin-Madison as part of the International School on Extrinsic Curvature Flows, the talk delves into the application of ordinary differential equation methods in analyzing curvature flows. Over the course of 1 hour and 16 minutes, gain insights into the mathematical intricacies of this topic, presented by ICTP Mathematics.