The Ricci Flow - Lecture by Richard Hamilton

Explore the intricacies of the Ricci flow in this comprehensive lecture by Richard Hamilton at ICBS2024. Delve into the mathematical foundations of Ricci curvature and its representation as a symmetric bilinear tensor on manifolds. Understand the connection between Ricci curvature and Einstein's observations on Riemannian manifolds. Examine the Ricci flow equation and its analogy to the heat equation for Riemannian metrics. Learn how the Ricci flow attempts to distribute curvature evenly across a manifold, with specific focus on three-dimensional manifolds with positive initial Ricci curvature. Investigate the formation of singularities in Ricci flow, including the neck pinch phenomenon. Discover how Ricci flow can be used to break down and reconstruct manifolds, providing insights into their diffeomorphic properties. This hour-long presentation offers a deep dive into the mathematical concepts and applications of Ricci flow, suitable for advanced students and researchers in differential geometry and related fields.