Title of the course: Introduction to Modern Techniques in Geometric Flows
Instructor: Prof. Albert Wood
Institution: Chinese University of Hong Kong
Dates: 1-6 September 2025
Prerequisites: Basic Differential Geometry, Basic PDE
Level: Graduate
Abstract: Geometric flows are a major area of study on the boundary of differential geometry and PDE theory, some key examples being the Ricci flow, Mean curvature flow, Willmore flow and Yamabe flow. The only millennium prize problem to date to be solved (the Poincaré conjecture) was achieved using the Ricci flow, and to this day flows continue to show great promise in tackling exciting unsolved problems in differential geometry.
In this lecture series we will study widely applicable techniques of modern geometric flows via the particular example of mean curvature flow – an area-decreasing flow of submanifolds; in particular, we will focus on singularity formation in the flow. Throughout, we will refer back to other important flows and illustrate how the techniques we study apply and have been used in those cases.
Time permitting, the topics I’d like to cover are: Huisken’s argument that singularities are modelled on shrinking solitons, Lojasiewicz arguments for uniqueness of singular models, and the Wazewski box argument for long-time existence results.
Language: English