
Lecture 20: Homogeneous Dynamics, Part 1
MIT mathematician Lawrence D. Guth opens a two-part detour within his Projection Theory course (18.156, Spring 2025) to introduce homogeneous dynamics and its connections to projection problems. He frames the field for students who have not seen it before, laying out the basic objects of study, the kinds of questions homogeneous dynamics asks about group actions and invariant measures, and why tools from projection theory turn out to be useful for understanding dynamical behavior on homogeneous spaces. The lecture runs about eighty minutes and is pitched as a friendly on-ramp rather than a deep technical dive, setting up definitions and motivating examples that the following lecture will build on. As with the rest of the course, the talk assumes graduate-level mathematical maturity but keeps the new material self-contained enough to follow without prior exposure to the subject.