Lawrence Guth continues MIT's 18.156 Projection Theory course with the second of two lectures on homogeneous dynamics. He presents the work of Lindenstrauss and Mohammadi on quantitative Ratner theorems, tracing how results about the equidistribution of orbits under unipotent flows can be made effective, with explicit rates rather than purely asymptotic statements. The core of the lecture shows how projection theory, the course's central toolkit for bounding how sets behave under linear projections, enters the proof of these quantitative results. Guth works through the structure of the argument at the board, connecting the geometric measure theory developed earlier in the course to this harder dynamical application. The lecture assumes familiarity with the course's prior material on projections and with basic homogeneous dynamics, and it is aimed at graduate students or researchers following the full sequence rather than newcomers to the subject.