
Contagious Structure in Projection Theory
Lawrence Guth continues MIT's graduate course 18.156, Projection Theory, with a lecture on the algebraic structure found in the set of exceptional directions for a projection problem. Guth builds on earlier results in the course to show how structure in one projection can propagate, or become contagious, across related directions, a phenomenon central to modern work on the Falconer distance problem and related questions in geometric measure theory. The seventy seven minute session runs as a continuous chalkboard argument, with Guth developing lemmas step by step and pausing to field student questions, typical of MIT OpenCourseWare's unedited lecture recordings. It assumes familiarity with the course's earlier lectures on projections and exceptional sets, making it most useful to viewers already following the 18.156 sequence rather than newcomers to the topic.