abstract: Collider experiments probe physics at the shortest distances by smashing protons together and measuring the debris produced by the collisions, with the ultimate goal of using the distribution of debris on the detector to infer the detailed short-distance physics. Optimal transport has emerged as an important tool for classifying collider events based on these distributions. In this talk, I will both discuss recent work using linearized optimal transport to classify collider events, as well as present progress on related theoretical questions, including approximation of Wasserstein-type metrics via wavelets and optimal transport formulations of the denoising problem.