In this talk, I explain how various concepts and techniques in quantum field theory and collider physics can be naturally translated into a new geometric language. Using the energy mover's distance, which quantifies the minimal amount of "work" required to rearrange one event into another, we can define a distance between pairs of collider events. This distance can then be used to triangulate the "space" of collider events and rigorously define various geometric objects. Many well-known collider observables, jet algorithms, and pileup mitigation schemes have a simple geometric interpretation, as does the important concept of infrared and collinear safety. Intriguingly, these ideas can be lifted from a distance between events into a distance between theories, with potential relevance for visualizing and interpreting data from the LHC.
