Special IAS High Energy Theory Seminar
Spacetime and Quantum Mechanics; Particles and "Strings"; Polytopes, Binary Geometries and Quiver Categories
This seminar will be presented in-person in Wolfensohn Hall at the IAS and on Zoom.
For contact-tracing purposes all off-campus attendees must register for this seminar:
All in-person attendees must be fully vaccinated and masks are required in all indoor spaces (except while actively eating). Additionally, all off-campus attendees are required to upload proof of vaccination via the IAS CrowdPass App .
Abstract: The past decade has seen the emergence of surprising new connections between the real-world physics of elementary particle scattering processes, and simple new mathematical structures in combinatorics, algebra and geometry. These ideas provide, in a number of examples, a different starting point for conceptualizing this basic physics, where the fundamental principles of spacetime and quantum mechanics are not taken as primary, but instead emerge from a more primitive mathematical rubric. In this talk I will illustrate these ideas in their most elementary setting, showing how the simplest particle scattering amplitudes are determined by avatars of famous polytopes known as (generalized) associahedra. I will also show how the combinatorial relationships captured by the facets of these polytopes remarkably admit a "curvy" realization in terms of "binary geometries", with the physical interpretation of generalizing particles to "strings". I will finally discuss the most basic mathematical ideas underlying and generalizing these structures, involving categories of quiver representations.