“Spacetime and Quantum Mechanics, Particles and Strings, Polytopes and Binary Geometries”
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 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 simplest setting, showing how the most basic 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", having the physical interpretation of generalizing particles to strings. This talk will be entirely self-contained; no previous knowledge of either the relevant physics or mathematics will be assumed or needed