Explore cutting-edge connections between particle physics and mathematics in this high-energy theory seminar. Delve into how elementary particle scattering processes relate to combinatorics, algebra, and geometry, challenging traditional views of spacetime and quantum mechanics. Examine how simple particle scattering amplitudes are determined by generalized associahedra polytopes, and discover the concept of "binary geometries" that extend the notion of particles to "strings". Investigate the mathematical foundations underlying these structures, including categories of quiver representations. Gain insights into new approaches for conceptualizing fundamental physics, where spacetime and quantum mechanics emerge from more primitive mathematical principles.