The last few years have seen the emergence of a new way of thinking about scattering amplitudes of particles and strings based on combinatorial and geometric ideas. Starting from the kinematic associahedra and ``surfacehedra” in the simplest toy model of colored scalars, to their stringy extensions based on curves on surfaces, to amplitudes of pions and gluons which have revealed new features of these real-world theories. Similar combinatorial/geometric structures have also been discovered underpinning cosmological correlators for conformally coupled scalars. These objects have revealed profound connections between fundamental physics and new areas of mathematics at the intersection of combinatorics, algebra and geometry.

This program will bring together physicists, cosmologists and mathematicians, to consolidate and synthesize these exciting, diverse developments and more importantly, to tackle big open questions and explore entirely new questions.