Quantum field theory is a century old, yet beyond weak coupling we still cannot compute how particles interact. Low-energy QCD is the classic example: we scatter hadrons in experiments, but cannot derive their collisions from first principles. This internship explores a fresh idea: use the number of spacetime dimensions, d, as a small parameter. The 1/d expansion has reshaped other fields, making mean-field theory exact in statistical physics and opening new analytic windows on black holes. For scattering in quantum field theory, it is still waiting to be built. The project grows out of our recent map, obtained with the S-matrix bootstrap, of which interactions are allowed in dimensions 3 to 12, using only the consistency of relativity and quantum mechanics. We found surprising new phases appearing at special dimensions. These results touch a deep puzzle: in high dimensions, string theory may be the only consistent option (string universality), yet our bounds seem to allow interactions without gravitons. Is a graviton hiding somewhere in these amplitudes? You can explore this analytically, numerically, or both, in a small, friendly team in Annecy, close to CERN, with regular one-to-one supervision.