Dilute Bose gas with three-body interaction: recent results and open questions

Contribution to the Proceedings of the XX International Congress on Mathematical Physics, Geneva 2021.International audienceWe review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schrödinger equation to describe the ground state energy of a Bose--Einstein condensate, where the nonlinearity strength is determined by a zero scattering problem. Several open questions will also be discussed