In 2021, he received the Henri Poincaré Prize from the International Association of Mathematical Physics, "for outstanding contributions to the analysis of quantum many-body problems ranging from the electronic structure of large atoms to the Lee-Huang-Yang asymptotics of the ground state energy of dilute Bose gases".

[6] Solovej deals with mathematical questions in atomic physics (large atoms and molecules in the Thomas-Fermi model and the Hartree-Fock method), solid-state physics (the Bose-Einstein condensate, Bogoliubov transformation, quantum dot, Heisenberg model and others) and in many-body quantum mechanics (the stability of matter, the Lieb-Thirring inequality and others).

He is co-author, together with Elliott H. Lieb, Robert Seiringer, and Jakob Yngvason, of a monograph on the mathematics of the Bose gas.

In 2014, with Elliott H. Lieb, he proved Wehrl's conjecture on the mininimum entropy of quantum spin systems.

In 2020, with Søren Fournais, he proved the Lee-Huang-Yang conjecture on the ground state energy of dilute Bose gases.