Weak KAM approach to first-order mean field games

I will give a short introduction to mean field games first, and then talk about our two recent works on first-order mean field games: existence of solutions of contact mean field games (with X. Hu); a semi-discrete approximation scheme for mean field games (with R. Iturriaga). Our methods come from weak KAM theory for Hamiltonian and contact Hamiltonian systems.