Appears in collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

I will discuss Lagrangian fibrations and foliations in shifted symplectic geometry and their relevance to the problem of global existence of potentials. I will describe constructions ofisotropic foliations on moduli spaces and will discuss the associated potentials as well as some applications to quantum field theory and non-abelian Hodge theory. This is based on joint works with Calaque, Katzarkov, Toën, Vaquié, and Vezzosi.