Wang is a leading international researcher in non-linear partial differential equations and applications, mainly to geometry and optimal transportation. He has solved major outstanding problems, including the Chern conjecture and the affine Plateau problem in affine geometry, the existence of Ricci solitons on toric Kahler manifolds in complex geometry and the higher order Yamabe problem in conformal geometry. In optimal transportation, he was involved in the final resolution of the Monge problem and the discovery of conditions on costs to ensure regularity. His international recognition includes an invited talk at the International Congress of Mathematics and the Morningside Gold Medal.