He is known for his work in applied mathematics, with applications to fluid mechanics and material science.
In addition, he has worked on multiscale modeling and the study of rare events.He has also made contributions to homogenization theory, theoretical models of turbulence, stochastic partial differential equations, electronic structure analysis, multiscale methods, computational fluid dynamics, and weak KAM theory.
He is currently a professor in the Department of Mathematics and Program in Applied and Computational Mathematics at Princeton University, and the Beijing International Center for Mathematical Research at Peking University.
Since 2015, he has been the inaugural director of the Beijing Institute of Big Data Research.