 Cao is a former Associate Director, Institute for Pure and Applied Mathematics (IPAM) at UCLA.He has held visiting Professorships at MIT, Harvard University, Isaac Newton Institute, Max-Planck Institute, IHES, ETH Zurich, and University of Pisa.Professor Cao has received the John Simon Guggenheim Memorial Foundation Fellow (2004) and Alfred P. Sloan Foundation Research Fellowship (1991–1993).