She teaches at Princeton University as of 1998. Before that, she held visiting positions at University of California-Berkeley; Institute for Advanced Study, Princeton, N.J.; and Swiss Federal Institute of Technology, Zurich, Switzerland.[3] She served at Swiss Federal Institute of Technology as a visiting professor in 2015.[4]
In 2004,[5] she was interviewed by Yu Kiang Leong for Creative Minds, Charmed Lives: Interviews at Institute for Mathematical Sciences, National University of Singapore, and she declared:
«In the mathematical community, we should leave room for people who want to do work in their own way. Mathematical research is not just a scientific approach; the nature of mathematics is sometimes close to that of art. Some people want individual character and an individual way of working things out. They should be appreciated too. There should be room for single research and collaborative research».[6]
Chang's life was profiled in the 2017 documentary film Girls who fell in love with Math.[7]
Chang, Sun-Yung A.; Yang, Paul C. Conformal deformation of metrics on . J. Differential Geom. 27 (1988), no. 2, 259–296.
Chang, Sun-Yung Alice; Yang, Paul C. Prescribing Gaussian curvature on . Acta Math. 159 (1987), no. 3–4, 215–259.
Chang, Sun-Yung A.; Yang, Paul C. Extremal metrics of zeta function determinants on 4-manifolds. Ann. of Math. (2) 142 (1995), no. 1, 171–212.
Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. The scalar curvature equation on 2- and 3-spheres. Calc. Var. Partial Differential Equations 1 (1993), no. 2, 205–229.
Chang, Sun-Yung A.; Gursky, Matthew J.; Yang, Paul C. An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. (2) 155 (2002), no. 3, 709–787.
Chang, S.-Y. A.; Wilson, J. M.; Wolff, T. H. Some weighted norm inequalities concerning the Schrödinger operators.Comment. Math. Helv. 60 (1985), no. 2, 217–246.
Carleson, Lennart; Chang, Sun-Yung A. On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. (2) 110 (1986), no. 2, 113–127.
Chang, Sun-Yung A.; Fefferman, Robert Some recent developments in Fourier analysis and -theory on product domains. Bull. Amer. Math. Soc. (N.S.) 12 (1985), no. 1, 1–43.
Chang, Sun-Yung A.; Fefferman, Robert A continuous version of duality of with BMO on the bidisc. Ann. of Math. (2) 112 (1980), no. 1, 179–201.