Interface of Probability Theory, Functional Analysis and Convex Geometry. In particular, small deviations of Gaussian processes; metric entropy of function spaces and operators; and intrinsic volumes of convex bodies.
- Gao, F. Li, V.W. and Wellner, J. How many Laplace transforms of probabilities densities are there? Proc. Amer. Math. Soc. 138 (2010), no. 12, 4331–4344.
- Gao. F. and Wellner, J. Rate of convergence of the Maximum Likelihood Estimator of a k-monotone density. Sci China Ser A, no. 7, 1525–1538.
- Blei, R.C; Gao, F; and Li, V.W. Metric entropy of high dimensional distributions. Proc. of Amer. Math. Soc. 135 (2007): 4009-4018.
- Gao, F and Li, V.W. Small ball probabilities for the Slepian Gaussian fields. Trans. Amer. Math. Soc. 359 (2007), 1339-1350.
- Gao, F Metric entropy of convex hulls in Hilbert spaces. Bull. London Math. Soc. 36 (2004) 460-468.