[1] Probability and stochastic processes: approximation of partial sums, central limit theorems and other weak convergence theorems in finite and infinite-dimensional spaces, empirical central limit theorems, probability in Banach spaces, isoperimetric inequalities and concentration of measure, large deviations, random sets, decoupling methods, dependence
[2] Statistics: Asymptotics, approximation theorems, maximum likelihood and generalizations including the maximum product of spacings method, exponential families