Symmetric generating functions, permutation statistics and basic hypergeometric series

First, I will present a series of classical results on symmetric generating functions and permutation statistics, including the classical results by Carlitz, Roselle and Scoville (1966), by Garsia and Gessel (1978), by Gessel and Reutenauer (1993), etc. Second, I will focus on my recent work on the refined enumerations of permutations with respect to the Eulerian and Stirling statistics, establishing their connections to transformation formulas of basic hypergeometric series.