Combinatorics of gamma-positivity

Gamma-positivity implies unimodality for palindromic polynomials. The idea behind it stems from work of Foata, Schutzenberger and Strehl on the Eulerian polynomials. I will present my work on this theme from the view point of permutation statistics, from q-Eulerian polynomials to Gessel’s gamma-positivity conjecture, to our recent exciting connections found between multiset Eulerian polynomials and weakly increasing trees, as well as some of my favorite conjectures.