Christos Athanasiadis: Equivariant gamma-positivity

Abstract

Gamma-positivity is a powerful method to prove
unimodality for polynomials with real symmetric coefficients.
It appeared in the seventies, in work of Foata and Sch\"utzenberger
on the Eulerian polynomials and attracted attention more recently,
after work of Br\"anden on poset Eulerian polynomials and Gal on
flag triangulations of spheres. This talk will focus on a natural
equivariant analogue of this concept. Basic examples generalize the
gamma-positivity of Eulerian, derangement and binomial Eulerian
polynomials and their analogues for r-colored permutations. Open
questions, and some theorems, coming from group actions on
simplicial complexes, toric varieties and Rees products of
posets, will be discussed.