Speaker: Kyle Petersen, DePaul University
Title: Surrounding Gessel's conjecture
Abstract: One of the nicest properties of the Eulerian polynomials is their ``gamma positivity." This condition implies symmetry and unimodality of the coefficients. The two-sided Eulerian polynomial is the generating function for the joint distribution of descents and inverse descents. Gessel has conjectured the two-sided Eulerian polynomials possess a two-dimensional kind of gamma positivity. I will discuss various interpretations and generalizations of the two-sided Eulerian polynomials. Each generalization has the same conjectural two-dimensional gamma positivity as the two-sided Eulerian polynomials.