** 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.