Mirkó Visontai: The Eulerian polynomials of type D have only real roots.

Descents are one of the extensively studied permutation statistics.
Their generating functions are given by the so-called Eulerian polynomials. 
Descents and hence Eulerian polynomials can be generalized to all Coxeter 
groups. Francesco Brenti showed that several results in the classical theory
of Eulerian polynomials extend to the general case. In particular, he showed
that the real-rootedness of Eulerian polynomials can be extended to type B 
and the exceptional groups and conjectured that the Eulerian polynomials of 
type D have only real roots. 

In this talk I will give a proof of Brenti's conjecture using the inversion sequence
representation of permutations. This is joint work with Carla Savage at NCSU.