Title: Divided symmetrization, quasisymmetric functions and the Peterson variety
Speaker: Vasu Tewari, Penn
Abstract: The procedure of divided symmetrization was introduced by A. Postnikov in the context of computing volume polynomials of various classes of permutahedra. This procedure takes a multivariate polynomial as input and outputs a scalar, which in many cases is a combinatorially interesting quantity.
In this talk, I will describe how performing divided symmetrization is equivalent to reducing multivariate polynomials modulo the ideal generated by the homogeneous quasi-symmetric polynomials of positive degree in a fixed number of variables. I will subsequently discuss how divided symmetrization can be used to understand the Schubert expansion of the Anderson-Tymoczko class of the Peterson variety. Along the way, we will encounter familiar combinatorial objects such as flagged tableaux, reduced pipe dreams, P-partitions and various Catalan objects.
This is joint work with Philippe Nadeau at Institut Camille Jordan.
Seminar URL: https://research.math.osu.edu/gcis/
