Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2019

Speaker:  Vasu Tewari, University of Pennsylvania
Title: Divided symmetrization, Schubert polynomials and quasisymmetric functions
Time: 2:30 PM, Monday, September 23, 2019
Place:  Malott 206

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 cohomology 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.


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