ALGB Seminar: Cesar Ceballos (Universität Wien)
Title: Hopf Dreams and Diagonal Harmonics
Abstract: Pipe dreams are certain combinatorial objects that play a fundamental role in the combinatorial understanding of Schubert polynomials and various geometric structures. In this talk, I will describe a Hopf algebra structure on a family of pipe dreams and present two applications. The most remarkable one regards the Frobenius characteristic of the space of multivariate diagonal harmonics, a relatively young exciting area that concerns the action of the symmetric group on a polynomial ring on a multi-set of variables. This is joint work with Nantel Bergeron and Vincent Pilaud.