UW Combinatorics and Geometry Seminar: Lucas Gagnon

Schubert polynomials concretely embody the remarkable connection between the geometry of the flag variety  $GL(n)/B$and the combinatorics of the symmetric group. This talk will develop similar story for the forest polynomials recently introduced by Tewari–Nadeau by constructing a subvariety of  $GL(n)/B$that I will call the 'quasisymmetric flag variety' using an adaptation of the BGG construction of Schubert varieties. By studying the torus-equivariant cohomology of this space, one finds results that rhyme with the greatest hits of Schubert calculus, including a realization of its cohomology ring as the coninvariants of quasisymmetric polynomials. We end with a few connections back to ordinary Schubert calculus. This work is based on joint research with Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari.