Abstract:
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.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974