Algebraic Geometry and Combinatorics Seminar: Quasisymmetric and Coxeter flag varieties

Abstract: In algebraic combinatorics, \emph{quasisymmetric} and \emph{Coxeter--Catalan} describe two common philosophies for generalizing classical objects and deepening results.  One area where neither philosophy has made serious headway is the Schubert calculus of the complete flag variety.  In this talk I will introduce a toric complex $\mathrm{QF}\ell$ that is simultaneously a quasisymmetric and Coxeter-Catalan generalization of the complete flag variety.  I will go on to explain how $\mathrm{QF}\ell$ is the right generalization (because its combinatorics are nice enough to do actual computations) and also an interesting generalization (because it is still connected to classical Schubert calculus).  Based on work with N. Bergeron, P. Nadeau, H. Spink, and V. Tewari.

Host: Martha Precup