Title: Minuscule Coxeter Dressians
Abstract: Matroids combinatorially abstract independence systems and have deep connections throughout mathematics. One characterization of matroids is given by (0,1)-polytopes with edge directions in the type A root system. In this case, edges capture "symmetric exchange" between bases. Regular matroidal subdivisions of polytopes are well studied. In particular, they are closely related to a tropical prevariety known as the Dressian, which is a subfan of the secondary fan of a given matroid polytope. Coxeter matroids generalize usual matroids, and can be characterized in terms of polytopes with edge directions in root systems beyond type A. Coxeter matroids which are said to be "minuscule" and possess the "strong exchange" property are the most honest incarnations of usual matroids outside type A. We will discuss subdivisions of minuscule Coxeter matroid polytopes, and study tropical prevarieties which (in most cases) capture subdivisions into cells which possess the strong exchange property.
The advanced seminar begins at 4:00 pm s.t..