Jon Pål Hamre (KTH Stockholm) - Chow classes of matroids and standard Young tableaux

To each matroid we associate a class in the Chow ring of the Grassmannian. We develop a new combinatorial approach for computing these Chow classes, by first focusing on snake matroids and then extending our results via valuativity to Lattice path matroids, and further to any matroid. Our main contribution identifies the Poincaré dual of the Chow class of a snake matroid with a specific ribbon Schur function, providing an explicit formula for its coefficients in the Schubert basis as the number of standard Young tableaux of a given shape with a prescribed descent set. As consequences, we recover and simplify classical results such as Gessel--Viennot’s enumeration of permutations with fixed descent sets, and formulas for the volume of lattice path matroids. Furthermore, we use our results to show that certain Schubert coefficients are positive for all connected paving matroids.