Algebraic and Enumerative Combinatorics - Leo Jiang

Title: Real matroid Schubert varieties, zonotopes, and virtual Weyl groups

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.

Abstract: Every linear representation of a matroid determines a matroid Schubert variety whose geometry encodes combinatorics of the matroid. When the representation is over the real numbers, we show that the topology of these varieties is completely determined by the combinatorics of zonotopes. As an application, we compute the fundamental groups. When the real matroid Schubert variety comes from a Coxeter arrangement, we show that the equivariant fundamental group is a “virtual” analogue of the corresponding Weyl group.