Student Combinatorics and Algebra Seminar


Abstract 

The theory of matroids unifies & generalizes topics from graph theory, linear algebra, and field extensions. Not only do matroids extend these objects (matroids, for example, allows us to define the "dual" of a nonplanar graph), but a number of other combinatorial objects have matroids associated to them (collections of vectors, polytopes, simplicial complexes, etc). The theory of oriented matroids unifies some of the same topics, now carrying the extra data of an orientation. In this talk, we explore two motivational examples of oriented matroids: a collection of vectors and the faces of a hyperplane arrangement. We will use this pair of examples to motivate and explore the notion of oriented matroid duality. 