Talking About Combinatorial Objects Student Seminar: Oriented Matroids

Seminar | September 22 | 1-2 p.m. | 748 Evans Hall

 Melissa Sherman-Bennett, UC Berkeley

 Department of Mathematics

Oriented matroids are matroids whose defining subsets are "signed" in some way; a prototypical example is the ordered bases in a set of vectors, together with their orientations. Many familiar objects are oriented matroids, including directed graphs, vector configurations, and hyperplane arrangements. As with matroids, there are many ways of defining an oriented matroid, each stemming from the properties of a different combinatorial object. This talk will introduce oriented matroids via the circuit, dual pair, and chirotope axiom systems, focusing on the motivations for each axiom system and the connections between them. Note that basic knowledge of matroids will be assumed.