Thesis Defence: On the axiomatization of infinite oriented matroids

Kaioke Begay, supervised by Dr. Amy Wiebe, will defend their thesis titled “On the axiomatization of infinite oriented matroids” in partial fulfillment of the requirements for the degree of Master of Science in Mathematics.

An abstract for Kaioke Begay’s thesis is included below.

Defences are open to all members of the campus community as well as the general public. This examination will be offered in hybrid format.  Registration is not required to attend in person, but please email amy.wiebe@ubc.ca to receive the Zoom link for this defence.

Abstract

Oriented matroids are traditionally defined on finite ground sets. While standard matroids have been successfully generalized to the infinite setting without sacrificing matroid duality, the same generalization for oriented matroids proves challenging. In this thesis, we explore the connection between affine oriented matroids and oriented matroids in order to guide our understanding of the challenges of creating an axiomatic definition of infinite oriented matroids. We further illustrate some of these challenges by constructing a simple geometric example in the infinite case. We ultimately
propose a set of circuit axioms which consider circuits to be conformally minimal rather than support minimal. We provide evidence that by viewing circuits in this way, it may be possible to extend oriented matroids to the infinite setting in much the same way as non-oriented matroids.