I'll introduce a combinatorial analog to linear dependency in complex space, phased matroids, with foundations analogous to those for oriented matroids. I'll show three equivalent axiomatizations of phased matroids.
This is from a paper by Laura Anderson and Emanuele Delucchi, “Foundations for a theory of complex matroids” (Discrete & Computational Geometry 48 (2012), no. 4, 807–846).
This is the first half of Ms. Su's admission-to-candidacy examination. The examining committee consists of Laura Anderson (chair), Michael Dobbins, and Thomas Zaslavsky.