Morphisms, Minors, and Minimal Obstructions to Convexity of Neural Codes

How can we arrange convex sets in Euclidean space? Versions of this question arise in many combinatorial and geometric contexts: hyperplane arrangements, the study of polytopes and simplicial complexes, optimization, and more. We'll look at convex codes, a relatively recent topic of research that seeks to answer this question very generally. We'll discuss an abstract framework for studying convex codes, some geometric theorems that help us understand them, and see how they differ fundamentally from more classical topics like d-representability.