Matt Baker, Georgia Tech
11:30 AM - 12:30 PM
Hyperrings and hyperfields are similar to their non-hyper counterparts, but addition is allowed to be multi-valued. After giving some examples, we use hyperfields to present a simultaneous generalization of the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call such objects matroids over hyperfields. In fact, there are (at least) two natural notions of matroids over a hyperfield F, which we call weak and strong F-matroids. We give different ``cryptomorphic’’ axiom systems for such matroids, discuss duality theory, and present sufficient conditions which guarantee that the notions of weak and strong F-matroids coincide (for a given hyperfield F). If time permits, we will discuss some connections to tropical geometry and the theory of Berkovich spaces.
Event contact: dinesh dot thakur at rochester dot edu