Graphs and Matroids Seminar

Title: Representability of Matroids

Abstract: I will go over some negative results regarding characterizations for the class of representable matroids. This will mostly focus on complexity theoretic results, but I will touch upon others. Specifically, we will see that proving non-representability of a matroid requires, in the worst case, an exponential number of rank-function queries.

This will mostly focus on results by Seymour; Geelen, Gerards, and Whittle; Mayhew, Newman, and Whittle; and Ben David, Campbell, and Geelen.