Monday, March 8, 3pm ET (8pm GMT, 9am Tue NZDT)
Nick Brettell, Victoria University of Wellington
The excluded minors for 2-regular matroids, and for Hydra-5-representable matroids
The 2-regular matroids are a generalisation of regular matroids (which are representable over all fields), and near-regular matroids (which are representable over all fields of size at least three). Hydra-5-representability characterises matroids with precisely six inequivalent representations over GF(5). I will present the following recent result: any excluded minor for the class of 2-regular matroids, or for Hydra-5-representable matroids, has at most 17 elements. In fact, we can say more about potential excluded minors with 16 or 17 elements. This leads us tantalisingly close to an excluded-minor characterisation for these two classes. In this talk, I will give some background to why these classes are of interest, discuss the long road towards proving this result, give some key ideas from the argument, and discuss where to from here.
Joint work with James Oxley, Charles Semple, and Geoff Whittle.