Tutte seminar - Peter Nelson

The Density Hales-Jewett Theorem and matroid theory

Abstract:

The Density Hales-Jewett theorem is a powerful tool in Ramsey theory that finds a highly structured subset in an arbitrary dense set of strings over a finite alphabet. A direct consequence for matroids is that any dense GF(q)-representable matroid of huge rank contains a large restriction isomorphic to an affine geometry over GF(q). I will show that the same statement holds for matroids in any fixed minor-closed class that grows at similar rate to the class of GF(q)-representable matroids, and discuss some related results and conjectures. 

This is joint work with Jim Geelen.