Friday, October 5, 2012
3:30 pm, MC 5158

Peter Nelson
University of Wellington

The Density Hales-Jewett Theorem and matroid theory.

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.