The ErdosStone Theorem for finite geometries
The ErdosStone Theorem for finite geometries

Peter Nelson, Victoria University of Wellington
Fine Hall 224
For any class of graphs, the growth function h(n) of the class is defined to be the maximum number of edges in a graph in the class on n vertices. The ErdosStone Theorem remarkably states that, for any class of graphs that is closed under taking subgraphs, the asymptotic behaviour of h(n) can (almost) be precisely determined just by the minimum chromatic number of a graph not in the class. I will present a surprising version of this theorem for finite geometries, obtained in joint work with Jim Geelen. This result is a corollary of the famous Density HalesJewett Theorem of Furstenberg and Katznelson.