Modular flats and bundles of arrangements
Abstract: In this talk we will illustrate some of the ways in which combinatorics is brought to bear on topological problems in the context of complex hyperplane arrangements, specifically with respect to the "homotopy-type conjecture" and the "K(Pi,1) problem." Matroids play a central role, serving as coordinate-free combinatorial models of arrangements. Modular flats in matroids correspond to bundle projections of hyperplane complements. Special classes of arrangments can be parametrized by graphs, and counter-examples to topological conjeuctures may be found within these classes by constructing graphs according to certain recursive rules.