Abstract: We will explore some of the connections between three parameters that measure the complexity of a subset of $R^n$: the covering numbers of the set, the expectation of the supremum of the gaussian process indexed by the set, and the combinatorial dimension of the set (roughly speaking, the latter measures the extent coordinate projections of the set contain ``cubic" structures).

We will then show how these parameters can be used in empirical processes theory, and (if time permits), present some applications in probability and geometry.