Extremal combinatorics and random graphs

One of the classical assertions in extremal combinatorics is the Erdos-Ko-Rado theorem, which establishes the size of a largest family of pair-wise intersecting k-element subsets of an n-element set. In the talk, we will exhibit the history of the problems related to the theorem. We will show that these problems are in the real core of contemporary discrete analysis. We will stress its connections to coding theory, combinatorial geometry, algebraic topology. We will pay the greatest attention to a recent probabilistic interpretation of the problem — in terms of random graphs.