Abstract:
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.
