Leírás
Many important theorems and conjectures in combinatorics, such as the theorem of Szemerédi on arithmetic progressions and the Erdős-Stone Theorem in extremal graph theory, can be phrased as statements about families of independent sets in certain uniform hypergraphs. These hypergraphs have a clustering phenomena, which can be summarized in a general theorem, called as Container Theorem, and the method is the container method. The method seems to be surprisingly applicable for enumerating problems, extremal questions in random environment, and proving the existence of some combinatorial structures. In this talk we skip the applications, but provide a short, complete proof of a variant of the container lemma for 3-uniform hypergraphs. The pace of the proof will be slow and in a discussion style, the focus will be on to make sure that the audience understands it.