Sparse pseudorandom objects (10frg131)

Objectives

The aim of the meeting is to bring together a number of experts in the area, so they can review the current knowledge of the topic, and address certain specific extremal problems in hypergraphs for which these newly emerging methods should be effective. One challenging task would be to state and prove the KLR-Conjecture in the simplest case for hypergraphs.

Let us remark that the simplest case of the Conjecture for graphs is quite elementary, but even the statement of the KLR-Conjecture in the hypergraph case is, by no means, easy to guess. However, there is a possibility that there is a new approach to addressing some of the above problems and that, unlike the KLR-Conjecture and the Regularity Lemma for hypergraphs they can be expressed in a simple and natural way. Moreover there is a variety of other results, concerning sparse pseudorandomness, which still remain open. One of the most interesting is the question if, in the case when we know that the KLR-Conjecture holds (and is relatively easy to prove), one can show an analog of the so called Blow-up Lemma, which is another important result for pseudorandom structures. It states that not only a pseudorandom structure contains the correct number of small graphs, but it also contains all large graphs provided they are sparse enough.