Sparse Pseudorandom Objects

It has been known for a long time that many mathematical objects can be naturally decomposed into a ‘pseudorandom’, chaotic part and/or a highly organized ‘periodic’ component. Theorems or heuristics of this type have been used in combinatorics, harmonic analysis, dynamical systems and other parts of mathematics for many years, but a number of results related to such ‘structural’ theorems emerged only in the last decades. A seminal example of such a structural theorem in discrete mathematics is Szeméredi’s Regularity Lemma, which was discovered by Szeméredi in the mid-seventies when he proved his famous result on arithmetic progressions in dense subsets of natural numbers. It states that the set of edges of any dense graph can be ‘nearly decomposed’ into ‘pseudorandom’ bipartite graphs. The Regularity Lemma has long been recognised as one of the most powerful tools of modern graph theory. The aim of the meeting was to follow this structural theme and investigate structural results for sparse combinatorial objects. The meeting brought together a number of experts in the area together with several junior researchers and PhD students.