Probabilistic methods to study independent sets in hypergraphs

Many questions, both in pure and applied mathematics, but also in biology, chemistry, computer science and physics can be encoded in the combinatorial setting of independent sets in hypergraphs. The goal of the project is to focus on two particular methods that can be used to study these objects, namely the method of hypergraph containers, as well as the random greedy process. A particular focus is put on applications to the study of certain arithmetic problems, such as the so-called “solution-free process” with respect to a particular linear equation, or the typical structure of sets in an (arbitrary but fixed) abelian group with small h-fold sumset.