Title: Subgroups of just infinite branch groups

Abstract: A group is just infinite if it is infinite but all of its proper quotients are finite. Branch groups form one of the three possible classes into which just infinite groups can fall, according to Wilson's classification. They also often have unusual algebraic and geometric properties, such as periodicity and intermediate growth, which makes them quite intriguing. In this talk, we will focus our attention on the question of determining which finitely generated groups embed into a given just infinite branch group, and the way in which they can be embedded. We will present new results that will allow us to obtain very precise answers for groups possessing a property known as the Subgroup Induction Property. This is joint work with Rostislav Grigorchuk, Paul-Henry Leemann and Tatiana Nagnibeda.