and the Baum–Connes conjecture and the development and study of related group-theoretic notions such as topological amenability, asymptotic dimension, uniform embeddability into Hilbert spaces, rapid decay property, and so on (see e.g.). Interactions with the theory of quasiconformal analysis on metric spaces, particularly in relation to Cannon's conjecture about characterization of hyperbolic groups with Gromov boundary homeomorphic to the 2-sphere. Finite subdivision rules, also in relation to Cannon's conjecture. Interactions with topological dynamics in the contexts of studying actions of discrete groups on various compact spaces and group compactifications, particularly convergence group methods Development of the theory of group actions on -trees (particularly the Rips machine), and its applications. The study of group actions on CAT(0) spaces and CAT(0) cubical complexes, motivated by ideas from Alexandrov geometry. Interactions with low-dimensional topology and hyperbolic geometry, particularly the study of 3-manifold groups (see, e.g.,), mapping class groups of surfaces, braid groups and Kleinian groups. Introduction of probabilistic methods to study algebraic properties of "random" group theoretic objects (groups, group elements, subgroups, etc.). A particularly important development here is the work of Gromov who used probabilistic methods to prove the existence of a finitely generated group that is not uniformly embeddable into a Hilbert space. Other notable developments include introduction and study of the notion of generic-case complexity for group-theoretic and other mathematical algorithms and algebraic rigidity results for generic groups. The study of automata groups and iterated monodromy groups as groups of automorphisms of infinite rooted trees. In particular, Grigorchuk's groups of intermediate growth, and their generalizations, appear in this context. The study of measure-theoretic properties of group actions on measure spaces, particularly introduction and development of the notions of measure equivalence and orbit equivalence, as well as measure-theoretic generalizations of Mostow rigidity. The study of unitary representations of discrete groups and Kazhdan's property (T) The study of Out(Fn) (the outer automorphism group of a free group of rank n) and of individual automorphisms of free groups. Introduction and the study of Culler-Vogtmann's outer space and of the theory of train tracks for free group automorphisms played a particularly prominent role here. Development of Bass–Serre theory, particularly various accessibility results and the theory of tree lattices. Generalizations of Bass–Serre theory such as the theory of complexes of groups. The study of random walks on groups and related boundary theory, particularly the notion of Poisson boundary (see e.g.). The study of amenability and