Low-dimensional topology; Unitary representations and Invariant measures;
Metric geometry; Complexity theory and Randomization.
invariants and asymptotic geometry of groups;
Isoperimetric functions, growth functions, distortion;
Geometric actions of discrete groups, quasi-isometries;
Amenable groups, groups with Kazhdan's property (T);
Burnside's groups, "exceptional groups" (infinite "monsters");
Sofic and hyperlinear groups; Random groups;
Automatic groups, word hyperbolic groups, small cancellation theory;
Solvable, nilpotent, polycyclic groups;
Spectra of graphs, random walks, languages, automata;
Probabilistic methods on finite and infinite graphs, groups and algebras.