Geometric, analytic, combinatorial, and computational aspects of group theory;
  Low-dimensional topology; Unitary representations and Invariant measures;
  Metric geometry; Complexity theory and Randomization.

  Geometric 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.