Infinite graphs and groups: geometric, combinatorial, analytic, algorithmic, and asymptotic aspects.
  Randomness in graphs and groups. Group C*-algebras. Low-dimensional topology.
  Metric geometry. Complexity theory and automata. Expander graphs.  

  Geometric invariants and asymptotic geometry of groups.
  Isoperimetric functions, growth functions, distortion.
  Amenable groups, groups with Kazhdan's property (T).
  Burnside's groups, "exceptional groups" (infinite "monsters").
  Sofic and hyperlinear groups. Random groups.
  Automatic groups, Gromov 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.