** 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.