Recently, cluster methods have been used to solve a variety of sign problems
including those that arise in the presence of fermions. In all cases an
analytic partial re-summation over a class of configurations in the path
integral was necessary. Here the new ideas are illustrated using the example of
QCD at a finite density of static quarks. In this limit the sign problem
simplifies since the fermionic part decouples. Furthermore, the problem can be
solved completely when the gauge dynamics is replaced by a Potts model. On the
other hand in QCD with light quarks the solution will require a partial
re-summation over both fermionic and gauge degrees of freedom. The new approach
points to unexplored directions in the search for a solution to this more
challenging sign problem.Comment: Lattice 2000 (Plenary