I
will give two lectures introducing abstract polymer models and the cluster
expansion from statistical physics. I will describe some of the original
applications of these tools in statistical physics to understand phase
transitions in lattice spin systems, and then present applications of these
tools in combinatorics (understanding complex zeros of graph polynomials) and
computer science (approximate counting problems). The lectures will be
accessible to graduate students in combinatorics, probability, and computer
science and will include several directions for future work.