I plan to discuss how the location of complex zeros affects the computational complexity of partition functions. Partition functions are polynomials with positive integer coefficients enumerating various combinatorial structures (and typically originating in problems of statistical physics). This will be illustrated by the examples of the permanent of a matrix ("dimer model" in physics) and its higher dimensional versions ("polymer model" in physics), and, time permitting, the independence polynomial of a graph ("hard core model" in physics). Speaker(s): Alexander Barvinok (U. Michigan)