Abstract: Independent sets are of interest in both statistical physics and computer science; in the former as a discrete model of crystallization, and in the latter as a constraint satisfaction problem. This common interest has lead to some fruitful interactions beteween the two fields, and it motivates the study of random independent sets (aka: the hard-core lattice gas) on rather general bipartite graphs. I'll explain this motivation, which lead Sarah Cannon, Will Perkins, and myself to develop Pirogov--Sinai theory beyond it's traditional "Euclidean" setting. Using this tool we are able to discuss phase coexistence (and more) for the hard-core lattice gas in some generality.