Ofer Zeitouni - Weizmann Institute of Science The study of Polymers in Zd leads to the study of the stochastic heat equation with multiplicative noise, and that one in turn relates to the KPZ equation via a logarithmic Hopf-Cole transformation. I will describe some recent results in which Zd is replaced by other infinite graphs, both regular and disordered. Joint work with Clement Cosco and Inbar Seroussi.