I will sketch three projects in opinion dynamics. (1) The popular Hegselmann-Krause model of opinion dynamics assumes that you are persuaded to change your views only by those whose views are not too far from yours to start with. The model predicts the emergence of “echo chambers” --- groups of people with identical views --- with different echo chambers holding starkly different views. Alternatively, we might assume that you are persuaded by your neighbors. This model would predict the emergence of “red states” and “blue states” --- large-scale geographic regions in which one or the other view dominates --- with milder differences in views. This can be seen as akin to the well-known fact that iterative methods for Laplace’s equation smooth rapidly but converge slowly. In a computational study, we combined the two ideas, and in some instances found geographically coherent echo chambers --- large-scale geographic regions with views starkly different from those in other regions. We applied our model to attitudes about COVID vaccines in the United States, reproducing some aspects of reality. (2) The Hegselmann-Krause model is discrete. We propose ODE and PDE analogues and analyze some of their properties. (3) We model two candidates maneuvering opportunistically to maximize their share of the vote while opinions in the electorate evolve as well. The optimal candidate strategy (not just the outcome) can depend discontinuously on voter behavior. The underlying mathematical mechanism is a saddle-node bifurcation.