The optimal placement of turbines in a wind farm is critical to the maximization of power production. In this paper, we develop a new mathematical programming approach for wind farm layout optimization. We use Jensen's wake decay model to represent multi-turbine wake effects. We develop mixed integer linear and quadratic optimization formulations and apply them to several example layout cases in the literature. Compared to previous approaches, our models produce layouts that tend to be more symmetric and that generate slightly more power. Our formulations solve quickly, allowing a decision maker to efficiently explore the impact of different turbine densities in a wind farm.