Topics in Variational Methods

This course consists of two parts: a general introduction to variational methods in PDE, and a more focused foray into some special topics. For the former we will cover the direct method in the calculus of variations, various notions of convexity, Noether's theorem, minimax methods, index theory, and gamma-convergence. For the latter we will focus on several specific problems of recent interest, with emphasis on the Ginzburg-Landau energy functional.