On the shape of infinite dimensional energy landscapes

The feature of infinite dimensional energy landscapes that is best understood, when it exists, is the absolute energy minimizer. Many recent results in applied analysis can be viewed as works that probe additional details of the energy landscape. We will study a sample of such problems that focus on features such as the height of energy barriers, the crossover from one minimizer to another as a function of a critical parameter value, applications of the Lojasiewicz-Simon condition for long-time convergence, and sufficient conditions for dynamic metastability.