Aubry-Mather theory and Ergodic Optimization, a dictionary
Rafael Ruggiero (PUC-Rio)

Aubry-Mather theory and ergodic optimization have both an important point in common: they are of variational nature. However, ergodic optimization is in many senses a theory with "less convexity"than Aubry-Mather theory. Despite this fact, many important tools of Aubry-Mather theory have been "adopted"by ergodic optimization with great success in recent years. The purpose of the talk is to give geometric ideas (no proofs) of the basic concepts involved in Aubry-Mather theory, and their corresponding versions in ergodic optimization, We finish with a survey of recent developments in ergodic optimization from Aubry-Mather point of view.