Ergodic theory is a powerful set of tools used to study transformations that preserve length or area (or even more generally, measures). The purpose of this talk is to discuss the very first notions of the theory, including Birkhoff's celebrated ergodic theorem. If time permits, we'll see an elementary and some nice applications. Knowing the basics of measure and integration theory would be ideal but being able to accept some intuitive facts on faith should be enough.
This talk should be accesible to everyone - elementary analysis recommended.