We would like to discuss in these lectures three prob- lems of homogenization and their interplay. They are:

A) The construction of plane-like solutions to the minimal sur- face equation in periodic media.

B) Pulsating wave solutions to a combustion problem and its homogenization limit.

C) Existence of homogenization limits for solutions to fully linear equations in ergodic random media.

We will try to point out what the main techniques are, and their common aspects.

This paper reports on joint work with E. Urban that completes a proof of the Main Conjecture of Iwasawa Theory for a broad class of elliptic curves and modular forms. As such, it is concerned mainly with special values of $L$-functions of modular forms and the ways which they get packaged together (such as in $p$-adic $L$-functions).