Bernouilli numbers, Eisenstein series and cyclotomic units (Colloquium AGA)

I will recall what are the objects of the title and explain how one can combine them in a new way to explain a deep Theorem of Mazur and Wiles (proving a conjecture of Iwasawa)  that gives a formula for the cardinality of the odd p-part of the class groups of cyclotomic fields in terms of Bernouilli numbers.