In the first half of the talk I will recall two classical theorems - Dirichlet’s class number formula
and Stickelberger’s theorem. Stark and Brumer gave conjectural generalisations of these statements.
We will see formulations of some of these conjectures. In the second half of the talk we will restrict
to a special case of the Brumer-Stark conjecture. Here p-adic techniques can be used to resolve the
conjecture. We will see a sketch of this proof. This is joint work with Samit Dasgupta.