*Diophantine equations in characteristic p and finite automata*

Abstract

I will explain how the theory of finite automata can be relevant to
describe the solutions of some Diophantine equations defined over
fields of characteristic p. This approach applies in particular to
the Skolem-Mahler-Lech theorem, the S-unit equation, and some case
of the Mordell-Lang Theorem. An especially interesting feature of
the method is that it leads to effective results. This is a joint
work with Jason Bell.