The aim of arithmetic geometry is to solve equations on integers by
geometric methods. One of the most prominent achievements of this
approach is certainly the Langlands program, which makes a connection
between representations of the absolute Galois group of $\mathbb Q$ and certain
adelic representations of reductive algebraic groups. In the early
2000's, Christophe Breuil suggested the existence of a purely $p$-adic
version of the Langlands correspondence and supported his vision by
numerous examples. Almost twenty years after, the $p$-adic Langlands
correspondence has become a major topic in number theory.
Besides, following the rapid development of computer science throughout
the 20th century, a large panel of algorithmical tools has been deployed
and are now quite performant, in particular for attacking questions in
Number Theory. A computational approach to the (classical) Langlands
correspondence has been already investigated in recent times as well.
We believe that the time has come to begin to extend it to the $p$-adic
This conference is a first step towards this perspective.
It will bring together the most internationally recognized experts in
$p$-adic Langlands correspondence on the one hand and effective aspects
of the Langlands correspondence on the other hand.
Young researchers, and more generally researchers who are familiar with
one side (either the abstract one or the effective one) and are willing
to learn the other side, are particularly encouraged to attend our
event: a enthousiastic program with 2 mini-courses, a bunch of short
lectures and an introduction to the mathematical software SageMath
is specially designed for them.