Conference - p-adic Langlands correspondence: a constructive and algorithmic approach Sep 2, 2019 to Sep 6, 2019 read more
Rennes, from september 2nd to september 6th 2019
Organization board: Xavier Caruso, Agnès David, Lionel Fourquaux, David Lubicz
Scientific board: Jean-Marc Couveignes, Kiran Kedlaya, Ariane Mézard, Sandra Rozensztajn
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 Langlands correspondence.
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.