Research report 2021 - Max Planck Institute for Mathematics
Langlands correspondence and p-adic geometry
Max-Planck-Institut für Mathematik, Bonn
SummaryThe Langlands correspondence predicts a profound connection between algebra and analysis. This connection is deep and still largely conjectural. However, in recent years there has been exciting new progress toward its resolution, thanks to the introduction of striking new geometric techniques. In this report, I give an impressionistic introduction to the Langlands correspondence, and indicate the ideas behind these recent developments.