Working session: The geometric Langlands conjecture. Abstracts from the workshop held April 3--9, 2016 (Q1700625)

Summary: The Langlands program is a vast, loosely connected, collection of theorems and conjectures. At quite different ends, there is the geometric Langlands program, which deals with perverse sheaves on the stack of \(G\)-bundles on a smooth projective curve, and the local Langlands program over \(p\)-adic fields, which deals with the representation theory of \(p\)-adic groups. Recently, inspired by applications to p-adic Hodge theory, Fargues and Fontaine have associated with any \(p\)-adic field an object that behaves like a smooth projective curve. Fargues then suggested that one can interpret the geometric Langlands conjecture on this curve, to give a new approach towards the local Langlands program over \(p\)-adic fields.