Objective The Langlands program is a conjectural framework for understanding the deep relations between automorphic forms and arithmetic. It implies a parameterization of representations of Galois groups of (local or global) fields in terms of representations of (p-adic or adelic) reductive groups. While making progress in the Langlands program often means overcoming significant technical obstacles, new results can have concrete applications to number theory, the proof of Fermat's Last Theorem by Wiles being a key example.Recently, V. Lafforgue has made a striking breakthrough in the Langlands program over function fields, by constructing an `automorphic-to-Galois' Langlands correspondence. As a consequence, this should imply the existence of a local Langlands correspondence over equicharacteristic non-archimedean local fields.The goal of this proposal is to show the surjectivity of this local Langlands correspondence. My strategy will be global, and will involve solving global problems of strong independent interest. I intend to establish a research group to carry out the following objectives, in the setting of global function fields:I. Establish automorphy lifting theorems for Galois representations valued in the (Langlands) dual group of an arbitrary split reductive group.II. Establish cases of automorphic induction for arbitrary reductive groups.III. Prove potential automorphy theorems for Galois representations valued in the dual group of an arbitrary reductive group.IV. Establish cases of soluble base change and descent for automorphic representations of arbitrary reductive groups.I will then combine these results to obtain the desired surjectivity. This will be a milestone in our understanding of the Langlands correspondence for function fields. Fields of science social sciencespolitical sciencespolitical policiescivil societynongovernmental organizationsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsarithmeticsprime numbersnatural sciencesmathematicspure mathematicsarithmeticsL-functionsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2016-STG - ERC Starting Grant Call for proposal ERC-2016-STG See other projects for this call Funding Scheme ERC-STG - Starting Grant Host institution THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Net EU contribution € 1 094 610,00 Address TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge United Kingdom See on map Region East of England East Anglia Cambridgeshire CC Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 094 610,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE United Kingdom Net EU contribution € 1 094 610,00 Address TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge See on map Region East of England East Anglia Cambridgeshire CC Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 094 610,00