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This workshop, sponsored by AIM and the NSF, This workshop, sponsored by AIM and the NSF will be devoted to the study of V. Lafforgue's groundbreaking work on the automorphic implies Galois direction of the Langlands conjecture for reductive groups over global function fields.

The primary goals will be:

To give a detailed exposition of the proof of V. Lafforgue's theorem.

Present related developments such as the Yun-Zhang proof of the Gross-Zagier type formula for function fields, the Genestier-Lafforgue construction for the local Langlands correspondence, and the connections with Fargues-Fontaine curve.

Discuss potential further developments that the ideas from V. Lafforgue's work lead us to. 

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.