Explore an in-depth lecture on the Langlands correspondence for curves over local fields, presented by David Kazhdan at the International Mathematical Union. Delve into recent results and conjectures aimed at constructing an analog of the theory of automorphic functions on moduli spaces of bundles on curves over local fields, covering both archimedean and non-archimedean cases. Gain insights into this complex mathematical topic through a 39-minute presentation, complemented by detailed slides available for further study and reference.