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Arithmetic geometry and the Langlands program, including:• geometry of rigid analytic varieties, perfectoid spaces, diamonds, etc.• p-adic period domains, local shtukas, the Fargues-Fontaine curve• étale cohomology: perverse sheaves, nearby cycles, étale cohomology of stacks and non-archimedean analytic spaces• representations of p-adic groups• p-adic automorphic forms