The theory of (phi, Gamma)-modules provides powerful techniques for studying p-adic Galois representations of a p-adic field. Recently, Emerton and Gee constructed the moduli stack of (phi, Gamma)-modules in the Banach case. The moduli stack is now often referred to as the Emerton–Gee stack and has brought new perspectives to the Galois deformation theory. This year, Emerton, Gee, and Hellmann circulated a survey paper on their forthcoming work on the moduli stack of (phi, Gamma)-modules in the analytic case. The latter moduli is an Artin stack in rigid analytic geometry and will play a crucial role in the categorification of the p-adic Langlands program.
The workshop aims to study these moduli stacks of (phi, Gamma)-modules. We also plan to include discussions on formal algebraic stacks and rigid analytic Artin stacks.