Abstract
In recent years, there has been growing interest in realizing the collection of Langlands parameters in various settings as a moduli space with a geometric structure. In particular, in the p-adic Langlands program, this space should come in two different forms of moduli spaces of (\phi, \Gamma)-modules: there is the "Banach" stack (also called the Emerton-Gee stack), and the "analytic" stack. In this talk, we shall discuss a proof of a recent conjecture of Emerton, Gee and Hellmann concerning the overconvergence of etale (\phi, \Gamma)-modules in families, which gives a link between the two different moduli spaces.
