The category of p-adic representations of $Gal(\overline{Q_p}/Q_p)$ embeds fully faithfully into the category of equivariant vector bundles on the Fargues-Fontaine curve. In this talk we present recent work, where we show every such equivariant vector bundle descends canonically to a locally analytic vector bundle, an object equipped with a connection. Next, we shall focus on potentially semistable locally analytic vector bundles (for example, these coming from potentially semistable representations of $Gal(\overline{Q_p}/Q_p))$. We shall explain how to interpret invariants of these objects in terms of solutions to p-adic differential equations on the locally analytic vector bundle.