Title: Locally analytic vector bundles on the Fargues-Fontaine curve
Abstract: 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 familiar invariants of these objects in terms of solutions to a p-adic differential equation on the locally analytic vector bundle.