The p-adic monodromy theorem

In this talk I will discuss a new proof of the p-adic monodromy theorem in p-adic Hodge theory using the theory of diamonds and Analytic Geometry à la Clausen and Scholze. This new perspective does not use explicitly  the classical theory of p-adic differential equations but the geometric aspects of Fargues-Fontaine curves and properties of the Fargues-Fontaine de Rham stack. If time permits I will mention the relation of this theory with Hyodo-Kato cohomology. 

This is based on works in progress with Johannes Anschütz, Guido Bosco, Arthur-Cesar Le Bras  and Peter Scholze.