I'm curious about Faltings' "A $p$-adic Simpson correspondence". Do you know more detailed, introductory, expositions, surveys, texts of seminars on that?

Edit: Annette Werner's survey "Vector Bundles on Curves over $\mathbb{C}_p$" seems to be related.

Edit: The first part of a "new approach for the p-adic Simpson correspondence, closely related to the original approach of Faltings, but also inspired by the work of Ogus and Vologodsky on an analogue in characteristic p>0". Another related article.

Edit: today new in arXiv - "Non-abelian Hodge theory for algebraic curves over characteristic p"