In the Fall of 2016, I’m teaching a graduate topics class on p-adic Hodge theory here at Columbia. The course website can be found here.
Update (5/6/2o16): An earlier version of the course description contained a rather optimistic statement regarding Harris’s conjecture. I’m very grateful to Peter Scholze for pointing out an oversight in my proof sketch and for some helpful discussions around these matters; after further reflection, I’m now convinced the strategy I had in mind will go through in the so-called “HN-reducible” case, and that there are very good reasons why it cannot work in any greater generality than this. In any case, I’m sorry for any confusion which the original course description might have generated!