Patching and the p-adic Langlands program for GL(2, Q_p)
  We present a new construction of the p-adic local Langlands correspondence for GL(2, Q_p) via the patching method of Taylor--Wiles and Kisin. This construction sheds light on the relationship between the various other approaches to both the local and global aspects of the p-adic Langlands program; in particular, it gives a new proof of many cases of the second author's local-global compatibility theorem, and relaxes a hypothesis on the local mod p representation in that theorem. 
Ana Caraiani, Matthew Emerton, Toby Gee, David Geraghty, Vytautas   Paskunas and Sug Woo Shin
math.NT