Cycles in the chamber homology of GL(3)

Let F be a nonarchimedean local field and let GL(N) = GL(N,F). We prove the existence of parahoric types for GL(N). We construct representative cycles in all the homology classes of the chamber homology of GL(3).Comment: 45 pages. v3: minor correction

Patching and the p-adic Langlands program for GL(2)(Q(p))

We present a new construction of the -adic local Langlands correspondence for 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 the global aspects of the -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 representation in that theorem