Number Theory Seminar

The p-adic local Langlands correspondence is well understood
for GL_1 of a p-adic field and for GL_2(Q_p). In general, for GL_n of a
p-adic field, the situation appears to be much more complicated. In this
talk I will describe an approach to the problem that uses global
methods, namely, completed cohomology and the Taylor--Wiles method. The
talk is based on joint work with Caraiani, Emerton, Gee, Paskunas and
Shin.