(Note that this is a Tuesday -- there is a conference in the Sky Lounge on May 3.)
The "classical" Langlands correspondence relates n -dimensional Galois representations to representations of GLn(Qp), both over the field of complex numbers. The mod p (resp. p -adic) Langlands correspondence is an analogue of this correspondence over a field of characteristic p (resp. over a p -adic field). So far it has only been established for n≤2, with powerful applications to the modularity of Galois representations. In this talk I will explain some recent progress for n>2 . No background on the Langlands program will be assumed.