this talk will be geared towards a general audience. assuming only familiarity with p-adic numbers, we will first discuss the local langlands correspondence for gl(n), and explain why it's a wide-ranging generalization of local class field theory. then we will follow emerton and helm in trying to extrapolate it to a correspondence between representations over more general local rings -- whereupon we reformulate the conjectural ihara lemma in this language. the latter is a big open problem for n>2, which occurred in work of clozel, harris, and taylor, in their attempt to mimic the proof of fermat's last theorem in the context of gl(n).