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).