I will describe recent work, joint with G. Savin, in which we prove a dichotomy result for generic cuspidal representations of the exceptional group G_2, over a p-adic field. This result reduces the local Langlands conjectures for generic cuspidal represenations G_2 to the corresponding conjectures on the classical groups PGL_3 and PGSp_6. These corresponding conjectures are proven and "almost proven", respectively. Our methods include a study of the theta correspondence in the groups E_6 and E_7, a uniqueness result for "Shalika periods" in PGSp_6, and various incarnations of Spin L-functions. The talk will include much background on exceptional groups and the local Langlands conjecture, accessible to a general number theoretic audience. I aim to present a precise summary of our results, with hints about the method of proof.

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