Poles of the Standard L-function and Functorial Lifts for G2

This is part 2 of 2 of an expanded version of the speaker’s talk from last semester.

The functoriality conjecture is a key ingredient in the theory of automorphic forms and the Langlands program. Given two reductive groups G and H, the principle of functoriality asserts that a map r:G^->H^ between their dual complex groups should naturally give rise to a map r*:Rep(G)->Rep(H) between their automorphic representations. In this talk, I will describe the idea of functoriality, its connection to L-functions and recent work on weak functorial lifts to the exceptional group of type G_2.