Theta correspondence and Arthur packets

In his 1989 paper, Adams conjectured that the theta correspondence should exhibit functorial behavior with respect to Arthur packets. The conjecture is known to be true when the rank of the target group is sufficiently large. However, it is also known to fail in a number of small-rank examples. Describing all the situations in which the conjecture holds thus becomes an interesting problem.
The talk will begin with a brief historical overview of the main ingredients: the theta correspondence and Arthur's classification of automorphic representations. After formulating the conjecture, I will present new results which provide an answer to the above question. This is joint work with Marcela Hanzer.