Speaker: Alexander Hazeltine (University of Michigan)

Title: The theta correspondence and functoriality

Abstract: In a letter to Howe in 1975, Langlands speculated that the theta correspondence could be an instance of functoriality. This later turned out to be false as the theta correspondence does not always preserve L-packets. In 1989, Adams proposed a remedy: instead of L-packets, the theta correspondence should preserve A-packets. Mœglin showed that Adams was mostly correct, but also that there are examples where Adams' conjecture fails: there exists a representation lying in an A-packet whose theta lift does not lie in any A-packet. The goal of this talk is to generalize Adams' conjecture to ABV-packets (also called micro packets). We will discuss how the generalization explains the failure of Adams' conjecture, along with providing some evidence for the generalization.