Analysis, Spectra and Number Theory, a Conference in Honor of Peter Sarnak’s 61st Birthday

In this talk we will review the recent progress on this conjecture, including Kim-Sarnak/Blomer-Brumley's 7/64 through its automorphic inputs which includes several cases of Langlands functoriality. We will then discuss the conjecture in some generality in terms of Arthur parameters and generic Arthur packet conjecture, on which there has been quite a bit of progress locally, and its implication towards a general Ramanujan conjecture for globally generic cusp forms. Some of the results are consequences of local Langlands correspondence for GL(n), which time permitting we will discuss them further.