After discussing the local Langlands correspondence (LLC) briefly, we define a global Artin L-function attached to any cuspidal automorphic representation of a reductive group over a number field and any finite-dimensional representation of its L-group with the hope that understanding the automorphic side may tell us something about the Artin side. We then discuss the possible general approaches to understanding the automorphic side in general, including a discussion of degenerate models of Moeglin-Waldspurger for any irreducible admissible representation, connecting them to the wavefront set (WFS) of the representation. We conclude by presenting a conjecture of A. Hazeltine, B. Liu, H-C. Lo and myself on understanding WFS for any irreducible admissible representation.

Bio: Freydoon Shahidi is an Iranian-American mathematician. Shahidi earned his doctorate from Johns Hopkins University in 1975, under the supervision of Joseph Shalika. He is presently a Distinguished Professor at Purdue University. His research is in the Langlands Program and in particular the Langlands-Shahidi method. He is a Fellow of the American Academy of Arts and Sciences and a Fellow of AMS.