Introduction
The 2002 IAS/Park City Mathematics Institute on "Automorphic Forms and their
Applications" took place in Park City, Utah from July 1 to July 20. Approximately
57 from the graduate program plus many of the research program participants at-
tended different portions of the Graduate Summer School. The school was narrowed
to cover topics related to developments in analytic aspects of the subject as well
as a number of introductory courses on relevant topics. The lectures were divided
into six general areas:(1) Basic Theory of Eisenstein Series by Armand Borel and Joseph Bernstein,
(2) Converse Theorems and Langlands-Shahidi Method by James Cogdell and
Freydoon Shahidi,
(3) Ramanujan Conjectures and Applications, e.g., Ramanujan Graphs by
Laurent Clozel, Wen-Ching Winnie Li and Alaine Valette,
( 4) Analytic Theory of G L(2) Forms and L-functions by Phillipe Michel,
(5) Arithmetic Quantum Chaos by Zeev Rudnick and Audrey Terras,
(6) Unipotent Flows on r \ G and Applications by Alex Eskin.Also, Peter Sarnak gave two introductory lectures outlining the topics covered by
the Graduate Summer School.
The present volume contains the lectures of A. Borel, L. Clozel, J. Cogdell,
W. Li, P. Michel, F. Shahidi and A. Terras, together with a manuscript by David
Vogan, "Isolated unitary representations", which is related to the topic covered by
Clozel.
Recent important instances of Langlands Functoriality Conjecture, including
the existence of the third and the fourth symmetric powers of cusp forms on GL(2)
as automorphic forms on GL(4) and GL(5) established by Kim and Shahidi, have
relied on applying Converse Theorems of Cogdell and Piatetski-Shapiro to ana-
lytic properties of certain automorphic £-functions, obtained from the Langlands-
Shahidi method. This is a method which relies on the study of the constant and
non-constant terms of Eisenstein series attached to generic cuspidal automorphic
representations of Levi subgroups of maximal parabolic subgroups of quasi-split
connected reductive groups over number fields. It thus relies on a good under-
standing of the theory of Eisenstein series.
Lectures by Borel and Bernstein have addressed these issues by covering both
the general aspects of the theory of automorphic forms on G(AF ), i.e., that of un-
derstanding L^2 (Zc(Ap)G(F)\G(Ap)) or classically L^2 (r\G) for a reductive group
G over a number field F. This is the content of Borel's lectures. On the other
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