Report for the academic year - Libraries - Institute for Advanced Study

ENRICO BOMB1ERI, IBM von Neumann Professor
JEAN BOURGAIN
PIERRE DELIGNE
ROBERT P. LANGLANDS, Hermann Weyl Professor
ROBERT D. MacPHERSON
THOMAS SPENCER
AVI WIGDERSON
ARMAND BOREL
ATLE SELBERG
The largest program in the School of Mathematics for 1999-2000 was the special year in
the analytic theory of automorphic forms and L-functions. This program was organized by
P. Sarnak of Princeton University, H. Iwaniec of Rutgers University, who was the Distin-
guished Visiting Professor for the year, and School Faculty members E. Bombieri and
R. Langlands. The special year focused on the analytic theory of GL(2) automorphic func-
tions and its application to classical problems in number theory; spectral problems in quan-
tum chaos; and the analytic theory of general L-functions such as the Riemann Hypothe-
sis. (There was some material on automorphic functions for other groups, but this was
stressed less. This will be the subject of a special year at the Institute in 2000-2001.)
Aside from informal interactions, the main activity of this special year was a series of
lectures held three times per week, and designed to be accessible to a fairly general math-
ematical audience. This was a very successful approach, since modular forms tend to be
considered by mathematicians coming from very different scientific backgrounds. Lec-
tures were given by H. Iwaniec, P. Sarnak, E. Kowalski, D. Bump, B. Conrey, F. Shahidi,
J. Cogdell, W. Kohnen, H. Jacquet, K. Soundararajan, D. Ramakrishnan, H. Kim,
S. Friedberg, R. Murty, D. Goldfeld, H. Stark, N. Katz, A. Panchishkin, M. Furusawa,
P. Michel, J. VanderKam, S. Boecherer, P. Cohen, S. Zhang, W. Li, Y. Choie, A. Perelli,
A. Zaharescu, S. Wolpert, Z. Mao, T. Watson, S. Johansson, S. Kudla, R. Heath-Brown,
S. Rallis, W. Luo, and E. Coins.
L. Lafforgue of CNRS - Orsay gave a series of three lectures on his spectacular recent
proof of the Langlands correspondence over function fields. Z. Rudnick of Tel Aviv Uni-
versity gave a series of two lectures on number theoretic problems in quantum chaos.
P. Deligne gave a series of two lectures showing how to get information about trigono-
metric sums, a very concrete object, 1-adic cohomology, usually seen as rather abstract.
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