Report for the Academic Years 1987-1988 and 1988-1989

THE SCHOOL OF MATHEMATICS
The Herman Weyl Lectures were given by L. KadanofF on "Chaos and Univer-
sality" [three lectures, January 26-February 4, 1988]. Lectures in commemoration
of Ame Beurling were given on January 4, 1988 by L. Carleson, P. Malliavin and
L. Ahlfors.
Academic Activities of the School: Academic Year 1988—89
In the academic year 1988-89 the School had a special program on dynamical
systems and invited L. Carleson as distinguished visiting professor. The dynami-
cal systems seminar was very active, often meeting two or three times a week.
Among many other topics and speakers in this seminar, Professor Carleson gave
several lectures explaining the proof due to him and M. Benedicks, that the
Henon map has a so-called strange attractor. The Henon map is a simple area-
contracting map from two-dimensional space to itself that exhibits a complicated
chaotic behavior when iterated in computer simulation. Despite many attempts,
until Carleson's work with Benedicks, this behavior, which is also observed in
many physical systems with dissipation, could not be explained analytically.
A. Douady gave the 12th Marston Morse Memorial Lectures. The lectures,
entided "Holomorphic Surgery," took place on December 5, 7 and 8 and dealt
with holomorphic dynamical systems.
There were two other smaller areas of concentration, with only a few visitors:
partial differential equations and representations of p-adic groups. In particular,
there was a seminar devoted primarily to a presentation of the work of C. Bush-
nell, P. Kutzko and L. Morris on GLn, as their research developed during the
course of their visit.
In term I, a seminar on "Lie groups and quadratic forms" continued the previous
year's seminar on approximations by irrational quadratic forms and then contin-
ued in term 11 as a seminar on "locally symmetric varieties."
In the number-theory seminar, G. Fallings gave a series of talks on his recent
work on p-adic cohomology of algebraic varieties in term I. Then, during term
II, E. Bombieri gave a course on diophantine approximation.
In July, good use was made of the facilities of the Institute by the Clavius group,
a group of Catholic mathematicians, mainly geometers, who assembled here for
a month of seminars and discussions.
As usual, the organized activities of the academic years 1987-88 and 1988-89 are to
be viewed only as a part of the matiiematical Hfe at the Institute. Of equal, or greater,
importance are individual research and the many informal discussions between members
andfaculty, for which the Institute provides a most favorable environment.
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