The American Mathematical Society held its thirty-seventh annual Sum-
mer Research Institute at the University of California at Santa Cruz, Santa
Cruz, California, from July 10 to July 30, 1989. The focus of this institute
was several complex variables and complex geometry. The members of the
AMS Committee on Summer Institutes that selected this program were Eric
Friedlander, Steven L. Kleiman, Paul H. Rabinowitz, Thomas C. Spencer,
Robert B. Warfield, Jr., and John Wermer (chair). The institute was sup-
ported in part by a grant from the National Science Foundation. The Orga-
nizing committee for the institute consisted of Eric Bedford, John D'Angelo,
Robert E. Greene, and Steven G. Krantz (chair). All of the organizers edited
these proceedings.
The institute explored recent developments in the geometry and function
theory of several complex variables. An attempt was made to create a dia-
logue among the different methodologies in the subject: differential geometry,
algebraic geometry, partial differential equations, harmonic analysis, and clas-
sical methods. Each week there were two series of several connected lectures
(called the Principal Lectures) representing important directions in the field
of emphasis for that week. These were intermixed with single hour lectures.
Both the connected series of talks and the hour lectures were presented in the
mornings and early afternoons. The last three hours of every day consisted
of two parallel sessions of briefer seminar lectures.
Principal lectures
Week One
Nessim Sibony, Weakly Pseudoconvex Domains
Sergey Pinchuk, The Scaling Method and Holomorphic Mappings
Week Two
Ngaiming Mok, Problems in Kahler Geometry Related to Hermitian
{Locally) Symmetric Spaces
Jean Pierre Demailly, Holomorphic Morse Inequalities
Week Three
David Catlin, Extensions ofCR Structures
John Erik Fornaess, Lp Estimates for 5
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