As a sequel to the International Conference on the Algebraic and Arithmetic
Theory of Quadratic Forms in Talca and Puc´ on (Chile) 2002, whose proceedings
were published as volume 344 of this series, another conference with the same title
was held in December 2007 in Frutillar in the southern part of Chile. This volume
contains the proceedings of the meeting, which was attended by 90 participants
from North and South America, Asia and Europe.
The talks at the conference covered the full range of topics that constitute
the theory of quadratic forms, from the algebraic theory with its connections to
algebraic K-theory, (real) algebraic geometry, and Galois cohomology to the arith-
metic theory with its connections to analytic number theory, geometric problems,
optimization, and coding theory. The papers in this proceedings volume reflect the
diversity of the talks given at the conference and range from survey articles, serving
as an introduction to important results of recent years, to articles presenting new
research results and open problems.
The editors gratefully acknowledge financial support for the conference from
the following sources:
(1) Proyecto Anillo, ACT 05, PBCT, Conicyt
(2) Universidad de Talca, Proyecto ”Reticulados y Ecuaciones”
(3) Royal Society International Joint Project ”Differential Forms and their
Applications to Quadratic and Bilinear Forms”
The conference would not have been possible without the great efforts by the local
organizing committee, headed by M. I. Icaza and M. O’Ryan, that took care of all
the logistic and organizational problems and the many little worries of the partici-
pants. The editors Chan, Hoffmann and Schulze-Pillot owe much debt to Ricardo
Baeza for bringing this meeting into existence and coordinating the scientific pro-
gram and the editing process of this volume. All four editors thank the AMS for
publishing this volume and the staff of the AMS for all the support in the editing
process. Last but not least we thank all the participants for traveling long distances
and for their varied contributions that made the meeting such a scientific success.
Ricardo Baeza
Wai Kiu Chan
Detlev W. Hoffmann
Rainer Schulze-Pillot
February 2009
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