This volume of the AMS Contemporary Mathematics series contains the pro-
ceedings of the international workshop on Diophantine Methods, Lattices, and
Arithmetic Theory of Quadratic Forms, held at the Banff International Research
Station, Canada, November 13 - 18, 2011. The goal of this workshop was to bring
together people working in the following areas:
1. Classical arithmetic and algebraic theory of quadratic forms and lattices.
2. Diophantine problems and the theory of height functions.
3. Extremal lattice theory and spherical designs.
In spite of the close connections between these areas, it is quite rare for mathemati-
cians working in these subjects to meet altogether for a joint workshop.
The workshop was organized by W. K. Chan, L. Fukshansky, R. Schulze-Pillot,
and J. Vaaler, who are also the editors of the current volume. There were 41
invited participants at the workshop, delivering a total of 6 plenary (hour long)
and 16 invited (30 minute long) talks. The meeting was overshadowed by the
sudden and unexpected death of Professor Boris B. Venkov in Aachen, Germany
just days before the workshop. Venkov’s important contributions to the theory of
lattices and spherical designs played a central role at the conference. This volume
is dedicated to the memory of Boris Venkov.
The current volume features 19 papers, 2 of which are surveys. In particular,
the first article of this volume details Venkov’s influential work on lattices and
spherical designs. All the articles presented here have been rigorously refereed
according to the high standards of publication required by the AMS Contemporary
Mathematics series. The topics presented are well balanced to reflect the multiple
themes discussed at the conference. We hope that this collection becomes a welcome
addition to the existent literature on the subject.
We wish to thank the Banff International Research Station for the wonderful
hospitality, as well as tremendous administrative, technical, and financial support in
hosting this workshop. We would also like to thank the Number Theory Foundation,
whose generous travel funding made it possible for junior participants to attend our
workshop. Finally, we would like to thank the referees for their work in ensuring
the high quality of this collection.
Wai Kiu Chan,