This volume contains the proceedings of the
International Workshop on Diophantine Methods, Lattices, and
Arithmetic Theory of Quadratic Forms, held November 13–18, 2011, at
the Banff International Research Station, Banff, Alberta, Canada.

The articles in this volume cover the arithmetic theory of
quadratic forms and lattices, as well as the effective Diophantine
analysis with height functions. Diophantine methods with the use of
heights are usually based on geometry of numbers and ideas from
lattice theory. The target of these methods often lies in the realm of
quadratic forms theory. There are a variety of prominent research
directions that lie at the intersection of these areas, a few of them
presented in this volume:

Representation problems for quadratic forms and lattices over
global fields and rings, including counting representations of bounded
height.

Small zeros (with respect to height) of individual linear,
quadratic, and cubic forms, originating in the work of Cassels and
Siegel, and related Diophantine problems with the use of
heights.

Hermite's constant, geometry of numbers, explicit reduction
theory of definite and indefinite quadratic forms, and various
generalizations.

Extremal lattice theory and spherical designs.

Readership

Graduate students and research mathematicians
interested in number theory, in particular in Diophantine problems,
quadratic forms, and lattices.