Diophantine Methods, Lattices and Arithmetic Theory of Quadratic Forms

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 generalisations. Extremal lattice theory and spherical designs.