Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms

The study of equations over the integers or the rational numbers is the subject of diophantine geometry. This also includes generalizations to finite extensions of the rationals, their rings of integers, and also to function fields over a finite field, and the rings of polynomials therein. This is a vast subject, in which a variety of methods from geometry, analysis, and arithmetic are used. For our intended workshop we focus on problems involving height functions, methods from the geometry of numbers, and the arithmetic of lattices with quadratic and hermitian forms. In the sections to follow we present a brief overview of a few directions in the theories of height functions and of quadratic forms, in particular concentrating on the interplay of these two lively areas.