Convex and Discrete Geometry

Main fields of research

Convex Geometry	In Convex Geometry, geometric and analytic methods are used to study convex sets and convex functions. Therefore Convex Geometry is situated between Analysis and Geometry. In the research unit especially the following problems are studied: Affine geometry of convex bodies Approximation of convex bodies by polytopes Properties of typical convex bodies in the sense of Baire categories Valuations on the space of convex bodies and on function spaces
Geometry of Numbers	Geometry of Numbers forms a bridge between convexity, Diophantine approximation and the theory of quadratic forms. Today it is an independent problem-oriented field of mathematics having relations with coding theory, numerical integration, computational geometry and optimization. Geometry of Numbers has a long tradition in Vienna and in the research unit the following problems are studied: Diophantine approximation Products of inhomogeneous linear forms Inverting Minkowski's theorem on linear forms