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Research
(Convex Geometry, Discrete Geometry, Geometry of Numbers and Applications)
- Relations between discrete and continuous functionals, e.g. lattice point enumerator and mixed volumes.
- Variants of classical theorems of geometry of numbers (e.g. Minkowski´s 1st and 2nd theorem) and successive minima variants.
- Parametric density and its application to finite and infinite packings and coverings, e.g. to degenerate packings (sausages).
- Parametric density and its application to crystallography.
- Contributions to infinite packings and coverings, e.g. dense packings of ellipsoids and mixed spheres.
- Applications to linear and convex optimization.
- Polyhedral maps, in particular combinatorially regular polyhedra.
- Building up a sphere packing database.
- Construction of polyhedral models of Klein's quartic.