Research on Geometry of Numbers and Convex Geometry

14.02.2003 - 14.02.2005
Research funding project
The main goals of the proposed research project are an extension and improvement of the results obtained within the framework of FWF Project M672. We propose to continue our research in the following directions: -Investigation of the duality between simultaneous Diophantine approximation of rationals and Siegel's Lemma. This duality provides new tools for the study of various Diophantine problems. -A problem of Erdös and Moser. Properties of the k-dimensional unit cube. -Decompositions of integer vectors with respect to Euclidean and sup norms. We plan to use a new approach obtained during the current grant period. -Investigation of simultaneous Diophantine approximation algorithms using recent results on simultaneous Diophantine approximation of rational numbers by rational numbers with smaller denominators. -Properties of lattices. DOTU matrices. Problems of Minkowski and Mordell. We also plan to continue to study convex geometry with its applications. In particular, the following questions are planned to be addressed: affine surface area and valuations (Professors Monika Ludwig and Reitzner), approximation of convex bodies, distribution of point sets on Riemannian manifolds and applications of these to signal processing and numerical integration, stability problems (Professor Gruber).

People

Project leader

Institute

Grant funds

  • FWF - Österr. Wissenschaftsfonds (National) Austrian Science Fund (FWF)

Keywords

GermanEnglish
diophantische ApproximationenDiophantine approximation
sukzessive Minimasuccessive minima
Geometrie der Zahlengeometry of numbers
konvexe Körperconvex bodies

Publications