Polygons in symmetric spaces and buildings with applications to algebra

• Applicant: Professor Dr. Bernhard Leeb
• Subject Area: Mathematics
• Term: from 2003 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5407455

This project belongs within the framework of metric spaces with curvature bounded above. It concerns the geometry of nonpositively curved spaces of higher rank, that is, of symmetric spaces of noncompact type and Euclidean buildings. We will study some basic questions such as restrictions on the side lengths of polygons and in relation with this develop further the general geometric structure theory. As for the methods, comparison geometry, building theory and Lie theory play the main role in our investigations, and apart from this there is influence by ideas from symplectic geometry and algebraic geometry. Although the questions we are mainly interested in as well as the methods are geometric, there are serious applications to algebraic problems, such as Eigenvalues of a Sum problem going back to H. Weyl and the Decompositon of Tensor Products problem in representation theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry