Spherical intrinsic volumes

• Applicant: Dr. Dennis Amelunxen
• Subject Area: Mathematics
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 218401980

The goal of the project is the analysis of the statistical properties of spherical intrinsic volumes and its applications in the areas of convex programming and compressed sensing. The intrinsic volumes for closed convex sets are generalizations of the usual notion of volume. In the spherical case, or in the case of convex cones, one gets for each cone a discrete probability distribution. Many probabilities associated with a cone can be described in terms of the corresponding probability distribution given by the intrinsic volumes. The statistical properties of the spherical intrinsic volumes thus play a decisive role in the analysis of these probabilities. Some applications in the area of convex programming already exist and should be further extended. In the context of compressed sensing the intrinsic volumes are not yet sufficiently treated and a transfer of the developped techniques appears to be reasonable and promising.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. James Renegar