Research

Computational and Discrete Geometry is interconnected with other areas of mathematics, sciences and engineering, such as analysis, combinatorics, mathematical programming / optimization, number theory, topology, coding theory, digital communication, analog-to-digital conversion and data compression, higher dimensional crystallography and rigidity / flexibility of structures (including protein folding), visualization, etc.

The above multi-faceted portrait of the discipline is a good model of the research program pursued by CCDG: we strive to advance both the theoretical and the applied frontiers of computational and discrete geometry.

We are particularly delighted to mention that the research program of CCDG is a priority direction within the research plan of the Department of Mathematics and Statistics, and as such, is intrinsically connected to the Strategic Research Areas at the University of Calgary (see Strategic Research Plan), namely, Information Technologies (“Creating Technologies and Managing Information for the Knowledge Society”) and Translation Research for clinical practices (“Advancing Health and Wellness”). Discrete and geometric algorithms are ubiquitous to information technologies, with application areas ranging from signal and data processing to human-machine interaction including visualization. Algorithms and models for optimal design of radiation therapy for cancer treatment constitute one of the application areas actively pursued by CCDG.

Some ongoing research projects in which students might be involved are described here:

• Convex 4-polytopes
• Graph Connectivity
• Radiotherapy Design