About Us

The goal of CCDG is to maintain an active research program in the broad area of computational and discrete geometry, including both theoretical research and applications of the theory to sciences and engineering.

The name discrete geometry, which at one time stood mainly for the areas of packing, covering and tiling, has gradually grown to include such areas as combinatorial geometry, convex polytopes, and arrangements of points, lines, planes, circles and other geometric objects in the plane and in higher dimensions. Similarly, computational geometry, which referred not long ago to simply design and analysis of geometric algorithms, has in recent years broadened its scope to include the study of geometric problems from a computational point of view, including also computational convexity, computational topology, and questions involving the combinatorial complexity of arrangements and polytopes. Thus, the area Computational and Discrete Geometry is interdisciplinary and has important relations to many other vital mathematical fields such as topology, combinatorics, probability theory, geometric analysis. At the same time, it is on the cutting edge of modern applications such as mathematical programming, coding theory, solid modeling and computational structural biology, etc.

To list just a few active directions pursued within our center, we mention

• kissing numbers and sphere packings with applications to cryptography,
• folding and unfolding including Dürer's problem on edge unfolding of convex polyhedra,
• ball-polyhedra with relationship to classical polytopes and rigidity,
• volume inequalities in Euclidean and non-Euclidean spaces,
• shortest billiards,
• geometric graphs,
• convex polytopes with special facial and combinatorial structures,
• transversal and Helly-type theorems in geometry, combinatorics and topology,
• polytope curvature based on central paths and its relationship to the polytope diameter,
• large-scale high-performance structured optimization with applications to radiation therapy for cancer treatment.

We strive to

• be a top research center in computational and discrete geometry within Canada,
• maintain a dedicated state-of-the-art high-performance computational laboratory accessible to local members of CCDG,
• maintain top-level graduate and undergraduate research programs,
• offer exciting undergraduate and graduate courses in the broad area of computational and discrete geometry,
• host weekly CCDG seminars dedicated to active research areas within the group,
• host a prestigious monthly Fejes-Tóth lecture series in computational and discrete geometry,
• host a regular stream of research visitors,
• host the high-level free peer-reviewed Contributions to Discrete Mathematics electronic journal serving a broad community of discrete mathematicians,
• cultivate partnerships with other research groups, both in Canada and abroad.