Advancing the Interplay Between Geometry, Analysis and Combinatorics
Computational discrete geometry is a rapidly developing discipline on the boundary of mathematics and computer science. It enables researchers to tackle important problems in areas like robotics, computer graphics, pattern recognition, crystals and quasicrystals, and manufacturing processes.
Dr. Karoly Bezdek, Canada Research Chair in Computational and Discrete Geometry, is one of the world's leading researchers in computational and discrete geometry. He is known for resolving (with Robert Connelly of Cornell University) the 1955 Kneser-Poulsen Conjecture, which is one of the best-known open questions of computational and discrete geometry in more than 40 years.
Bezdek’s research interests are in discrete, convex, combinatorial, and computational geometry, including some aspects of geometric analysis, geometric rigidity and optimization. He has published more than 120 research articles.
Bezdek’s research program belongs to the broad area of computational and discrete geometry. He and his research team are studying the mathematical possibilities of packings, coverings, tilings, polytopes, ball-polyhedra, billiards and sphere arrangements (molecules). They are also investigating contact graphs, crystallization and the volumetric geometry of molecules.
In the course of his research, Bezdek also intends to target longstanding conjectures with a combination of methods from discrete, convex, combinatorial and computational geometry, geometric analysis and optimization.
This research will help solve fundamental problems in geometry, and has applications in information theory, chemistry, physics and engineering.