Volume Inequalities for Arrangements of Convex Bodies

Karoly Bezdek is a Professor and Director - Centre for Computational & Discrete Geometry, Pure Mathematics at University of Calgary. He received his Ph.D. in mathematics at the ELTE University of Budapest. He holds a first tier Canada chair, which is the highest level of research funding awarded by the government of Canada

Volume Inequalities for Coverings - the influence of the Hadwiger-Levi Conjecture (1955). On the density and symmetry of covering Euclidean d-space by translates of a convex body. Covering numbers and weighted coverings – volumetric estimates. The Hadwiger-Levi conjecture and its equivalent formulations. The status of the Hadwiger-Levi conjecture: progress and results for covering by smaller homothets in dimensions two and higher. A computer based approach. Quantifying covering and illumination: the covering and illumination parameters of convex bodies. The vertex and covering indices of convex bodies – volumetric estimates. X-raying and covering by planks and cylinders. Volume Inequalities for Sphere Arrangements – the influence of the Kneser-Poulsen Conjecture (1955). Theorems of Kirszbraun, Kneser and Brehm. The status of the Kneser-Poulsen conjecture. Aspects of the Kneser-Poulsen conjecture.