Centre for Computational and Discrete Geometry
Welcome to the University of Calgary's Centre for Computational & Discrete Geometry (CCDG), an academic research centre housed within the Department of Mathematics & Statistics and supported by the Canada Research Chairs Program, Canada Foundation for Innovation, Natural Sciences and Engineering Research Council of Canada, Faculty of Science and the Department of Mathematics and Statistics.
Organizers: Karoly Bezdek, Nikolai Dolbilin, Egon Schulte and Marjorie Senechal
This workshop, sponsored by AIM and the NSF, will be devoted to modeling the geometry of condensed matter. The workshop will focus on "soft packing" and "nested clustering" phenomena in discrete geometric structures and their applications to understanding the internal atomic structure of solids and fluids. In particular, the workshop seeks to integrate the theories of tilings, coverings, and packings, and to develop new discrete geometric concepts and tools needed to study aperiodic structures such as aperiodic crystals. For more details visit the CCDG page of the workshop and the workshop website.
Authors: Károly Bezdek (U of C) and Muhammad A. Khan (U of C)
Journal: Aequationes Mathematicae
Abstract: Covering a convex body by its homothets is a classical notion in discrete geometry that has resulted in a number of interesting and long-standing problems. Swanepoel introduced the covering parameter of a convex body as a means of quantifying its covering properties. In this paper, we introduce two relatives of the covering parameter called covering index and weak covering index, which upper bound well-studied quantities like the illumination number, the illumination parameter and...