PROBLEMS AND RESULTS ON COVERING SYSTEMS

This is an introduction to the important aspects of covers of Z by residue classes and covers of groups by cosets or subgroups. The field is connected with number theory, combinatorics, algebra and analysis. It is quite fascinating, and also very difficult (but the results can be easily understood). Many problems and conjectures remain open, some nice theorems and applications will be introduced. Perhaps my favorite problem of all concerns covering systems.