This grant supports the research of Professor J. Rush to work in coding theory, the geometry of numbers and the relationship between the two. He will work on dense lattice packings, thin lattice coverings and multiple packings and coverings. This research falls in the interface between combinatorics and number theory. Number theory and combinatorics both started from attempts to systematize the very first of all mathematical activities, counting. These fields have had an explosive development in the past few decades because of their importance in communications and information technology, for example the design of cellular networks.
