Linking geometric problems to physics could open door to new solutions: Torquato started on his new approach after learning from a colleague about the quantizer problem and seeing parallels with other studies on the ground state in physics. He already was familiar with the covering problem because of his interest in sphere-packing puzzles.
The covering and quantizer problems are major problems in discrete mathematics and information theory, according to Henry Cohn, a mathematician with Microsoft Research New England in Cambridge, Mass. These quandaries have, however, received much less attention than related problems such as packing, Cohn said, because "they seem to be far more subtle and complicated and thus much more difficult to study."
Torquato's study, he added, develops the theory from a physics perspective and builds new connections with the theory of energy minimization and ground states.