Linking geometric problems to physics could open door to new solutions

A Princeton scientist with an interdisciplinary bent has taken two well-known problems in mathematics and reformulated them as a physics question, offering new tools to solve challenges relevant to a host of subjects ranging from improving data compression to detecting gravitational waves. Salvatore Torquato , a professor of chemistry , has shown that two abstract puzzles in geometry - known as the "covering" and "quantizer" problems - can be recast as "ground state" problems in physics. Ground state problems relate to the study of molecule systems at their lowest levels of energy and have numerous applications across scientific disciplines. Torquato's conclusions are reported in a paper that was published online Nov. 10 by Physical Review E. "This paper describes what I believe to be a wonderful example of the deep interplay between geometry and physics," Torquato said. The problem of determining the ground states of special interacting particles, which is relevant to studies of conditions of materials approaching absolute zero, is directly applicable to these math questions, he explained. "In other words," Torquato said, "what appear to be abstract mathematical problems can be related to the cooling of special liquids that undergo phase transitions to crystal states at a temperature of absolute zero.