Sphere-Packing Expert Torquato Links Two Math Problems to Physics

November 29, 2010

Salvatore Torquato (Princeton University), who made a breakthrough in sphere-packing last year, may have done it again. He claims that "covering" and "quantizer" geometry problems can be recast as "ground-state" problems in physics.

Covering and quantizer problems are major concerns in discrete mathematics and information theory. Ground-state problems relate to the study of molecule systems at their lowest levels of energy.

"One consequence is new insights into the role of randomness and disorder," said Henry Cohn (Microsoft Research New England). "I'm also intrigued by the potential use for detecting gravitational waves, which would be a remarkable application of mathematics."

Scientists attempting to analyze data from gravitational wave detectors may, therefore, be able to use Torquato's findings to design software tools for more accurate searches through high-dimensional data sets.

Reporting his findings in a paper in Physical Review E (November 10, 2010), Torquato, who won SIAM's Kleinman Award in 2007, drew connections to two other mathematical conundrums, including the sphere-packing problem and the density-fluctuation (number-variance) problem, the latter of which is related to a classical problem in number theory.

"These results may have important implications across many fields, which speaks to the fundamental nature of the problems," Torquato said.

For more, see the Math in the News item "Packing of Tetrahedra Illuminates Nature of Matter" (August 20, 2009).

Source: News at Princeton (November 16, 2010)

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1001

Start Date:

Monday, November 29, 2010