AMHERST, Mass. Contributing geometric and topological analyses of micro-materials, University of Massachusetts Amherst mathematician Robert Kusner aided experimental physicists at the University of Colorado (UC) by successfully explaining the observed "beautiful and complex patterns revealed" in three-dimensional liquid crystal experiments. The work is expected to lead to creation of new materials that can be actively controlled.
Kusner is a geometer, an expert in the analysis of variational problems in low-dimensional geometry and topology, which concerns properties preserved under continuous deformation such as stretching and bending. His work over 3 decades has focused on the geometry and topology of curves, surfaces and other spaces that arise in nature, such as soap films, knots and the shapes of fluid droplets. Kusner agrees with physicist and lead author Ivan Smalyukh of UC Boulder that their collaboration is the first to show in experiments that some of the most fundamental topological theorems hold up in real materials. Their findings appear in the current early online issue of Nature.
UMass Amherst's Kusner explains, "There are two important aspects of this work. First, the experimental work by the Colorado team, who fabricated topologically complex micro-materials allowing controlled experiments of three-dimensional liquid crystals. Second, the theoretical work performed by us mathematicians and theoretical physicists while visiting the University of California Santa Barbara's Kavli Institute for Theoretical Physics (KITP). We provided the geometric and topological analysis of these experiments, to explain the observed patterns and predict what patterns should be seen when experimental conditions are changed."
Kusner was the lone mathematician among four organizers of last summer's workshop on "Knotted Fields" at KITP, which led to this work. The workshop engaged about a dozen other mathematicians and about twice
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University of Massachusetts at Amherst