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Shepler a principal investigator for $132,000 NSF math grant

Working at the intersection of geometry and algebra in an area of math called homological algebra, Anne Shepler, associate professor of mathematics, studies symmetries and the deformations that arise when scientists intentionally mitigate these symmetries.

“Scientists revel in the miraculous symmetries of nature - for example, symmetry governing crystals, molecules, DNA, quantum systems, even starfish. But scientists also seek ways to look beyond the symmetry into the true heart of nature. We deform a given space or algebra in order to reveal hidden properties and attributes,” Shepler says.

Anne Shepler, Associate Professor of MathematicsShepler serves as principal investigator on a $132,187 National Science Foundation research grant award with Sarah Witherspoon, mathematician at Texas A&M University.

In their project, Collaborative Research: Cohomology and Deformations of Algebras, the two researchers propose a theory of deformations using skew group algebras and Hochschild cohomology that integrates the work of different mathematical fields: invariant theory, combinatorics, ring theory, homological algebra and representation theory.

The greater mathematical community shows interest in Shepler and Witherspoon’s work since deformation algebra is prevalent among many mathematical areas. The potential for impact affects other disciplines, too, such as chemistry, biology, computer science and physics.

By studying all possible families of deformations, Shepler and Witherspoon place the original scientific system in a wider context. Shepler explains,  “In scientific studies, we often get sidetracked with small details and accidental characteristics of a system; if we view, instead, the entire system as a single screen shot in a movie of morphing systems, we obtain new results on the original.” 

— Julie West, Office of Research and Economic Development

Posted on: Tue 07 February 2012

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