Kevin Iga Publishes New Study on Adinkras and Laplacians

Dr. Kevin Iga, a professor of mathematics at Seaver College, recently published the research article, “Eigenvalues and critical groups of Adinkras,” alongside his collaborators Caroline Klivans, Jordan Kostiuk, and Chi Ho Yuen in the scholarly journal Advances in Applied Mathematics. This article takes two mathematical concepts, Adinkras and Laplacian matrices, and studies the potential relationship existing between them.

Adinkras are diagrams that encode much of the mathematical structures of supersymmetry. The concept of supersymmetry attempts to discover and understand the behavior of the smallest particles in atoms. Specifically, supersymmetry delves into the relationship between bosons and fermions – two classes of subatomic particles. 

Laplacians, on the other hand, reveal how each point on a graph might be related to the points surrounding it. This concept is more grounded in everyday experiences, as it can be used to understand elements in nature – such as rolling waves. 

Working closely with Caroline Klivans, a professor at Brown University and expert in Laplacian behavior, Iga helped to deduce that the diagrams produced by Adinkras create insightful questions about Laplacians. By connecting Adinkras and Laplacians, Iga and his team of researchers are able to take a series of complex graphs and simplify them. 

“[This process] didn’t turn something hard to something easy,” says Iga describing the discovery. “[This process] turned something impossible into something hard…well, medium hard, maybe.”  

Iga began studying Adinkras because of an initial interest in the concept of supersymmetry. In 2004, Sylvester J. Gates Jr. and Michael Faux introduced the concept of Adinkras in a research article, and Iga immediately felt as though he could contribute to this subject. Although stepping away from his general research focus (an area of topology which investigates four-dimensional manifolds using Seiberg-Witten equations) and turning toward Adinkras was a risk, Iga felt secure in his choice. 

“One thing about being at Pepperdine was that I felt I had the freedom to take the risk.” says Iga. “There are many academic institutions out there that are only looking at how many publications you have made. Pepperdine cares about the number of publications, but the expectation is not so onerous that I felt pressure to maximize how many papers I was publishing to the exclusion of exploring a new field.”

Although the exact use of Adinkras and Laplaciens in the natural world is not clear at this point, Iga is confident that, eventually, the two concepts and their relationship could serve as an exciting starting point for future discoveries.

“People think that science is advanced by the word ‘eureka',” says Iga, quoting Isaac Asimov. “More often than not science is advanced by the phrase, ‘huh, that’s funny.’”

To learn more about Iga's project, visit Advances in Applied Mathematics's webpage.