Mathematics formula K-Theory used to advance understanding of topological materials
August 10, 2023 - Dani Rae Wascher
Terry Loring, distinguished professor of Mathematics and Statistics, recently published and co-authored a new research piece involving his research on K-theory with the major advances in applications to critical problems in physics. The new research study titled, “Revealing topology in metals using experimental protocols inspired by K-theory,” was recently published in the nature communications journal. Loring used mathematical properties of K-theory to help advance the understanding of topological materials in the physics world.
The main focus of the study was to discover how electricity, sound, or light can be trapped in a portion of a material. “This experiment was done in what is called a meta-material, built from individual sound resonators coupled in a fashion that mimics how atoms can come together to form a crystal. Three-dimensional printing allows us to make customized resonators that we join in a precise way to make the physics match the mathematics,” explained Loring. The study was part of a larger project that covered many areas of physics.
According to Loring, there are different forms of K-theory that arise in many different mathematical fields, however, the form of K-theory that he used in this study was focused on being best suited for studying matrix models of physical systems.
Loring explains that matrices are simply square tables of numbers, with a peculiar rule for how two matrices are multiplied. This rule has an asymmetry in it that leads to having AB and BA sometimes being very different, meaning that the commutative law for multiplication is violated.
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