Grant: Discovery Grants Program - Individual

My research involves using a set of tools called K-theory to study mathematical structures called C*-algebras (read see-star), groups, and quantum groups. C* algebras are objects that are used, among other things, to represent the observable quantities, such as position and momentum, in some models in physics. In these models, groups act on the C*-algebras to describe the evolution of the system through time, or other changes of reference frame. Quantum groups are generalisations of groups that first arose in modern physics, when the structures of classical physics were viewed as special limiting cases in which one allowed a fundamental constant of nature called Planck's constant to be neglected. They can, in some cases, be described as C*-algebras with certain additional structures, called co-multiplications. My research program looks to classify C*-algebras with the extra structure of either a group action or a co-multiplication using tools from K-theory. A classification of this kind is much more than just a list. It is more like having a collection of owner's manuals than a list of licence plate numbers--one can read off the interesting structural features from the labels.