Our expertise in the theory of special functions and its connection with representation theory lies in between these categories. Our aim is to cover mathematical physics from a broad point of view, including all of the four traditional disciplines of mathematics, viz.
The work falls into three broad categories: - The formal development of geometric algebra has been patchy and a number of important subjects have not yet been treated within its framework.
For something as really new as "try getting a few flakes of graphite transferred by van-der-waals adhesion to sticky tape from a 6B pencil mark on paper to a glass slide, and then four-point microprobe it under a microscope to measure the carrier lifetime and conductivity within a monocrystalline domain of graphite", that would never have got funding because it was too novel; those sometimes get called "Friday Afternoon Experiments" and tend to be a byproduct of having the basic research equipment doing something more ordinary for the rest of the week.
To support this contention, reformulations of Grassmann calculus, Lie algebra theory, spinor algebra and Lagrangian field theory are developed.
However, we also work on topics in classical mathematical physics, like symplectic geometry and the theory of integrable systems.
The Dirac equation forms the basis of this gauge theory, and the resultant theory is shown to differ from general relativity in a number of its features and predictions. Analysis, Algebra, Geometry, and Stochastics.
Research Our research primarily involves structures that originated or matured in the context of quantum mathematical physics in the tradition of von Neumann, such as representation theory, operator algebras, and noncommutative geometry.
The third details an approach to gravity based on gauge fields acting in a fiat spacetime.