## Cameron Kemp

My research is directed towards quantum simulators and their proficiency to express dynamics which are entirely divorced from our classical intuitions. A particularly neat example with a plethora of purely quantum phenomena is the Fractional Quantum Hall Effect whereby the novel phase of the confined fluid admits anyonic excitations, the statistics of these fractionally charged quasiparticles are neither fermionic nor bosonic; the underlying strongly correlated electrons collectively minimise their interaction energy via ordering themselves into topological bound states known as composite fermions, the associated even number of magnetic flux quanta attached to each electron potentiates non-local degrees of freedom in the system wherein one vortex from each composite fermion Cooper pair together constitute a two-dimensional Hilbert space in its own right. On the mathematical side of things, I'm currently immersing myself into Geometric Algebra (and its extension to Geometric Calculus) as a unified language for Mathematical Physics; under this rubric, any n-dimensional vector space is extended to a 2^n dimensional Clifford Algebra via the geometric product, the invertibility of the geometric product (and the fact that objects and operators live in the same algebra) allows one to more easily solve source and field equations as well as packaging simultaneous equations into one compound equation e.g. Maxwell's four vector equations simply fall into one multivector equation and its solution is cast into a generalised Cauchy integral.