My research interests lie in the intersection of topology, geometry and physics. My doctoral research is in Mathematical Physics, focused primarily on the geometric and topological aspects of string theory.
Specifically, I look at local and global aspects of various types of T-duality. The simplest example of T-duality says that string theory on a cylinder of radius R is equivalent to string theory on a "dual" cylinder of radius 1/R. When a background Kalb-Ramond field is introduced (the string analogue of the electromagnetic field) the geometry, and more interestingly the topology, of the "dual" spacetime changes. In a more sophisticated treatment, T-duality is a relationship between differentiable manifolds with additional structure such as a complex, symplectic, or Riemannian structure. T-duality has a natural description in terms of the generalised geometry of Hitchin, which replaces structures (such as a Riemannian metric) on the tangent bundle with structures on the direct sum of the tangent and cotangent bundles. T-duality is related to Mirror Symmetry, a mathematical conjecture concerning Calabi-Yau manifolds, and has applications to supergravity in ten and eleven dimensions. I've recently become interested in various generalisations of T-duality, and their relation to M-theory and higher structures. The generalisations are Poisson-Lie T-duality, spherical T-duality, non-abelian T-duality, and non-isometric T-duality. My thesis investigates geometric and topological aspects of these various dualities.
I also have an interest in other areas of mathematics and physics. These areas include (but are not limited to) wild and non-compact knot theory (including potential applications to statistical mechanics and quantum field theory) and mathematical aspects of general relativity.
I studied a Bachelor of Science (Physics) / Bachelor of Mathematics at the University of Wollongong from 2009 to 2012. While there, I was able to go on international exchange to McMaster University in Canada, earning an international studies minor in the process. While still at Wollongong, I completed an honours degree in Operator Algebras and Statistical Mechanics, under the supervision of Associate Professor Adam Rennie. Since February 2014, I have been studying for a PhD at the Australian National University under the supervision of Professor Peter Bouwknegt.