**Email:**mark.bugden@anu.edu.au**Office:**John Dedman Building LG103**Phone:**+61 2 6125 1007

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.