## Research Interests

I am generally interested in topics from high energy and mathematical physics, especially pertaining to topology and geometry. These especially relate to Supersymmetric field theories and compactification of string theories.

According to the Coleman-Mandula theorem, the only possible non-trivial internal symetry of a quantum field theory is supersymmetry. Supersymmetry has generally nice properties such as unification of the standard model couplings, anomaly cancellation in quantum gravity, and cancellation of infrared divergences. N=2 Supsersymmetric field theories are especially interesting because they offer enough complexity to demonstrate the rich connection between supersymmetric field theories and algebraic topology as in Seiberg-Witten electric-magnetic duality. They also provide tools for studying strongly coupled quantum field theories and studying aspects of string theories. Among the most important of these is something called BPS states. These are a class of non-perturbative stats which are stable to small perturbations and relate to many phenomena such as the entropy of supersymmetric black holes, topology, integrable systems, knot theory, and a plethora of other topics.