- Algebraic geometry
- Symplectic geometry
- Differential geometry
- Representation theory
- Mathematical physics
- Gauge theory
- Mirror symmetry
Please click here to see my published research articles and preprints.
Algebraic geometry Algebraic topology Differential geometry Enumerative geometry Higgs bundles Integrable systems Invariant theory Mathematical physics Mirror symmetry Moduli spaces Pure mathematics Quantum matter Quiver varieties Representation theory Symplectic geometry Vector bundles
I am a mathematician at the University of Saskatchewan, specializing in algebraic, differential, and symplectic geometry, especially their relationship to mathematical physics and representation theory.
For some time I have been interested in the properties of Higgs bundles and the Hitchin system, but also use Higgs bundles to probe other geometric structures on manifolds and varieties. At the same time, I am interested in the application of techniques from pure mathematics, especially algebraic geometry and topology, to the study and discovery of quantum condensed matter, which includes topological insulators and other novel materials. The interdisciplinary Centre for Quantum Topology and Its Applications (quanTA), of which I am Director, has been assembled for this purpose.
You can read more about my work and teaching on my home page.