I'm a mathematical physicist. In the past, I've worked on applications of algebra and geometry in mathematical physics, especially classical and quantum general relativity, topological quantum field theory, and related models. I recently shifted focus: I'm now working mainly on artificial intelligence and quantum computation. I'm finding this an exciting shift, not only because I'm learning more mathematics and computational techniques, but also because I see a lot of potential for crossover with my previous work.

I'm currently on faculty at Concordia University St. Paul. Previously, I was an NSF VIGRE Postdoc at U.C. Davis (2007-2010), then a postdoc at the University of Erlangen, where I held positions in both the Department of Mathematics and the Institute for Quantum Gravity.

My Research

My current research focus is on mathematical areas of computation. But I've done a wide variety of work in the mathematical sciences. Some of the topics I've worked on include:

• Hopf algebra gauge theory and its relation to Kitaev models in condensed matter physics and quantum computation.
• Cartan geometry and its applications, especially in general relativity and related theories.
• Group theory and generalization: Lie groups, quandles, groupoids, supergroups, Hopf algebras (or quantum groups), and 2-groups (or categorical groups).
• Gauge theory in topology, physics, and geometry.
• Experimental high-energy particle physics.
• Research in industry on gamma spectroscopy methods, and on radiation effects on electronics.
• Research with students: My students have worked on music theory, random walks on groups, geometry, lattice gauge theory, quandles, Cartan geometry and spin networks.

My profiles on: google+, inspire, arXiv, google scholar, mathematics genealogy project, researchgate, LinkedIn, Udacity.

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