I specialize in mathematical physics, in particular higher gauge theory. I have been using algebraic topology (mainly bundle theory and homotopy theory), differential geometry, higher category theory, harmonic analysis, spectral theory, and symplectic geometry in my research to answer questions in gauge theory, geometry, condensed matter, and information theory. I am also interested in the mathematical foundations of quantum theory, quantization itself, and quantum gravity including the information paradox.
- Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps, with Karen K. Y. Lee, Yehuda Avniel, and Steven G. Johnson, Phys. Rev. B 81, 155324 (2010); doi: 10.1103/PhysRevB.81.155324
Gauge invariant surface holonomy and monopoles
Theory and Applications of Categories, Vol. 30, 2015, No. 42, pp 1319-1428.
- Categorical entropy
- Path integrals for surface holonomy (with V. P. Nair)
- The diagonal representation for group coherent states with applications to quantum optics and entropy (with V. P. Nair)
- Condensed matter for mathematicians with an emphasis on topological phases of matter
- Covering 2-group 2-bundles with connection
- The quantum Hall effect and gravity
- Non-abelian 2-group Dijkgraaf-Witten theory