I work mostly in quantum information, in particular quantum fault-tolerance and quantum complexity theory.  I enjoy problems involving the interplay between combinatorial and geometric ideas.

Recent work of mine includes the construction of a class of quantum codes that have optimal asymptotic properties in terms of information storage density and error correction capabilities (joint work with J. Eberhardt), the proof of the NLTS conjecture (joint work with A. Anshu and C. Nirkhe), which demonstrates robustness of quantum mechanical entanglement, and the discovery of a new phase of matter called "topological quantum spin glass" (joint work with B. Placke, T. Rakovszky and V. Khemani).