• Quantum information theory
• Many-body physics
• Complexity theory
• Hamiltonian complexity
• Hamiltonian simulation
• CP maps (a.k.a. quantum channels)
• Entanglement theory
• Probability theory
• Algebraic geometry
• Learning any other interesting new maths I come across…

That'll do for now.

You can find a (possibly not-quite-up-to-date) list of my publications on this web site with links to the papers, as well as the slides from some of my talks. For a more up-to-date list, try the arXiv.