My research interests lie in algebraic and computational aspects of quantum field theories.
Mostly I work in applications of category theory to quantum information science, the former being an algebraic setting of 2+1 dimensional topological quantum field theories. In particular I study fusion categories that model particle-like objects that arise in 2+1 dimensional topological phases of matter and their application for topological quantum information processing.
In summer 2017 I was an intern in the computational physics lab at HRL Laboratories, where I worked on mathematical aspects of quantum computing with semiconductor quantum dots.
- Symmetry defects and their applications to topological quantum computing. C. Delaney, Zhenghan Wang. (In preparation.)
- Local unitary representations of the braid group and their application to quantum computing. C. Delaney, Eric C. Rowell, Zhenghan Wang. arXiv:1604.06429
- Dyson-Schwinger equations and the theory of computation. C. Delaney, Matilde Marcolli."Feynman Amplitudes, Periods and Motives", Clay Math Institute and AMS.arXiv:1302.5040
- Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees. Susama Agarwala, C. Delaney. Journal of Mathematical Physics, Volume 56, Issue 4, April 2015. arXiv:1302.4004