I spent five years as a visiting assistant professor at Bucknell University. I previously held a postdoctoral position at Louisiana State University where I studied the mathematics of quantum information theory with Mark Wilde and the rest of the Quantum Science and Technology Group. I am interested in how ideas from functional analysis can be applied to problems in quantum information. I am also interested in operator algebras and how ideas from harmonic analysis on groups can be extended to locally compact quantum groups.
Before coming to Baton Rouge, I was a postdoc in the Mathematics Department of Universidad Complutense de Madrid, working with the Mathematics and Quantum Information research group lead by David Perez Garcia.
I received my Ph.D. in Mathematics from the University of Illinois at Urbana-Champaign. My thesis advisor was Professor Zhong-Jin Ruan and my thesis title was "Noncommutative Lp-spaces Associated with Locally Compact Quantum Groups". This involved studying the interaction between the quantum group and the structure of the noncommutative Lp-space constructed using the Haar weight.
You can see my Google Scholar profile at this link.
Locally compact quantum groups,
Noncommutative Lp spaces,
Quantum information theory,
Quantum game theory,
Quantum many-body systems.
Operational Meaning of Quantum Measures of Recovery (with Christoph Hirche, Ciara Morgan, Jonathan P. Olson, Kaushik P. Seshadreesan, Jon Watrous, and Mark M. Wilde, Physical Review A 94 (2), 022310)
Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication (with Milán Mosonyi, and Mark M. Wilde, Communications in Mathematical Physics 344 (3), 797-829)
Rank-One Quantum Games (with Marius Junge, Carlos Palazuelos Cabezon, and David Perez Garcia) (computational complexity, 24 (1), 133-196)
Joint system quantum descriptions arising from local quantumness (with Marius Junge, Miguel Navascues, David Perez Garcia, and Ignacio Villanueva) (Communications in Mathematical Physics 322 (2), 501-513)
A physical approach to Tsirelson's problem (with Miguel Navascues, David Perez-Garcia, and Ignacio Villanueva) (Foundations of Physics 42 (8), 985-995)
A Hausdorff-Young inequality for locally compact quantum groups, Internat. J. Math., 21 (2010), no. 12, 1619–1632.
Noncommutative L_p spaces associated with locally compact quantum groups (Ph.D. thesis)
Available at: http://www.ideals.illinois.edu/handle/2142/16895