I work in quantum computer science, more precisely on the mathematical foundations of physics, especially quantum mechanics, and its logical aspects. My weapons of choice are category theory, functional analysis, and order theory; specifically, monoidal categories, operator algebras, and orthomodular lattices. I suppose you could say that my ultimate goal is to really understand the category of Hilbert spaces, in particular categorical aspects of a choice of basis.
For a very gentle introduction to the ideas behind my work, see "The state of quantum computer science".
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