In finite dimensions, an *operator system* is a
linear subspace of the n x n complex matrices which
contains the identity matrix and is stable under Hermitian
transpose. Recently these objects have come to be
understood as a "quantum" analog of finite simple graphs.
This point of view arose in quantum error correction and
has a good theoretical basis. I will discuss some of the many
interesting and basic questions which come out of this idea,
including a quantum Ramsey theorem, a quantum Turan
problem, and the notion of quantum chromatic number.
The last of these can be seen as a kind of paving problem.
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