Mathematical Physics Seminar

The parallels between classical and quantum variables are quite
striking. This is particularly evident for such notions as classical and
quantum entropy, where the latter might seem like a naive generalization
of the former. The success of this correspondence can be understood if one
uses von Neumann's idea that mathematics itself can often be quantized.
The quantum versions of Banach spaces and their ordered versions are the
operator spaces and operator systems and these provide the natural
framework for quantum information theory and (presumably) statistical
mechanics. We will begin with a "trivial" matrix convexity proof of a
famous theorem of Lieb, and conclude with some open problems about
non-commutative Legendre transforms and differentials.