Structure and applications of real C*-algebras

For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C*-algebras. Over the last thirty years, that situation has changed, and it's become apparent that real C*-algebras have a lot of extra structure not evident from their complexifications. At the same time, interest in real C*-algebras has been driven by a number of compelling applications, for example in the classification of manifolds of positive scalar curvature, in representation theory, and in the study of orientifold string theories. We will discuss a number of interesting examples of these, and how the real Baum-Connes conjecture plays an important role.

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