The Mathematics of Non-Locality and Contextuality

There is a rich mathematical structure underlying work on non-locality and contextuality in quantum foundations. The study of non-locality and contextuality can be expressed in a unified and generalised form in the language of sheaves or bundles, in terms of obstructions to global sections. These obstructions can, in many cases, be witnessed by cohomology invariants. Cohomology is one of the major tools of modern mathematics, which until now has been conspicuously absent from both theoretical computer science, and quantum information. We are now beginning to understand how this tool can be brought to bear on some key issues in quantum information and foundations, and also on a number of topics in logic and classical computation which can be seen to have the same structure.