I will recall basic notions of operator K-theory as a non-commutative (C*-algebra) generalisation of topological K-theory. Twisted crossed products will be introduced as generalisations of group C*-algebras, and a model of Karoubi's K-theory, which makes sense for super-algebras, will be sketched. The motivation comes from physics, through the study of quantum mechanical symmetries, charged free quantum fields, and topological insulators. The relevant theorems, which are interesting in their own right but scattered in the literature, will be consolidated.

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We are looking for a better understanding of how a lithium wall can improve energy confinement in a tokamak plasma. Improved energy confinement can make a big difference to the minimum size of tokamak that could produce a fusion power gain.

"We consider certain distinguished extensions of the field F_p((t)) of formal Laurent series over F_p, and look at questions about their model theory and Galois theory, with a particular focus on decidability."