Supersymmetry in curved space

The project aims to explore supersymmetric field theories in curved space and some of their applications. An initial part of the project to compute generalised Spencer cohomology in order to determine Killing spinor equations whose solutions generate a Lie superalgebra. One then determines the geometries admitting such Killing spinors and for each such geometry the corresponding supersymmetry algebra. Studying the unitary representation theory of these supersymmetry algebras one determines the natural supermultiplets in each geometry and one can then construct supersymmetric field theories. These can then be applied to supersymmetric localisation of quantum field theories.