Simone Noja

In this talk I will introduce a (super-)mathematical perspective on the pure spinor superfield formalism, showing how to recover supersymmetry multiplets from geometric data related to the nilpotence variety of a certain Poincaré superalgebra. After discussing some lower dimensional examples, I will focus on the case of supersymmetry in six dimensions, where the nilpotence variety is a Segre manifold, and I will hint at a generalization of the formalism in the direction of derived algebraic geometry. If time permits, I will discuss how nilpotence varieties of some classical Lie superalgebras are related to the superconformal field theories.