The lectures will start with a pretalk at 11 am, followed by a research talk, with a brief break in-between.

Abstract (pretalk): We will discuss how the results to follow can be contextualized by way of the so-called pure spinor superfield formalism—a universal construction for producing off-shell supermultiplets. After recalling the construction, we will illustrate that a way of interpreting the construction is by replacing spacetime with a certain dg ringed space built from the datum of a superconformal structure.

Abstract (research talk): Let M be a smooth supermanifold and n be a supertranslation algebra. Given this data, Manin defined a superconformal structure of type n on M as an odd maximal dimensional distribution on M whose symbol is isomorphic to n at every point. In this talk, we will illustrate how symmetries and deformations of such structures unify and generalize constructions in Lie theory and supersymmetric physics. We associate a sheaf of dg Lie algebras to a superconformal structure; in physical examples, H^0 returns the global superconformal algebras classified by Nahm and Kac-van de Leur whilst H^1 reproduces conformal supergravity multiplets studied in the physics literature. This talk is based on joint work with Fabian Hahner, Ingmar Saberi, and Brian Williams.