Ingmar Saberi

Nilpotence varieties

I'll discuss a class of geometric spaces, termed nilpotence varieties, that have deep connections to many phenomena in supersymmetric quantum field theories, in particular to twisting and to the construction of supermultiplets. Examples of these spaces have been present in the literature for many years, in the context of the pure spinor formalism, but the connection to twisting and the relationship of that procedure to the construction of supermultiplets was only remarked on recently. I'll sketch a large-scale overview of this connection, give some remarks on how nilpotence varieties appear naturally in the study of the representation theory and the cohomology of supersymmetry algebras, and (depending on time) discuss a few points of outlook for future work. In recognition of the fact that many of the ingredients of this big picture may be new to some in the audience, I'll do my best to keep things as down-to-earth as I possibly can, to give a self-contained set of definitions, and to illustrate those definitions with examples. The hope will be to convey how the geometry of nilpotence varieties provides a unifying perspective on many seemingly isolated constructions in the recent literature.