Structure in the moduli space of vacua of low dimensional supersymmetric quantum

This Project involves the investigation of the moduli space of vacua of supersymmetric
quantum eld theories. The sets of zero-energy congurations, or moduli space of vacua, of a quantum
eld theory contains rich algebro-geometric structure. For a large set of supersymmetric quantum
eld theories this structure is related to nilpotent varieties in Lie algebras. These nilpotent varieties
are well understood for the classical Lie algebras in the mathematical literature and investigation of
the interpretation of this and related structures in a physical context is the main aim of this project.
The supersymmetric quantum eld theories also have an interpretation as the low energy dynamics of
superstring theory embeddings. The interplay between these embeddings, the quantum eld theories,
the geometry of the moduli spaces of vacua, and potential generalizations of all therein, is the central
area of concern.