We construct a derived generalization of the pure spinor superfield formalism and prove that
it exhibits an equivalence of dg-categories between multiplets for a supertranslation algebra …

We introduce the class of principal symmetric ideals, which are ideals generated by the orbit
of a single polynomial under the action of the symmetric group. Fixing the degree of the …

Under reasonable assumptions, a group action on a module extends to the minimal free
resolutions of the module. Explicit descriptions of these actions can lead to a better …

This thesis discusses the pure spinor superfield formalism and its applications, specifically in
the context of twisted eleven-dimensional supergravity. We start by developing the pure …

We introduce the package HighestWeights for Macaulay2. This package provides tools to
study the representation-theoretic structure of free resolutions and graded modules over a …

Finite group actions on free resolutions and modules arise naturally in many interesting
examples. Understanding these actions amounts to describing the terms of a free resolution …