I'm interested in the construction and analysis of supersymmetric field theories and their twists. Here, my method of choice is the pure spinor superfield formalism (https://arxiv.org/abs/2111.01162) which systematizes previous approaches from the physics literature using homological algebra and algebraic geometry. We used a 'derived' enhancement of the formalism to prove that there is an equivalence of categories between supermultiplets and a certain category of modules (https://arxiv.org/abs/2205.14133). These results can be applied in various directions: for example we classify a certain class of multiplets using simple well known things from geometry such as line bundles on projective spaces (https://arxiv.org/abs/2206.08388). In the future, I hope to say something more about twisted supergravity, holography and superconformal aspects. As a first step in this endeavour, we computed the maximal twist of eleven-dimensional supergravity (https://arxiv.org/abs/2106.15640).