[Working title] Derived and spherical $\delta$-rings

In my PhD, I study animated and derived $\delta$ and $\lambda$-structures as well as an analogue for $\mathbb{E}_\infty$-rings based on the Tate-Frobenius. This includes comparing different approaches to defining (nonconnective) derived algebraic structures as well as extending the current understanding of spherical Witt vectors. Further, I work on formalizing certain properties enjoyed by the categories of derived (delta/lambda)-rings which should lead to a theory of non-additive stable infty-categories and non-additive stabilization. My research projects are joint with Thomas Nikolaus, Benjamin Antieau, Dmitry Kubrak and Joost Nuiten.