October 29, 2024

**Title:** *Perfection in Homotopical Algebra (MI talk)*

**Speaker:** Vignesh Subramanian

In this talk, I will introduce an analogue of the Frobenius homomorphism for commutative algebra in characteristic p within the context of homotopical algebra and an appropriate notion of perfection. I will discuss how this construction can be utilized to study the homotopy theory of spaces localized at a single prime. As an application, I will demonstrate how this framework can be used to study fixed points of group actions.