Abstract: Persistent equivariant cohomology measures not only the shape of the filtration, but also attributes of a group action on the filtration, including in particular its fixed points. We give an explicit description of the persistent equivariant cohomology of the circle action on the Vietoris-Rips metric thickenings of the circle. Our computation relies on the Serre spectral sequence and the Gysin homomorphism. Joint with Evgeniya Lagoda, Michael Moy, Nikola Sadovek, and Aditya De Saha, available at https://arxiv.org/abs/2408.17331.