Current Projects

We develop a general framework for defining Steenrod operations associated to any equivariant cohomology theory represented by a structured genuine G ring spectrum. As an application, we construct two infinite families of nonzero operations for all finite groups. 

In this paper we develop a general framework for defining equivariant power operations. We show how such operations interact with additive transfers, multiplicative norms, and relate these to the equivariant Steenrod operations we previously constructed. As an application, we examine the homology of equivariant iterated loop spaces. 

In this paper we compute the Atiyah Real K-theory of the classifying space for C2 equivariant principal Sigma2 bundles. We then use this to produce stable Adams operations and explore applications to equivariant geometry.