Current Projects
Current Projects
Equivariant Steenrod Operations
joint with Prasit Bhattacharya, Mingcong Zeng, Foling Zou
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.
Equivariant Dyer-Lashof Operations
joint with Prasit Bhattacharya
In this paper we develop a general framework for defining equivariant power operations for all finite groups. Using this framework, we study how these operations interact with HHR norms, additive transfers, restriction maps, and geometric fixed points. When restricted to operations which act on the mod p Bredon homology of "nice" spaces, we also develop Cartan formulas and Adem relations by studying the homology of certain equivariant classifying spaces. This framework extends previous work with Bhattacharya-W-Zeng-Zou for Steenrod operations.
Homology of Equivariant Iterated Loop Spaces
In this paper, we utilize the framework of equivariant Dyer-Lashof operations of Bhattacharya-W to study the homology of free algebras over the terminal N_infty G-operad. This generalizes the nonequivariant computation of J.P. May completed in the 70s. We then explore equivariant generalizations of the nonequivariant computation.
Real K-Theory of Equivariant Classifying Spaces
joint with Jackson Morris, Manyi Guo, Albert Yang
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.