Using Currents to Represent Steenrod Powers

This lecture explores how currents can be used to represent Steenrod powers in algebraic topology. Learn about the mod p cohomology ring of spaces and the additional module structure created by cohomology operations P¹, P², and beyond. Discover how these Steenrod powers help classify spaces and serve as the foundation for computing stable homotopy groups using the Adams spectral sequence. The presentation introduces the first geometric construction of maps between spaces of currents on spheres that encapsulate Steenrod power actions on cohomology rings, with potential applications in quantitative topology.