J. D. Quigley (University of Notre Dame) The Mahowald invariant in motivic, equivariant, and classical stable homotopy theory

The Mahowald invariant is a method for constructing nontrivial classes in the stable homotopy groups of spheres from lower dimensional classes. I will introduce this construction and recall Mahowald and Ravenel's computation of the Mahowald invariant of 2^i for all i . I'll then introduce motivic and equivariant analogs of the Mahowald invariant, outline the computation of the generalized Mahowald invariants of 2^i and \eta^i for all i , and discuss the relationship between these generalized computations and exotic periodicity in the equivariant and motivic stable homotopy groups of spheres.