Title: The motivic Mahowald invariant
Speaker: James Quigley (University of Notre Dame)
Abstract: The classical Mahowald invariant is a construction which produces nonzero classes in the stable homotopy groups of spheres from classes in lower stems. Mahowald and Ravenel showed that the Mahowald invariant of 2^i is the first nonzero class in the positive degree stable stems in Adams filtration i, supporting the conjecture that the Mahowald invariant increases chromatic height. In this talk, I will define an analog of the Mahowald invariant in the setting of motivic stable homotopy theory over the complex numbers. I will discuss two motivic analogs of Mahowald and Ravenel's classical computation and explain how these results relate to classical and exotic periodicity in the motivic stable stems.