The v_1-periodic part of the stable stems is connected to topological K-theory, the J-homomorphism, and the Mahowald invariant. In this talk, I will review these ideas and discuss their generalizations in motivic homotopy theory, or the homotopy theory of schemes. I will summarize a computation (joint with Dominic Culver) of the v_1-periodic part of the motivic stable stems over the complex numbers using a motivic analog of the bo-resolution. I’ll then describe the construction of some v_1-periodic families over general base fields using the motivic Mahowald invariant following Mahowald-Ravenel (joint with Jonas Irgens Kylling). Time permitting, I will discuss what these motivic Mahowald invariant calculations predict about v_1-periodicity in the motivic stable stems over general base fields.

There will be a pretalk 3:30 to 4:30 in Hylan 1106A as well.