Member; School of Mathematics
November 12, 2018
Computation of the stable homotopy groups of spheres is a long-standing open problem in algebraic topology. I will describe how chromatic homotopy theory uses localization of categories, analogous to localization for rings and modules, to split this problem into easier pieces, called chromatic levels. Each chromatic level can be understood using the theory of deformations of formal group laws. I will talk about recent results, and work in progress, at the second chromatic level. In particular, I will describe how we use representation theory to identify invertible objects at the second chromatic level. No knowledge of homotopy theory will be assumed! This talk is based on joint work with A. Beaudry, M. Hill and V. Stojanoska.