Algebraic Topology Seminar

Computation of the stable homotopy groups of spheres (stable stems) is a fundamental problem in topology. Despite their simple definition, which was available eighty years ago, these groups are notoriously hard to compute. All known methods only give a complete answer through a range, and then reach an obstacle until a new method is introduced.

In this talk, I will discuss a recent method that allows us to compute differentials in the Adams spectral sequence very effectively and therefore significantly extending our knowledge of stable stems. This method uses motivic homotopy theory over the complex numbers in an essential way. I will also discuss a generalization of this method over general base fields, and classical Adams differentials on the classes h_j^3.

This talk is based on several joint works with Tom Bachmann, Robert Burklund, Bogdan Gheorghe, Dan Isaksen, Hana Jia Kong and Guozhen Wang. Speaker(s): Zhouli Xu (University of California San Diego)