Abstract

The computation of stable homotopy groups of spheres is one of the most fundamental problems in topology. Despite its simple definition, it is notoriously hard to compute. It has connections to problems in many areas of mathematics, such as the problem of smooth structures on spheres. In this talk, I will discuss a recent breakthrough on this computation, which depends on motivic homotopy theory in a critical way. This talk is based on several joint works with Bogdan Gheorghe, Dan Isaksen, and Guozhen Wang.

About the speaker

Zhouli Xu is an Assistant Professor at the University of California, San Diego. He works in algebraic topology and focuses on classical, motivic and equivariant homotopy groups of spheres, with connections and applications to chromatic homotopy theory and geometric topology. His research accomplishments include his joint works with collaborators in proving that the 61-dimensional sphere has a unique smooth structure, proving a 10/8 + 4 theorem on the geography problem in 4-dimensional topology, developing the motivic deformation method and the Chow t-structure, and computing the classical and motivic stable homotopy groups of spheres in the previously unknown range of dimensions. Dr. Xu received his Ph.D. in Mathematics from the University of Chicago, and was a C.L.E. Moore Instructor at MIT. During his time at the University of Chicago, he received a Plotnick Fellowship and the Harper Dissertation Fellowship. He is an invited speaker at ICM 2022, St. Petersburg.