Beijing-Moscow Mathematics Colloquium (online)
Abstract
We will discuss the current state of knowledge of stable homotopy groups of spheres. We describe a computational method using motivic homotopy theory, viewed as a deformation of classical homotopy theory. This yields a streamlined computation of the first 61 stable homotopy groups and gives information about the stable homotopy groups in dimensions 62 through 90. As an application, we determine the groups of homotopy spheres that classify smooth structures on spheres through dimension 90, except for dimension 4. The method relies more heavily on machine computations than previous methods and is therefore less prone to error. The main mathematical tool is the Adams spectral sequence.
Bio
Guozhen Wang received PhD degree from MIT in 2015. From 2016, he is working at Shanghai Center for Mathematical Sciences, Fudan University. His research field is algebraic topology, including stable and unstable homotopy groups, applications of computers in homotopy theory, motivic homotopy theory and topological cyclic homology.
