Abstract: 

Motivic homotopy theory is an application of abstract notions of homotopy in the world of algebraic varieties.  It turns out that motivic homotopy theory gives us powerful tools in understanding classical homotopy theory.  In this talk, we will show how structures in the motivic stable homotopy categories can be used to compute both classical and motivic stable homotopy groups.

About the Speaker:

 Guozhen Wang is a chair professor at the Shanghai Center for Mathematical Sciences, Fudan University.  He has made groundbreaking progresses in the computation of stable homotopy groups, motivic homotopy theory, and topological cyclic homology.  In joint work with collaborators, he solved the uniqueness problem of smooth structures on the 61-dimensional sphere; calculated the first 90 stable homotopy groups of the sphere spectrum; established the Chow t-structure theory for stable motivic homotopy categories; and introduced the descending spectral sequence methods in the computation of topological cyclic homology.  He was an invited speaker at the International Congress of Mathematicians in 2022.