Homotopy Groups of Spheres - Computation Methods and Recent Progress

Explore the complex world of homotopy groups of spheres in this 50-minute conference talk by Zhouli Xu at BIMSA. Delve into the challenging problem of determining these abelian groups formed by continuous maps between spheres up to continuous deformations. Discover how the structures of homotopy groups of spheres interconnect with various topological topics, including the Hopf invariant problem, the Kervaire invariant problem, and the number of smooth structures on a given sphere. Review classical computation methods for these groups and learn about recent advancements using motivic homotopy theory and other techniques. Gain insights from Xu's joint work with Bogdan Gheorghe, Dan Isaksen, and Guozhen Wang in this illuminating presentation on a fundamental concept in topology.