Homotopy Groups of Spheres
Explore the intricate world of homotopy groups of spheres in this mathematics colloquium talk by Zhouli Xu from the University of California, San Diego. Delve into the complex problem of determining these abelian groups formed by based continuous maps between spheres, up to continuous deformations. Discover how the structures of homotopy groups of spheres are intricately connected to various important topics in topology, including the Hopf invariant problem, the Kervaire invariant problem, and the number of smooth structures on a given sphere. Gain insights into this challenging area of topology and its far-reaching implications in mathematical research during this 56-minute presentation at Stony Brook University's Mathematics Department Colloquium.