Department of Mathematics - Master Calendar

Abstract: One key goal of homotopy theory is to understand the stable homotopy groups of spheres. This problem naturally arises as a question about what homotopy theorists call spectra. Spectra are a fundamental concept in homotopy theory, analogous in many ways to abelian groups. This analogy allows classical algebra to extend into what Friedhelm Waldhausen termed "Higher Algebra," where spectra play the role of abelian groups. In this talk, we will discuss how this perspective suggests an approach to detecting patterns in stable homotopy groups of spheres, and how recent joint results with Burklund, Carmeli, Hahn, Levy, and Yanovski provide new asymptotic lower bounds on their size.