3:00–4:00 pm Eckhart 206
Title: Stable Homotopy and Higher Algebra
Abstract:
A fundamental problem in homotopy theory is to understand the higher homotopy groups of spheres, \(\pi_n(S^k)\). Freudenthal showed that for large \(k\), these groups depend only on the difference \(n-k\). The corresponding group for \(m=n-k\), denoted \(\pi^S_m\), is finite for \(m>0\), and the sequence of finite abelian groups \(\pi^S_m\) exhibits fascinating patterns. We shall survey how an “\(\infty\)-categorical” form of algebra, called higher algebra, places these patterns into an algebraic framework, and how these ideas allow us to give asymptotic bounds on the sizes of \(\pi^S_m\).