Olivetti Club

David Mehrle
Homotopy theory is hard so why bother?

Tuesday, April 23, 2019 - 4:30pm
Malott 406

One of the basic motivating questions of modern homotopy theory is the computation of the homotopy groups of spheres $\pi_k S^n$. One might expect that these homotopy groups are zero for $k > n$, as with the homology $H_k(S^n)$, but there are infinitely many nontrivial homotopy groups $\pi_k S^n$ with $k > n$. An example is given by the Hopf map $\eta \colon S^3 \to S^2$, representing an element of $\pi_3 S^2$. Computing these homotopy groups is hard, but we also know a lot more than you might think! In this talk I will survey what we know, how we know it, and what we have yet to learn. In the process, I’ll introduce some ideas central to modern homotopy theory and describe connections with geometry and algebra.

Refreshments will be served in the lounge at 4:00 PM.