turkmath.org

Given a sequence $\{G_n\}$ of groups and vector spaces $\{V_n\}$ where each $G_n$ acts on $V_n$, representation stability studies the eventual/uniform behavior of $V_n$ as a $G_n$-representation, as $n$ varies.

One of the most robust and applicable variants is when $G_n$ is the symmetric group on $n$ letters, categorified by the framework of FI-modules. In addition to giving an overview of FI-modules and consequences of their finite generation, I will discuss applications to the cohomology of configuration spaces, where several stabilization results can be obtained even when explicit computations are lacking.