Moduli spaces of algebraic curves of fixed genus and n marked points satisfy representation stability as n grows, meaning in particular that every Betti number grows polynomially in n. However the Euler characteristics grow superexponentially in n, so there must be LOTS of unstable cohomology. I’ll explain how tropical geometry gives access to part of the unstable cohomology, and relates it to configurations on graphs. With this, there is hope to recover a form of representation stability beyond the stable range. I will discuss the challenges and machinery that needs to be developed in order to interpret stability in genus > 2. Speaker(s): Nir Gadish (University of Michigan)