### What's behind the background?

It's a picture I generated as part of a project with Alessandra Iozzi investigating algebraic compactifications of $SL(2,\RR)$. The small regions are fundamental domains for the action of the symmetric group $S_5$ on (a subset of) $\RR^2$, and the colored numbers tell which permutations move which sides where. The quotient space is the moduli space of algebraic compactifications of $SL(2,\RR)$ which lie in the five-dimensional torus $T^5$.

Here is a clearer image:

A couple of the papers on my [p]reprints page are related to this project -- the ones with "boundary compactifications" in the title.