### 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.