Bar Natan, Duchin and Kropholler introduced conjugation curvature as a discrete Ricci
curvature for Cayley graphs of finitely generated groups. In joint work with Alden
Walker, we show that the solvable Baumslag-Solitar groups BS(1,n) have sets of
elements of positive, negative and zero conjugation curvature, and that these sets have
positive density in the group. To prove this, we use a lattice-based approach to produce
a geodesic representative for every element of the group, from which we derive a
word-length formula, all with respect to the standard generating set for BS(1,n). A
subset of these geodesic representatives forms a regular language, and in subsequent
work we use this language to give a new proof of the growth rate of BS(1,n).