  We show that the multi-commodity max-flow/min-cut gap for series-parallel
graphs can be as bad as 2, matching a recent upper bound Chakrabarti, Jaffe,
Lee, and Vincent for this class, and resolving one side of a conjecture of
Gupta, Newman, Rabinovich, and Sinclair.
  This also improves the largest known gap for planar graphs from 3/2 to 2,
yielding the first lower bound that doesn't follow from elementary
calculations. Our approach uses the {\em coarse differentiation} method of
Eskin, Fisher, and Whyte in order to lower bound the distortion for embedding a
particular family of shortest-path metrics into $L_1$.
