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Moduli spaces of hyperbolic surfaces with geodesic boundary components offixed lengths may be endowed with a symplectic structure via the Weil-Peterssonform. We show that, as the boundary lengths are sent to infinity, theWeil-Petersson form converges to a piecewise linear form first defined byKontsevich. The proof rests on the observation that a hyperbolic surface withlarge boundary lengths resembles a graph after appropriately scaling thehyperbolic metric. We also include some applications to intersection theory onmoduli spaces of curves.

The asymptotic Weil-Petersson form and intersection theory on M_{g,n}