Motivated by the BDS conjecture, we look at 1/N corrections to gluon amplitudes in N=4 SYM.Infrared divergences are analyzed in two formalisms, of Catani and of Sterman/Tejeda-Yeomans. I willanalyze the 1/N expansion of the IR divergences, and find some systematics, at 3-loops, and iterated to any number of loops. Then we observe that up to 2-loop we have an exact relation to graviton scattering in N=8 supergravity, with a simple interpretation in a 't Hooft-like picture, but the higher loop extrapolation is problematic. Finally, I discuss the transcendentality of amplitudes and Catani IR divergent operators

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