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I will talk about our recent paper, arXiv:1801.10605, focusing on the multi-Regge limit of the 7-gluon amplitude in planar N = 4 super Yang-Mills theory. In particular, I will discuss how to describe the latter in terms of a BFKL-type integral that is well-defined to arbitrary logarithmic accuracy, and how to determine the new building block of this integral, known as the central emission vertex, to next-to-leading order. The explicit evaluation of the integral up to 5 loops will also be reported.