Integrability in planar N=4 SYM has led to the development of the cutting-edge Quantum Spectral Curve (QSC), a Riemann-Hilbert problem for a handful of Q-functions which encode the spectrum of conformal dimensions. With the QSC the planar N=4 SYM spectral problem is solved - anyone with a laptop can compute the dimension of any operator at any coupling. In a handful of examples, structure constants have also been
shown to simplify enormously when expressed in terms of the QSC Q-functions, but no systematic derivation is available even at tree level.
Using recent advancements in the Separation of Variables program for high-rank integrable systems I will explain how to systematically obtain
the Q-function representation for tree-level structure constants in the SU(4) sector. Based on upcoming work with T. Bargheer, C. Bercini, and G. Lefundes.