I will give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a Riemann-Hilbert problem for a finite set of functions. I review the underlying QQ-relations starting from simple spin chain examples, and describe the special features arising for AdS/CFT. I will also present some pedagogical examples to show the framework in action. Lastly I will briefly discuss its recent applications for correlation functions. Based on the review arXiv:1911.13065. NOTE: online seminar using Zoom. Please register to the mailing list on integrability-london.weebly.com to participate.

The Quantum Spectral Curve (QSC) is a powerful integrability-based framework capturing the exact spectrum of planar N=4 SYM. We present first evidence that it should also play an important role for computing exact correlation functions. We compute the correlator of 3 scalar local operators connected by Wilson lines forming a triangle in the ladders limit, and show that it massively simplifies when written in terms of the QSC. The final all-loop result takes a very compact form, suggesting its interpretation via Sklyanin's separation of variables (SoV). We discuss work in progress on extending these results to local operators. We also derive, for the first time, the SoV scalar product measure for gl(N) compact and noncompact spin chains. Based on arXiv:1910.13442, 1907.03788, 1802.0423.