Conformal partial wave expansion provide Fourier-like decompositions of correlation functions in Conformal Field Theory. Despite their fundamental importance, conformal partial waves remain poorly understood, at least beyond the case of four local fields. In the last few years, a deep relation with integrable quantum mechanical models has emerged. It offers a wealth of powerful new algebraic methods to study and construct conformal partial waves e.g. for general supermultiplets, non-local (line-, surface-) operators and multi-point correlation functions. In my talk I will use ideas from harmonic analysis of the conformal group to embed conformal partial waves into the framework of Gaudin integrable models and then discuss several concrete ramifications as trigonometric and elliptic Calogero-Sutherland models. The latter are relevant for multi-point blocks of scalar fields. ----- Part of London Integrability Journal Club. Please register at integrability-london.weebly.com/registration.html if you are a new participant.

t.b.a. ------- Part of the London Integrability Journal Club. If you are not already registered, please sign up at integrability-london.weebly.com/registration.html. The link will be emailed.

The high energy behavior of physical scattering amplitudes challenged early string theory. With the discovery of gauge-string dualities the obstacle was overcome and today string theory provides precision results, in particular for the high energy limit. In my talk I will review the many facets of integrability in high energy scattering at weak, intermediate and strong coupling.

The solution of 2D Sigma models on superspaces (-groups,-cosets, etc.) is a problem with various potential applications in condensed matter theory and string theory, in particular in the context of the AdS/CFT correspondence. At the example of the PSU(1,1/ 2) sigma model, I shall illustrate some of the intriguing novel features of such theories, review a few recent results and assess the prospects for a complete or partial solution.