Explore the fascinating world of integrable sigma models at renormalization group fixed points in this hour-long lecture by J. Teschner from DESY. Delve into the quantization of these models as affine Gaudin models, gaining insights into the intersection of integrability, condensed matter physics, and quantum field theory. Uncover the mathematical structures and physical principles underlying these complex systems, and discover how they contribute to our understanding of fundamental phenomena in theoretical physics.