Sigma Models as Gaudin Models

I will explain how the duality between the sigma model of the complete flag manifold $U(3)/U(1)^3$ and the three-node Gaudin model allows to explicitly solve the classical and quantum problems for the sigma model, i.e., to find geodesics and calculate the spectrum of the Laplace operator on a flag manifold with an arbitrary invariant metric. Based on arXiv:2404.15900 and arXiv:2508.20889.