“Integrable structure of the SU(2) WZNW model "

The SU(2) Wess-Zumino-Novikov-Witten model is one of the best understood 2d conformal field theory. In this talk, I will discuss its integrable structure. In particular, I will give evidence for the existence of an infinite number of commuting higher-spin local charges built from the current algebra underlying this CFT. In the second half of the talk, I will discuss the diagonalisation of these commuting operators on the Hilbert space of the theory, formed by highest-weight representations of the current algebra. In particular, I will review a conjecture relating the spectrum of these operators to the properties of specific ODEs (within the so-called ODE/IM correspondence). This is based on 2601.20960 with Adrien Molines.