Anderson operator H on a closed Riemannian surface is the random perturbation of the Laplace operator by a space white noise random potential - a distribution of regularity <-1. The low regularity of the potential makes the construction of the operator as an unbounded operator on L2 a non-trivial task, that can nonetheless be tackled with the help of the tools developed a few years ago for the study of the so-called singular stochastic PDEs - M. Hairer was awarded the Fields medal in 2014 for his foundational contributions to this domain. The operator H can then be defined as a closed self-adjoint unbounded operator on L2 with discrete real spectrum bounded below. This interesting operator has a rich behaviour, related to a number of other objects like the polymer measure. We will see how to define its zeta determinant. It will turns out to satisfy a Polyakov-type anomaly formula.