In this talk, I will describe some results (joint work with Alberto Castano Dominguez and Luis Narvaez Macarro) on Hodge ideals for a specific class of divisors with non-isolated singularities. Hodge ideals as defined by Mustata and Popa generalize multiplier ideals and are given by the Hodge filtration on the module of meromorphic functions along a divisor. However, they are usually hard to determine. For a certain class of free divisors (e.g. free hyperplane arranngements), one can rely on specific symmetry properties of the Bernstein-Sato polynomial of the divisor, and a basic property of Hodge modules, called strict specializability, to give a purely algebraic description of all Hodge ideals. I will explain this approach, and discuss some significant examples. Speaker(s): Christian Sevenheck (TU Chemnitz)