Abstract: The celebrated Simpson’s tame nonabelian Hodge correspondence shows that the correct topological objects from the Betti side are the so-called filtered local systems, which are local systems with filtrations assigned to boundary divisors. However, such nonabelian Hodge correspondence was only known at the level of categories until recently, due to the lack of a construction of the moduli spaces of filtered local systems. In this talk, we will introduce filtered local systems and demonstrate a purely algebro-geometric construction of their moduli spaces. This method is applicable to general reductive groups. Based on joint work with Hao Sun.