Many of the most enigmatic materials where strong interactions between the electrons are crucial for a qualitative understanding of the material properties are two dimensional. Some examples are the copper-oxygen and iron-based superconductors, where the relevant physics takes place in two-dimensional atomic planes embedded in a three-dimensional crystal structure. Another example are the so-called moiré materials, which are intrinsically two-dimensional. Despite the many experimental examples of strongly interacting two-dimensional electron materials, a systematic theoretical understanding of these systems is still lacking. Given the intrinsic complexity of these material further progress will most likely have to come from numerical simulations. In this project I will therefore develop new simulation techniques and apply these to models of high-temperature superconductors and moiré materials.