The goal of the proposed internship is to complete the classification of perturbative symmetry indicators for moiré systems – an ambitious task grounded in elegant mathematics with direct impact on material selection and discovery when combined with large-scale numerical screening of databases. The mathematical theory for the project relies on elementary band representations of periodic systems. Your role will be to develop the full mathematical framework to apply this theory systematically to any pair of stacked or twisted materials. Once this classification is complete, we will be able to perform inexpensive numerical calculations to identify which materials are best suited for realizing topological phases.