Tight-binding Hamiltonians are simple yet versatile models of quantum matter. On complex geometries such as fractals or quasiperiodic lattices, they show rich physics: fractals challenge the usual bulk-boundary picture of topological phases, while quasiperiodic models host unconventional localization. Tensor networks, well established for quantum many-body systems, can also represent tight-binding Hamiltonians. Combined with kernel polynomial methods, they give spectral functions at a cost logarithmic in system size, reaching billions of sites. We recently extended this approach to a broad class of hierarchical lattices, including fractal and quasiperiodic ones. This internship will extend these methods to more complex models, along one of two directions depending on the student's interests: 1) Topological states on fractal lattices: implementing topological models, including magnetic-flux operators, and studying localization and edge properties on different fractals. 2) Quasiperiodic models in one and two dimensions: generalizing the Fibonacci-chain approach to two-dimensional substitution tilings to study their unconventional localization, and exploring categorical symmetries to represent the substitution rules. Both directions combine physical and methodological aspects.