Below there is a non-exhaustive list of student projects I am offering:
Mathematical aspects of Quantum Machine Learning (Mathematical Physics)
Symmetries in neural networks and statistical learning (Data Science/Pure Mathematics/Mathematical Physics)
Projected entangled pairs states (PEPS) and topological quantum field theories (Pure Mathematics/Mathematical Physics)
Effective field theories for topological quantum spin systems (Mathematical Physics)
Quantum group invariant entanglement measures (Pure Mathematics/Mathematical Physics)
A numerical approach to topological invariants of quantum lattice systems (Applied Mathematics/Mathematical Physics)
A more detailed description of some of these can be found on MS Prime.