When an electric conductor is placed in an external magnetic field which is perpendicular to the current flowing through it, a voltage difference is generated. Hall made this observation a long time ago, at the end of 19th century, and since then this phenomenon has found many applications, from building sensors to spacecrafts.
Since its discovery, various interesting versions of the Hall effect have been found, even leading to a Nobel prize. In particular, application of Hall's ideas to two-dimensional electron systems at low temperatures and strong magnetic fields has led to the discovery of a quantised generated voltage, and the discovery of the integer and non-integer quantum Hall effect.
The subject of the Hall effect is huge and very diverse, and depending on your preferences the projects can be shaped in different directions, from theoretical (which will touch on the open questions in front line research) to very practical (with particular emphasis on the applications).
You should take the Electromagnetism III module, and Quantum Mechanics III would be very useful.
For a first reading look at: