You can apply for this position if you want to start doctoral studies in Algebra, Group Theory, Geometry, Topology, Number Theory, or any combination of them. You can either suggest your own project, or work on the following topic.
Homology of small index subgroups in the Bianchi groups
The Bianchi groups are groups of special linear 2x2-matrices with a nice geometric action on hyperbolic space.
This beautiful action can be used to find out a lot about the group structure.
Also, the Bianchi groups admit a huge collection of small index subgroups, for which this has not yet been done.
One possibility for a doctoral student to arrive very quickly at the level of current research, is computation of invariants of these subgroups, e.g. their homology.
More on this topic can be found on the website
The PhD grant is a Hardiman Research Scholarship, and this requires preparing the application well before the deadline of November 18: