UL doesn't have many superstars, but Prof. James Gleeson is one of them. He's got a funded PhD scholarship available, details here.
Candidates should have (by Autumn 2012) a primary honours degree in Applied Mathematics, Mathematical Physics, or a related discipline. A good knowledge of applied probability and evidence of strong programming ability (in MATLAB or C++) are essential. The studentship includes University fees and an annual stipend of €18,000 for a period of four years.