Probabilistic Combinatorics

The work will focus on various problems in Probabilistic Combinatorics. There will be one big problem and several much less weighty problems initially suggested by the supervisor. Dvorak's big problem will be the so-called Lonely Runner Conjecture, the notorious conjecture made over fifty years ago, with applications in diophantine approximation, obstruction problems and graph theory. So far, rather little progress has been made with this conjecture, in spite of no less a mathematician working on it than Terry Tao.