Probabilistic Combinatorics

这项工作将集中在概率组合学的各种问题。会有一个大问题和几个不太重要的问题，最初由主管提出。德沃夏克的大问题将是所谓的孤独跑步者猜想，这是50多年前提出的臭名昭著的猜想，在丢番图近似、障碍问题和图论中有应用。到目前为止，这个猜想几乎没有取得什么进展，尽管有一位数学家在研究它，而不是特里·陶。

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.