Probabilistic Combinatorics

这项工作将集中于概率组合学中的各种问题。将会有一个大问题和几个监管者最初提出的不那么严重的问题。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，它在丢番图近似、障碍问题和图论中都有应用。到目前为止，这一猜想几乎没有取得什么进展，尽管有一位数学家正在研究它，就像陶渊明一样。

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.