Lonely Runners in Function Fields

The Lonely Runner Conjecture concerns the following problem. On a unit length circular track one considers k + 1 runners who all start at the same place and at the same time, each runner having a constant speed, with speeds being pairwise distinct. We say that a runner is lonely if all the other runners are of distance at least 1/(k + 1) from the runner. The conjecture ask whether each runner is lonely at some point in time. We will give a survey of results towards the conjecture and present some results concerning the function fields analogue, a joint work with Samuel Chow.