- Thursday, November 10, 2022 - 11:00am for
- Skiles 006
- Tom Bohman – Carnegie Mellon University – email@example.com – https://www.cmu.edu/math/people/faculty/bohman.html
- Gong Chen, Benjamin Jaye, Tom Kelly
Suppose n runners are running on a circular track of circumference 1, with all runners starting at the same time and place. Each runner proceeds at their own constant speed. We say that a runner is lonely at some point in time if the distance around the track to the nearest other runner is at least 1/n. For example, if there two runners then there will come a moment when they are at anitpodal points on the track, and at this moment both runners are lonely. The lonely runner conjecture asserts that for every runner there is a point in time when that runner is lonely. This conjecture is over 50 years old and remains widely open.
A coprime matching of two sets of integers is a matching that pairs every element of one set with a coprime element of the other set. We present a recent partial result on the lonely runner conjecture. Coprime matchings of intervals of integers play an central role in the proof of this result.
Joint work with Fei Peng