1350

Date | Dec 12, 2016 |
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Speaker | Keivan Mallahi-Karai |

Dept. | Jacobs University |

Room | 129-301 |

Time | 16:00-17:00 |

The famous Hadwider-Nielson problem asks for the smallest number $n$ such that the points of the plane can be partitioned into $n$ sets such that no two points in the same set are at distance $1$.

This problem, among many similar problems, can be reformulated in terms of the chromatic number of certain Cayley graphs. In this talk, I will discuss two recent results in this direction: one pertains to the Borel chromatic number of the unit-distance graph associated to quadratic forms over local fields. The other result is a lower bound on the chromatic number of Cayley graphs of finite groups of Lie type.

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