# Mathematics Colloquia and Seminars

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### $4m-3$ Lattice Points in the Plane

**Student-Run Applied & Math Seminar**

Speaker: | Thomas Hogan, UC Davis |

Related Webpage: | https://www.math.ucdavis.edu/~tahogan/ |

Location: | 3106 MSB |

Start time: | Fri, Apr 20 2018, 12:10PM |

Tverberg's theorem says that sufficiently many points in euclidean space can always be partitioned into $m$ subsets so that the intersection of the convex hulls of the $m$ subsets is non-empty. In the 1970's Doignon proposed a variant of Tverberg's theorem where the points are required to have integer coordinates. We will focus on this variant throughout the talk, and sketch the proof that any $4m−3$ (for $m≥3$) lattice points in the plane can be colored $m$ colors so that there is a lattice point in the intersection of the convex hulls of the $m$ colors. We will also discuss the analogous problem in higher dimensions.

Note special time and location.

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