In a series of three lectures, we will revisit three well-known examples of distance problems in discrete geometry: the Erdős Unit Distance Problem, the Erdős Distinct Distances Problem, and the Hadwiger-Nelson Problem.

We will cover recent solutions of the analogs of all three problems, and discuss how combinatorial, geometric, and probabilistic methods can be combined with tools from linear algebra, topology, and algebraic geometry to answer related questions. These talks are based primarily on recent joint works with Matija Bucić, Lisa Sauermann, Colin Defant, Noah Kravitz, and Daniel Zhu.

### Schedule

Title | Date/Time | Location |
---|---|---|

"Unit distances" | Dec. 5 4:00 p.m. |
180 Bevier Hall Reception in Bevier Hall Commons to follow |

"Distinct distances and equilateral numbers" | Dec. 6 4:00 p.m. |
4025 Campus Instructional Facility Refreshments available beginning at 3:30 p.m. |

"Coloring and ordering" | Dec. 7 4:00 p.m. |
4025 Campus Instructional Facility Refreshments available beginning at 3:30 p.m. |