Generalizations of the geometric de Bruijn Erdős theorem
- Date: Monday 2 December 2019, 15:30 – 16:30
- Location: Roger Stevens LT 06 (8.06)
- Type: Algebra, Logic and Algorithms, Logic, Seminars, Pure Mathematics
- Cost: Free
Pierre Aboulker, École Normale Supérieure, Paris. Part of the Algebra, Logic, and Algorithms Seminar Series.
A classic Theorem of de Bruijn and Erdős states that every noncollinear set of n points in the plane determines at least n distinct lines. The line L(u,v) determined by two points u, v in the plane consists of all points p such that u, v, and p are collinear. With this definition of line L(uv) in an arbitrary metric space (V, dist), Chen and Chvátal conjectured that every metric space on n points, where n is at least 2, has at least n distinct lines or a line that consists of all n points. The talk will survey results on and around this conjecture.