**Abstract:** 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

- dist(p, u) + dist(u, v) = dist(p, v) (i.e. u is between p and v) or

• dist(u, p) + dist(p, v) = dist(u, v) (i.e. p is between u and v) or

• dist(u, v) + dist(v, p) = dist(u, p) (i.e. v is between u and p).

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.

Venue: Av República 701, Sala 33.

Speaker: Pierre Aboulker

Affiliation: U. Nice-Sophia-Antipolis

Coordinator: Prof. José Verschae