I will talk about the maximal distance minimizer problem: the problem of finding for a given compact set $M$ and a given number $r>0$ such a closed connected set $Sigma$ that $M$ is contained in the closed $r$-neighbourhood of $Sigma$. I will give the definitions and basic information, provide the regularity properties, the solutions for some explicit sets and say a few words about the connection of this problem with Steiner tree problem. The problem could be stated in any metric space, but we work in Euclidean space. Everybody is welcome, no preliminaries needed.
Camille Labourie
