# Enrique Alvarado

Washington State University

**Talk Title: **Variants of Average Distance-type problems

**Abstract: **Given a compact subset of the plane and a small value r, out of all closed and connected subsets of the plane whose r-neighborhoods contain the compact set in question, which is the one with smallest 1-dimensional Hausdorff measure? This is an L-infinity version of the well-studied average distance problem originating from Optimal Transport. In this talk, we will go through some already known results and some new results which relates the problem to coverings and Steiner trees.