Short Talk: Seung-Yeon Ryoo

Assouad's embedding theorem states that doubling metric spaces embed bi-H\"olderly into Euclidean space. Optimal bounds for the distortion and target dimension are known. We conjecture that the distortion and target dimension can be simultaneously optimized. We demonstrate this on some class of metric spaces: nilpotent Lie groups, finitely generated groups of polynomial growth, doubling subsets of Hilbert space, and manifolds of nonnegative Ricci curvature.