Lipschitz embedding of compact metric spaces

An important topological theorem, due to K. Menger and G. Nobeling, states that any compact metrizable space of topological dimension m can be embedded in R^2m+1. In this talk, I will present the analogue for Lipschitz embeddings of metric spaces, whose proof is an application of the Baire category theorem as well as the topological version of the theorem. This result is due to Enrico Le Donne. I plan to conclude this talk with a discussion about my current research project, the BLD conjecture.