Attainment of conformal dimension on symmetric Laakso-type fractal spaces

The conformal dimension of a metric space X is the infimum of the Hausdorff dimensions of all metric spaces quasisymmetrically equivalent to X. Spaces that attain this infimum often exhibit desirable geometric and analytic properties, but determining whether attainment occurs is notoriously difficult. Indeed, the question remains open in most settings of interest. In joint work with Riku Anttila and Sylvester Eriksson-Bique, we improve the situation by fully resolving the question for the class of symmetric Laakso-type fractal spaces.