Explore a 51-minute mathematics lecture that delves into the uniformization problem for metric surfaces, examining conditions under which a metric space X, homeomorphic to a model surface M, can be parametrized with specific geometric and analytic properties. Learn about breakthrough findings from Bonk-Kleiner and Rajala, and discover why no additional assumptions are needed for weakly quasiconformal parametrization existence. Understand how locally geodesic spaces utilize energy-minimizing Sobolev mappings for parametrization construction, and examine the application of weakly quasiconformal uniformization in achieving 2-dimensional Lipschitz-volume rigidity results. Focus on cases where X possesses locally finite Hausdorff 2-measure, presented by Damaris Meier from the University of Fribourg at the Hausdorff Center for Mathematics.