Explore the geometry of random genus-0 hyperbolic surfaces through the lens of trees in this 58-minute conference talk by Timothy Budd. Recorded during the thematic meeting "Probability and Geometry in, on and of non-Euclidean spaces" at the Centre International de Rencontres Mathématiques in Marseille, France, on October 3, 2023. Delve into the intricate connections between hyperbolic geometry and tree structures, gaining insights into the probabilistic aspects of these mathematical objects. Access this video and other talks by renowned mathematicians on CIRM's Audiovisual Mathematics Library, featuring chapter markers, keywords, enriched content with abstracts and bibliographies, and a multi-criteria search function for easy navigation through mathematical topics.