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This lecture presents Vincent Guedj's work on establishing uniform estimates for Green's functions associated to Kähler forms as they evolve in large families with varying complex structures. Guedj explains how this research generalizes previous work by Guo, Phong, Song, and Sturm, and demonstrates how these estimates enable the establishment of diameter bounds and non-collapsing estimates for various families of canonical Kähler metrics. The talk covers joint research with T.D.Tô and was recorded during the thematic meeting "Families of Kähler spaces" on April 22, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this video and other mathematical talks through CIRM's Audiovisual Mathematics Library, which offers features like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search functionality.
