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Explore a 56-minute lecture by Guillaume Baverez that delves into integration by parts formulas in random conformal geometry and their applications. The talk examines how the Gaussian free field and Schramm-Loewner evolutions, as key examples of conformally invariant stochastic processes, respond to local conformal transformations. Learn how these variational formulas lead to integration by parts expressions that can be elegantly represented through the Virasoro algebra on the L2-space of measures. Discover the significant probabilistic implications of this algebraic structure, including a characterization of SLE and an innovative approach to the conformal welding of quantum surfaces. This Hausdorff Center for Mathematics presentation offers valuable insights for those interested in the intersection of probability theory, conformal geometry, and mathematical physics.
