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Explore a one-hour lecture on the Kontsevich geometry of combinatorial Teichmüller space, delivered by Alessandro Giacchetto from the Max Planck Institute for Mathematics. Delve into the combinatorial description of moduli spaces of curves discovered in the early 1980s and its impact on topology, including Kontsevich's proof of Witten's conjecture. Examine the combinatorial Teichmüller space that parametrizes marked metric ribbon graphs on surfaces, and learn about global Fenchel-Nielsen coordinates. Discover a formula for the Kontsevich symplectic form, analogous to Wolpert's formula for the Weil-Petersson form on ordinary Teichmüller space. Investigate methods for integrating geometric functions over combinatorial moduli spaces, with references to related work by collaborators J.E. Andersen, G. Borot, S. Charbonnier, D. Lewański, and C. Wheeler.
