Ghost Polygons, Poisson Bracket and Convexity in Anosov Representations

Explore a comprehensive lecture on ghost polygons, Poisson brackets, and convexity in the context of Anosov representations. Delve into the moduli space of Anosov representations of surface groups, examining natural functions such as length and correlation functions. Learn how to compute Poisson brackets using combinatorial methods and discover the stability of these functions under the Poisson bracket. Investigate the application of these concepts to the convexity of length functions, extending Kerckhoff's results on Teichmüller space. Begin with an introduction to Anosov representations, followed by precise definitions of the functions under consideration and an explanation of the combinatorial techniques involved. This 59-minute talk, presented by François Labourie from Université Côte d'Azur at the Institut des Hautes Etudes Scientifiques (IHES), is based on joint work with Martin Bridgeman and offers valuable insights into this advanced mathematical topic.