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Explore the fascinating world of dynamics on character varieties in this comprehensive lecture by William Goldman from the University of Maryland. Delve into the classification of locally homogeneous geometric structures and their relation to flat connections, drawing parallels to the classification of Riemann surfaces. Discover how these classifications lead to intriguing dynamical systems, often characterized by chaotic behavior. Examine specific examples, including Baues's theorem on the deformation space of complete affine structures on the 2-torus. Investigate the dynamics of relative character varieties represented as cubic surfaces in affine 3-space and their connection to symplectic leaves of invariant Poisson structures. Uncover the relationship between complex dynamics and intricate topology, particularly in the context of hyperbolic structures on surfaces. Throughout the lecture, gain insights into key concepts such as SL2C, GL2Z, mapping class groups, and the Weigel conjecture, culminating in a comprehensive overview of this captivating field of mathematical study.
