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Explore the dynamics of character varieties in this advanced mathematics lecture from the Big Ideas in Dynamics in Geometry conference. Delve into the action of the mapping class group Mod(S) on the SL(2, C)–character variety X(S) for hyperbolizable surfaces. Examine Bowditch's original ideas for the once-holed torus, including combinatorial methods relating character variety points to Markoff triples. Investigate generalizations to other surfaces like the four-holed sphere and three-holed projective plane, as well as extensions to SU(2,1). Discover the challenges in developing a general framework for these concepts and their connections to primitive-stable representations. Gain insights from this cutting-edge research presented by Sara Maloni from the University of Virginia, building on work with collaborators Palesi, Tan, and Lawton.
