Date: Wednesday, November 08, 2017
Location: 3866 East Hall (4:00 PM to 5:30 PM)
Title: The Goldman symplectic form on the Hitchin component
Abstract: Let S be a closed, orientable, connected surface of genus at least 2. We prove that any ideal triangulation on S determines a symplectic trivialization (with respect to the Goldman symplectic form) of the tangent bundle of the Hitchin component. One can then consider the parallel flows with respect to the flat structure given by this trivialization. We give a geometric description of all such flows in terms of explicit deformations of Frenet curves, and prove that all such flows are Hamiltonian. Applying this to a particular ideal triangulation allows us to find a maximal family of Poisson commuting Hamiltonian flows on the Hitchin component. This generalizes the wellknown fact that on Teichmueller space, the twist flows along a pants decomposition of S is a maximal family of Poisson commuting Hamiltonian flows. This is joint work with Zhe Sun and Anna Wienhard.
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Speaker: Tengren Zhang
Institution: CalTech
Event Organizer: Van Limbeek wouterv@umich.edu
