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BIRS Workshop Lecture Videos
Symplectic Structures on the moduli space of Schodinger Equations on Riemann Surfaces of fixed genus and the Goldman Bracket. Norton, Chaya
We will give a brief overview of the results contained in joint work with Bertola and Korotkin. The moduli space of Schodinger Equations over $M_g$ can be equipped with a symplectic structure by choosing a base section and identifying with $T^*M_g$. We prove homological coordinates are Darboux coordinates and characterize base sections giving equivalent symplectic structures. In addition we show the monodromy map is a symplectomorphism for base section Schottky, Wringer, and Bergman. These results can be compared with Kawai '96 (more recently Loustou '15, Takhtajan '17) where the map is shown to be a symplectomorphism with base Bers.
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