Symplectic
by Ahmadreza Khazaeipoul (University of Toronto)
In this talk, the Gelfand-Dikii Poisson structure is introduced as a Poisson structure on the space of n-th order Hill operators. For n=2, the space of Hill operators is identified with the dual of the Virasoro algebra at level one, making the Poisson structure linear. For n>2, the Poisson structure is quadratic. A coordinate-free construction of this Poisson structure is provided by the Drinfeld-Sokolov reduction. The symplectic leaves of this Poisson structure have been determined by Khesin and Ovsienko. In this talk, I will construct a symplectic groupoid integrating this Poisson structure and prove that it is Morita equivalent to a quasi-symplectic groupoid integrating the Cartan-Dirac structure on PSL~(n,R).