Hamiltonian Systems

Let $\Sigma$ be a compact, oriented surface with boundary. In work with Anton Alekseev, we found that the Teichmueller space of hyperbolic 0-metrics on $\Sigma$, up to isotopies fixing the boundary, is naturally a Hamiltonian Virasoro space. In more recent work with Ahmadreza Khazaeipoul, we give a similar construction for the deformation space of $RP(2)$-structures with nondegenerate boundary, and show that it is a Hamiltonian space for the groupoid integrating the Gelfand-Dikii Poisson structure.