Event № 772
The Teichmuller space of symplectic structuresis the quotient of the space of all symplectic forms by the action of the connected component of the diffeomorphism group. Teichmuller space of symplectic structures was first considered by Moser, who proved that it is a smooth manifold. The mapping class group acts on the Teichmuller space by diffeomorphism.
I would describe the Teichmuller space of symplectic structures in the few examples when it is understood (torus, K3 surface, hyperkahler manifold) and explain how the ergodic properties of the mapping group action can be used to obtain information about symplectic geometry.