A classical result of Goldman states that character variety of an oriented surface is a
symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface
acts by Hamiltonian vector fields on the character variety. I will describe a vast
generalization of these results, including to higher dimensional manifolds where the role of
the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology
of the manifold. These results follow from a general statement in noncommutative geometry.
In addition to generalizing Goldman's result to string topology, we obtain a number of other
interesting consequences including the universal Hitchin system on an algebraic curve. This
is joint work with Chris Brav.