Hamiltonian flows on character varieties

The character variety associated to a surface group and a semisimple Lie group comes naturally equipped with the so called Goldman symplectic form, and hence one can study Hamiltonian flows on it. One particular instance of such flows are twist flows along simple closed curves, which correspond to „length functions“. I will talk about ongoing work, where instead of considering functions on a single simple closed curve, I look at functions on multiple simple closed curves.