Moduli spaces of flat connections on oriented surfaces can be equipped with Goldman Poisson bracket. It is a classical theorem by L.Jeffrey and J.Weitsman that for G=SU(2) the resulting Poisson manifold becomes a phase space of a Liouville integrable system. I will talk about similar problem for groups of higher rank.
In my talk I will define a large family of Superintegrable systems (a.k.a. Degenerately integrable systems) on the moduli spaces of flat connections. Superintegrable systems on 2n dimensional phase space have k<=n Hamiltonians in involution and m>=n common first integrals, such that k+m=2n. Particular case of m=k=n corresponds to Liouville integrability.
Based on joint work with N.Reshetikhin arXiv:1909.08682
The talk will be via Zoom at:
https://utoronto.zoom.us/j/99576627828
Passcode: 448487