The Teichmüller space parametrizes Riemann surfaces of
fixed topological type and is fundamental in various contexts of mathematics
and physics. It can be defined as a component of the moduli space of flat G=PSL(2,R)
connections on the surface. Higher Teichmüller space extends these notions
to appropriate higher rank classical Lie groups G, and N=1 super Teichmüller
space likewise studies the extension to the super Lie group G=OSp(1|2).
In this talk, which reports on joint work with Yi Huang, Ivan Ip and Robert Penner,
I will discuss our solution to the long-standing problem of giving Penner-type
coordinates on super-Teichmüller space and its higher analogues and will
also talk about several applications of this theory including our recent
generalization of the McShane identity to the super case.
Bob Penner & Fanny Kassel