Georgia Institute of Technology College of Sciences

We give an overview of Teichmuller theory, the deformation theory of Riemann surfaces. The richness of the subject comes from all the perspectives one can take on Riemann surfaces: complex analytic for sure, but also Riemannian, topological, dynamical and algebraic.  In the past 40 years or so, interest has erupted in an extension of Teichmuller theory, here thought of as a component of the character variety of surface group representations into PSL(2,\R), to the study of the character variety of surface group representations into higher rank Lie groups (e.g. SL(n, \R)). We give a even breezy  discussion of that.  The first talk will begin with a segment that recalls scenes from the first overview in November.