GAAG seminar - Around Duke's theorem on equidistribution of closed geodesics

A celebrated result of Duke from the 80's says that closed geodesics on the modular curve equidistribute as the discriminant tends to infinfity. This is the real quadratic analogue of the equidistribution of CM-points on the modular curve associated to class groups of imaginary quadratic fields. I will discuss a number of generalizations of the result of Duke in the indefinite setting including; the distribution of the homology classes of closed geodesics and hyperbolic orbifolds associated to class groups of real quadr. fields (as defined by Duke-Imamoglu-Toth for the modular curve and extended by Peter Humphries, Ser Tan Peow and myself ). This is partly based on two works joint with Peter Humphries and Ser Tan Peow, respectively.