Abstract:

Equidistribution of "special" points is a theme of both analytic and geometric interest in number theory: in this talk I plan to deal with the case of CM points on Shimura curves. The first part will be devoted to a geometric description of the aforementioned curves and of their moduli interpretation. Subsequently, I plan to sketch an equidistribution result of reduction of CM points in the special fiber of a Shimura curve associated to a ramified quaternion algebra. Time permitting, I will mention how Ratner's theorem and subconvexity bounds on Fourier coefficients of certain theta series can be used to obtain two different equidistribution results.