Counting problems on the modular surface

Ara Basmajian

City University of New York (USA)

Abstract:

The modular surface  \[X\] is the punctured sphere with cone points of orders  \[2\] and  \[3\] ; equivalently  \[X\] is the quotient of the upper half- plane by the modular group,  \[PSL(2,\mathbb{Z})\] . In this talk, after setting up the basics, we’ll focus on various classes of geodesics and their growth rates (with respect to word length and geometric length) leading to several counting problems.