The maximum injectivity radius of hyperbolic 2-orbifolds

Given a hyperbolic surface, its maximum injectivity radius is the radius of the biggest disk we can isometrically embed in the surface. There are known upper and lower bounds for this radius which depend only on the topology of the surface. In this talk I will present some of these results and I will discuss the same problem in the case of surfaces with a hyperbolic metric and singular points (hyperbolic 2-orbifolds).