Abstract: Fix a smooth compact oriented surface of genus g (bigger or equal than two) and call it M. It is a consecuence of the Uniformisation Theorem that the space of Riemann Surface structures on M is the same as the space of hyperbolic metrics on M. We will use pants to describe the last one as a quotient of the product of 3g-3 copies of the upper half plane. This quotient is not a compact space, but there is only one way in which a sequence of metrics might diverge and is by developping a long neck(s). I`ll make this more precise at the end if I have time.
A better title would be Hyperbolic Surfaces..or something like that, but I couldn`t help myself after the calendar.