3-dimensional manifolds provides tools for Teichmüller theory:
the renormalized volume of quasifuchsian manifolds provides a
Kähler potential for the Weil-Petersson metric (Takhtajan,...) while
Thurston's Earthquake Theorem has a nice and relatively simple proof
based on the geometry of globally hyperbolic AdS manifolds (Mess).
After outlining those two results, we will explain how notions
from physics, like 3-manifolds with "particles" (resp. multi-black
holes) lead to extensions to the Teichmüller theory of hyperbolic
surfaces with cone singuarities (resp. with geodesic boundary).
(Joint works with Lecuire, Moroianu, Bonsante, Krasnov).