Uniformization theorem for triangulated piecewise linear surfaces

Uniformization theorem is one of the pillars of 19th century mathematics. In terms of closed orientable Riemannian 2-manifolds, it states that every such surface is conformally equivalent to a unique closed 2-manifold of constant positive, zero, or negative curvature. I will talk about how the uniformization theorem and the whole differential-geometric machinery behind it has been translated into the realm of discrete surfaces, and adapted to be suitable for computations.