The Uniformization Theorem states that every compact Riemann surface can be represented as a quotient of the complex unit disk by a group of isometries, which allows for the classification of Riemann surfaces in terms of simpler structures. This theorem provides a powerful connection between algebraic geometry and complex analysis, especially in the context of elliptic curves, as it enables the understanding of these curves through their uniformizations via the upper half-plane or the complex torus.
congrats on reading the definition of Uniformization Theorem. now let's actually learn it.