You’ve probably heard about “geometrization”, and you might know it was used to solve the Poincare Conjecture. But unless you’re a low-dimensional topologist, you may not actually know what geometrization is. We’ll discuss the general idea of applying geometric methods to topological problems, and do a hands-on example with curves on surfaces. No knowledge of Riemannian geometry will be assumed or needed, because I don’t have any myself.