The talk starts with a gentle introduction to minimal surfaces and basic notions from projective geometry. Using the Schwarzian derivative I will then explain how to construct a sequence of meromorphic differentials on every non-flat oriented minimal surface in Euclidean 3-space. A minimal surface is said to have degree n if its n-th differential is a polynomial expression in the differentials of lower degree. Various well-known minimal surfaces are identified as surfaces of low degree.

Based on joint work with Jacob Bernstein & Lukas Poerschke.