Summary
Polynomial equations, which are essentially made by adding and multiplying together variables, are among the most fundamental equations in mathematics and arise in many areas of science and engineering. The field of algebraic geometry seeks to classify the shapes defined by polynomial equations. The 1-dimensional shapes, called algebraic curves, have important applications in cryptography and string theory. The starting point for the classification of algebraic curves is Riemann's work in the 1850s, which introduced the concept of their moduli space -- a space in which each point corresponds t
