Caitlin Haedrich Mathematics Senior Thesis Talk

Caitlin will speak about “Rational Points on Elliptic Curves.” Elliptic curves are projective algebraic curves whose rational points have the unique property of forming an additive abelian group. We will build a basic understanding of elliptic curves including background on projective geometry and algebraic curves. We investigate the structure and function of the group law that allows us to move among the rational points on an elliptic curve. Finally, we use this background to prove Mordell’s Theorem which states that all rational points on an elliptic curve are finitely generated.