Questions about rational points on curves

Abstract: A rational point on a curve is a point whose coordinates are both rational numbers. When a curve has genus 2 or more, by a theorem of Faltings, there are always only finitely many rational points. Yet many more questions remain: how many rational points are there exactly? Is there an algorithm to find them all? I'll discuss these questions and more (ranging from the time of the ancient Greeks to the present), offer some answers, and highlight a selection of illustrative examples.

number theory

Audience: researchers in the discipline

K-State Mathematics Department Women Lecture Series