Abstract

In this talk, I invite number theorists and undergraduates to share some recreational math I did for the past five years. I will show you how to use quivers to solve Diophantine equations, to be more precise, how to use quivers to construct solvable Diophantine equations.

Along the way, you will see many classical objects, eg., quadratic equations, Elliptic curves, L-functions, and many new discoveries, eg., Laurent phenomenon and cluster algebras. The talk is full of examples and open problems. The first hour involves high school math only. But if you think this is just recreational math, I may prove you are wrong in the last ten minutes.