Georgia Institute of Technology College of Sciences

A motivating problem in number theory and algebraic geometry is to find all integer-valued solutions of a polynomial equation. For example, Fermat's Last Theorem asks for all integer solutions to x^n + y^n = z^n, for n >= 3. This kind of problem is easy to state, but notoriously difficult to solve. I'll explain a p-adic method for attacking Diophantine equations, namely, p-adic integration and the Chabauty--Coleman method. Then I'll talk about some recent joint work on the topic.