Diophantine Equations and p-adic Integration

Series: 
Research Horizons Seminar
Wednesday, November 15, 2017 - 12:10
1 hour (actually 50 minutes)
Location: 
skiles 006
,  
GT Math
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.