Diophantine Equations and p-adic Integration

Series: 
Research Horizons Seminar
Wednesday, November 15, 2017 - 12:10pm
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.