|Date:||Mon, October 6, 2014|
|Place:||Research II Lecture Hall|
Abstract: Let $f$ be a separable univariate polynomial with integral coefficients whose degree is odd and at least~3. Then the diophantine equation $y^2 = f(x)$ has only finitely many integral solutions. These solutions correspond to integral points on the hyperelliptic curve $C$ defined by the equation. I will discuss a $p$-adic method which can often be used to compute all integral points on $C$. This is joint work with Jennifer Balakrishnan and Amnon Besser.