### Mathematics Colloquium

# Steffen Müller

### (Oldenburg)

## "Computing integral points on hyperelliptic curves"

** Date: ** |
Mon, October 6, 2014 |

** Time: ** |
17:15 |

** 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.