# MAA

## Seminar

### Hilbert's tenth problem for function fields

Seminar Room 1, Newton Institute

#### Abstract

We will discuss how elliptic curves of rank one can be used to prove undecidability of Hilbert's Tenth Problem for function fields of characteristic zero, such as R(t) and C(t_1,...,t_n) (n at least 2).

The approach for function fields of positive characteristic is very different, and we will sketch some of the methods used there.