# Conferinta:

*The generalized Fermat equation x*^{3}+y^{4}+z^{5}=0

## Samir Siksek (Warwick Univ.)

**ABSTRACT:**

This talk is based on joint work with Michael
Stoll (Bayreuth). The equation of the title was suggested
by Zagier as the next case of the Generalized Fermat
Conjecture. Work of Edwards reduces this equation to the
determination of rational points on 49 hyperelliptic
curves of genus 14. Standard methods for determining
the rational points fail on many of these curves. We
describe a new technique which we call 'partial descent'
that succeeds in completing the determination of rational
points on these curves. We deduce that the only solutions
in coprime integers x, y, z satisfy xyz=0.

### Marti 15 Iunie, ora 11:00