Computational Algebra Seminar: Watkins, Creutz

Date: 20/06/13
Location: Carslaw 535
Time: 15:05-16:00
Name: Mark Watkins
Affiliation: University of Sydney
Title: Ranks of congruent number twists
Abstract: For each positive $d$, the elliptic curve $d*y^2 = x^3 - x$
has positive rank if and only if $d$ is the area of a right-angled
triangle with rational sides, the latter being a question of antiquity.
We do not address this question of positive rank per se, but rather
present the results of some experiments trying to find $d$ such that
the above elliptic curve has large rank. These can be seen as $d$ for
which there exist "many" rational-sided triangles of area $d$.


Date: 20/06/13
Location: Carslaw 535
Time: 16:15-17:10
Name: Brendan Creutz
Affiliation: University of Sydney
Title: 2-torsion Brauer classes on double covers.
Abstract: Let X be a smooth double cover of a geometrically ruled
surface over a separably closed field of characteristic different
from 2. I will discuss recent work in which we give a finite presentation
of the two-torsion in the Brauer group of X with generators given
by central simple algebras over the function field of X and relations
coming from the Neron-Severi group of X. I will also discuss some
of the motivation for this coming from arithmetic applications such
as computing Brauer-Manin obstructions to the existence of rational points.
This is joint work with Bianca Viray.