SMS scnews item created by Brendan Creutz at Mon 17 Jun 2013 1102
Type: Seminar
Distribution: World
Expiry: 20 Jun 2013
Calendar1: 20 Jun 2013 1500-1715
CalLoc1: Carslaw 535A
Auth: (bcreutz) in SMS-WASM

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.

ball Calendar (ICS file) download, for import into your favourite calendar application
ball UNCLUTTER for printing
ball AUTHENTICATE to mark the scnews item as read
School members may try to .