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Computational Algebra Group
Computational Algebra Seminar
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  • Mark Watkins
  • (University of Sydney)
  • Ranks of congruent number twists
  • 3pm–4pm, Thursday 20th June, 2013
  • Carslaw 707a
  • For each positive d, the elliptic curve d*y2 = x3 – 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.

  • Brendan Creutz
  • (University of Sydney)
  • 2-torsion Brauer classes on double covers
  • 4:15pm–5:15pm, Thursday 20th June, 2013
  • Carslaw 707a
  • 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.

The Computational Algebra Group is a research group within the School of Mathematics and Statistics, University of Sydney.
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