Algebraic Geometry and Number Theory with Magma

Institute Henri Poincaré Paris October 4 - 8, 2004

Pictures

Click here for pictures of the conference (taken by William Stein and Allan Steel).

Introduction

A week-long conference on the Computer Algebra system Magma and its applications to computational algebraic geometry and number theory was held October 4 - 8, 2004. The meeting was held at the Centre Emile Borel of the Institute Henri Poincaré, Paris, as part of the trimester on "Explicit Methods in Number Theory", organised by Belabas, Cohen, Cremona, Mestre, Roblot, Zagier.

For further information, mail John Cannon.

The meeting was built around the following types of activities:

Lectures describing recent developments in algorithms for algebraic geometry and arithmetic fields.
Talks describing significant applications of Magma to algebraic geometry or number theory.
Talks discussing potential algorithms or ideas for future directions in computational methods for algebraic geometry and arithmetic fields.
Short courses on the use of Magma in following areas:
- Arithmetic fields
- General algebraic geometry ie schemes
- Elliptic curves
- Curves of genus greater than 1
- Modular forms and modular abelian varieties

Lectures

Manjul Bhargava (IAS Princeton): A conjecture of Conway and Schneeberger on quadratic forms

Gavin Brown (Warwick): Graded rings over K3 surfaces

John Cannon (Sydney): An overview of algebraic geometry in Magma

John Cremona (Nottingham): Finding all elliptic curves with good reduction outside a given set of primes

Miles Reid (Warwick): Unprojection and Gorenstein rings in small codimensions

Josef Schicho (Linz): Deciding rational rationality of algebraic surfaces

Frank-Olaf Schreyer (Saarbrücken): Computation of cohomology of coherent sheaves

Allan Steel (Sydney): Computing Gröbner bases using linear algebra

William Stein (Harvard): Computations related to the BSD conjecture for modular abelian varieties using MAGMA

Jan Stevens (Goeteborg): Computing in singularity theory

Michael Stoll (IU, Bremen): Implementing the Brauer-Manin obstruction on curves

Short Courses

A number of short courses providing an introduction to the use of Magma in various branches of algebraic geometry and number theory will be presented. The lectures, in most cases, will be presented by people who have played a major role in the development of the corresponding machinery in Magma. Each course will comprise two one hour lectures. Some talks in the list below have still to be confirmed.