Algebraic Geometry and Number Theory with Magma
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4--8 October 2004
Centre Émile Borel, Institute Henri Poincaré

Programme of lectures and courses
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All lectures will be held in the Amphithéatre Hermite
For more information see www.ihp.jussieu.fr

Monday, October 4
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09:50-10:00
Opening Remarks

10:00-10:55 Manjul Bhargava (CMI/Princeton)
Universal quadratic forms and the Conway-Schneeberger 290-Conjecture

11:00-11:25 John Voight (Berkeley)
Computing the reciprocity law for CM points on Shimura curves

11:30-12:25 John Cannon (Sydney)
An overview of algebraic geometry in Magma

14:00-14:55 Short Course: Wieb Bosma (Nijmegen)
Arithmetic Fields I -- From Number to Field and beyond

15:00-15:55 Short Course: Gavin Brown (Warwick)
Schemes I -- General

16:15-18:15 College de France Lecture: Don Zagier (ENS)
Les séries Thêta

Tuesday, October 5
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10:00-10:55 Michael Stoll (Bremen)
Implementing the Brauer-Manin obstruction on curves

11:00-11:25 Josef Schicho (Linz)
Deciding rational rationality of algebraic surfaces

11:30-12:25 Gavin Brown (Warwick)
Graded rings over K3 surfaces

14.00-14:25 Janka Pilnikova (Linz)
Finding rational points on Severi-Brauer surfaces

14:30-14:55 Jean-Charles Faugère (Paris 7)
Algebraic attacks and cryptanalysis of HFE using Groebner bases

15:00-15:55 Jan Stevens (Goeteborg)
Computing in singularity theory

16:30-17:25 Short Course: John Cremona (Nottingham)
Elliptic Curves I

17:30-18:25 Short Course: William  Stein (Harvard)
Modular Forms I -- Modular symbols and modular forms

Wednesday, October 6
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10:00-10:55 Miles Reid (Warwick)
Unprojection and Gorenstein rings in small codimensions

11:00-11:25 Grégoire Lecerf (Versailles)
Evaluation techniques for polynomial system solving

11:30-12:25 Reynald Lercier (Rennes)
Elliptic curve point counting over finite fields

14.00-14:55 Tom Fisher (Cambridge)
Presentations of genus one curves

15:00-15:55 Frank-Olaf Schreyer (Saarbrücken)
Computation of cohomology of coherent sheaves

16:30-17:25 Short Course: Michael Stoll (Bremen)
Algebraic Curves I -- Hyperelliptic curves and curves of genus 2

17:30-18:25 Short Course: William  Stein (Harvard)
Modular Forms II -- Modular abelian varieties

Thursday, October 7
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10:00-10:55 William Stein (Harvard)
Computations related to the BSD conjecture for modular abelian
varieties using Magma

11:00-11:25 Markus Grassl (Karlsruhe)
Constructing algebraic-geometric codes using Magma

11:30-12:25 Allan Steel (Sydney)
Computing Groebner bases with linear algebra

14.00-15:30 College de France Lecture: Manjul Bhargava (CMI/Princeton)
Higher composition laws and applications

16:30-17:25 Short Course: John Cremona (Nottingham)
Elliptic Curves II

17:30-18:25 Short Course: Florian Hess (TU, Berlin)
Arithmetic Fields II -- Function Fields

Friday, October 8
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10:00-10:55 John Cremona (Nottingham)
Finding all elliptic curves with good reduction outside a given
set of primes

11:00-11:25 Emmanuel Hallouin (Toulouse)
Computation of a family of covers of P^1_C giving rise to totally
real PSL_2(F_8)-extensions of Q

11:30-12:25 Florian Hess (TU, Berlin)
Algorithms for function fields and curves with applications in 
cryptography and coding theory

14.00-14:55 Short Course: Michael Harrison (Sydney)
Schemes II -- Mappings

15:00-15:55 Short Course: Michael Stoll (Bremen)
Algebraic Curves II -- General curves