All talks are in the Stephen Roberts Lecture Theatre, which is close to the Carslaw building.
Time Monday Tuesday Wednesday Thursday Friday

Today's programme celebrates the 60-th birthday of
Alf van der Poorten

09:00 - 10:00

Invited Talks

Opening address
(09:15 - 09:30)

John Coates

Antoine Joux

The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems

Manjul Bhargava

Gauss Composition and Generalizations

Bjorn Poonen

Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over Rings of Algebraic Integers

Takakazu Satoh

On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields

10:00 - 10:30 Elliptic Curves - The Crossroads of Theory and Computation

Steven D. Galbraith,
Keith Harrison and
David Soldera

Implementing the Tate Pairing

Enrique Gonzalez-Jimenez,
Josep Gonzalez and
Jordi Guardia

Computations on Modular Jacobian Surfaces

Wieb Bosma and
Bart de Smit

On Arithmetically Equivalent Number Fields of Small Degree

Nils Bruin and
Noam Elkies

Trinomials ax^7 + bx+c and ax^8+bx+c with Galois Groups of Order 168 and 8x168

10:30 - 11:00 Morning Tea
11:00 - 11:30 Jean-Marc Couveignes and
Thierry Henocq

Action of Modular Correspondences around CM Points

Carl Pomerance and
Igor Shparlinski

Smooth Orders and Cryptographic Applications

Takashi Fukuda and
Keiichi Komatsu

An Application of Siegel Modular Functions to Kronecker's Limit Formula

Stephane Louboutin

Efficient Computation of Class Numbers of Real Abelian Number Fields

Mireille Fouquet and
Francois Morain

Isogeny Volcanoes and the SEA Algorithm

11:30 - 12:00 Andreas Enge and
Francois Morain

Comparing Invariants for Class Fields of Imaginary Quadratic Fields

Igor Shparlinski and
Ron Steinfeld

Chinese Remaindering for Algebraic Numbers in a Hidden Field

Tony Shaska

Genus 2 curves with (3,3)-split Jacobian and Large Automorphism Group

Ulrich Vollmer

An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields

Hae Young Kim
et al.

Fast Elliptic Curve Point Counting Using Gaussian Normal Basis

12:00 - 12:30 Helena Verrill

Transportable Modular Symbols and the Intersection Pairing

Paul Leyland et. al.

MPQS with Three Large Primes

Graham Everest,
Peter Rogers and
Thomas Ward

A Higher-rank Mersenne Problem

Jan Denef and
Frederik Vercauteren

An Extension of Kedlayas's Algorithm to Artin-Schreier Curves

12:30 - 14:30 Lunch
14:30 - 15:00 Florian Hess

An Algorithm for Computing Weierstrass Points

Jeremy Horwitz and Ramarathnam Venkatesan

Random Cayley Digraphs and the Discrete Logarithm

Henri Cohen,
Francisco Diaz y Diaz and
Michel Olivier

A Survey of Discriminant Counting

Noam Elkies

Curves Dy^2=x^3-x of Odd Analytic Rank

15:00 - 15:30 Wen-Ching Li,
Hiren Maharaj and
Henning Stichtenoth

New Optimal Tame Towers of Function Fields over Small Finite Fields

Joshua Holden

Fixed Points and Two Cycles of the Discrete Logarithm

Free for Excursion Michael Jacobson and
Alf van der Poorten

Computational Aspects of NUCOMP

Andrew Kresch and
Yuri Tschinkel

Integral Points on Punctured Abelian Surfaces

15:30 - 16:00 Tea Edlyn Teske and
Peter Ebinger

Factoring N = pq^2 with the Elliptic Curve Method

William McCallum

The Fundamental Group of the 37th Cyclotomic Field

Jaap Top and
Roland Auer

Some Genus 3 Curves with Many Points

16:00 - 16:30 Allan Steel

A New Scheme for Computing with Algebraically Closed Fields

Afternoon Tea
16:30 - 17:00 Marc Watkins and
William Stein

A Database of Elliptic Curves - First Report

Kazuto Matsuo,
Jinhui Chao and
Shigeo Tsujii

An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields

Alf van der Poorten and
Xuan Chuong Tran

Periodic Continued Fractions in Elliptic Function Fields

17:00 - 17:30 Antoine Joux and
Reynald Lercier

The Function Field Sieve is Quite Special