| Time | Monday | Tuesday | Wednesday | Thursday | Friday |
| Today's programme celebrates the 60-th birthday of Alf van der Poorten |
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09:00 - 10:00 Invited Talks |
Opening address (09:15 - 09:30)
John Coates
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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 |
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| 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 |
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| 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 |
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| 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 |
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| 17:00 - 17:30 |
Antoine Joux and Reynald Lercier The Function Field Sieve is Quite Special |
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