| 2004 | October, 1 | John Cremona (University of Nottingham) Finding all elliptic curves with good reduction outside a given set of primes. Abstract |
| October, 15 | Ian Kiming (Institute for Mathematical Sciences at the University of Copenhagen) Lifting mod pq Galois representations. Abstract |
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| October, 29 | François Morain (École Polytechnique) The fast version of the Elliptic Curve Primality Proving algorithm (ECPP) Abstract |
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| November, 19 | Bjorn Poonen (University of California at Berkeley) Rational curves in varieties over finite fields Abstract |
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| December, 3 | Samir Siksek (Sultan Qaboos University, Oman) Multi-Exponential Diophantine Equations Abstract |
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| December, 17 | Roger Oyono (Institut für experimentelle Mathematik, Essen) Non-hyperelliptic curves of genus 3 and their use in Cryptography Abstract |
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| 2005 | March, 4 | Juan Marcos Cerviño (Georg-August Universität, Gottingen) Endomorphism rings of supersingular elliptic curves Abstract |
| March, 11 | Tanja Lange (Technical University of Denmark). 11 h. Pairing computation on non-supersingular hyperelliptic curves Gerhard Frey (Institut für Experimentelle Mathematik, Essen). 12:30 h. Index-Calculus in Brauer groups of Local and Global Fields |
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| March, 18 | Everett Howe (Center for communications research, San Diego) A heuristic explanation of the distribution of Frobenius eigenvalues for principally-polarized abelian varieties. Abstract |
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| April, 1 | Alexei Skorobogatov (Imperial College, London) Brauer-Manin obstructions on Shimura curves |
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| April, 15 | Pierrick Gaudry (École Polytechnique, Paris) Discrete logarithm in elliptic curves over extension fields of small degree Abstract |
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| April, 29 | José Ignacio Burgos (Universitat de Barcelona) Teoría de Arakelov y fibrados hermíticos con singularidades logarítmicas Abstract |
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| May, 13 | Robin de Jong (Universiteit van Amsterdam) Explicit Arakelov geometry Abstract |
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| May, 27 | Håkan Granath (Max Planck Institut für Mathematik, Bonn) Genus 2 curves with quaternionic multiplication Abstract |
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| June, 10 | Henryk Iwaniec (Rutgers University, USA) Primes represented by polynomials Abstract |
Organizers: Josep Gonzàlez (josepg, at mat.upc.es) and Víctor Rotger (vrotger, at mat.upc.es)