This trimester took place at the Centre Émile Borel and presented state of the art in effective and computational aspects of algebraic number theory and arithmetic geometry.

La version française de cette page est disponible ici.

• Notes for the short course Computation of Heegner points are available here.


• Outline notes for the mini-course Abelian Stark conjectures have been updated (Dec. 12).


• Abstracts for the talk AGM pour les courbes de genre 3 non hyperelliptiques (lec. C. Ritzenthaler, Dec. 16) has been added.


• A revised version of the schedule is available (posted November 30).


• Abstracts for the talk Floating-Point LLL Revisited (lec. D. Stehle, Dec. 17) has been added.


• The schedule (.pdf) of the workshop Explicit arithmetic geometry (Dec. 6-10) has been added.


• Abstracts for the talk AGM and Borchardt's mean: applications to the computation of Riemann matrices and to the evaluation of modular forms (lec. R. Dupont, Dec. 16) has been added.


• Outline notes and basic facts and notations for the mini-course Abelian Stark conjectures are available.


• Course notes for the mini-course The modular approach to diophantine equations are available.


• Course notes for part of the long course Rational points on curves are available.


• Course notes for the short course The diophantine equation A x^p + B y^q = C z^r are available.


• Abstracts for the talks Formes modulaires de Hilbert et représentations galoisiennes (lec. M. Dimitrov, Nov. 8), Nouvelle méthode de comptage pour les points rationnels (lec. R. de la Bretèche, Nov. 15), Invariants de Legendre supérieurs (lec. L. Zapponi, Nov. 22), and Primes in arithmetic progressions (lec. B. Green, Nov. 29) have been added.


• Abstract for the short course The modular approach to diophantine equations (lec. Siksek) has been added.


• Abstract for the short course Algorithmes de comptage de points d'une courbe définie sur un corps fini (lec. P. Gaudry) has been added.


• Abstract for the short course Effective complex multiplication in small genus and applications to primality proving (lec. A. Enge, F. Morain, A. Weng) has been added.


• Abstract for the short course Descent on elliptic curves (lec. M. Stoll) has been added.


• D. Zagier will give two courses: one at the Collège de France on Séries Thêta, and the other one at the Ecole Normale Supérieure (ENS) on Formes quadratiques et corps quadratiques.


• Abstract for the short course Algorithms for finite fields (lec. H. Lenstra) has been added.


• A section for the talks has been added.


• Each workshop has its own web-page including access to on-line registration (click on the workshop title).

(click on title for more information)

John CREMONA: Elliptic curves

Bjorn POONEN: Rational points on curves

Don ZAGIER: Formes quadratiques et corps quadratiques

Don ZAGIER: Séries Thêta

(click on title for more information)

Michel BALAZARD & Éric SAIAS: Le critère de Nyman pour l'hypothèse de Riemann

Karim BELABAS: Introduction to the computer algebra system PARI/GP

Frits BEUKERS: The diophantine equation A x^p + B y^q = C z^r

Manjul BHARGAVA: Higher composition laws and applications

Jean-Marc DESHOUILLERS: Explicit methods in additive number theory

Andreas ENGE, François MORAIN & Annegret WENG: Effective complex multiplication in small genus and applications to primality proving

Eduardo FRIEDMANN: Barnes's multiple gamma function

Pierrick GAUDRY: Algorithmes de comptage de points d'une courbe définie sur un corps fini

Florian HESSE: Introduction to the computer algebra system MAGMA

Juergen KLUENERS & Gunter MALLE: Counting extensions of number fields

Hendrik LENSTRA Jr.: Algorithms for finite fields

Jean-François MESTRE: Autour de la moyenne arithmético-géométrique

Samir SIKSEK: The modular approach to diophantine equations

David SOLOMON: Abelian Stark conjectures

Michael STOLL: Descent on elliptic curves

Jaap TOP: Curves of small genus over finite fields

Fernando VILLEGAS: On the zeta function of certain character varieties

Mark WATKINS: Computations of Heegner points

(click on title for more information)

Régis de la BRETÈCHE: Nouvelle méthode de comptage pour les points rationnels

John BRILLHART: The Lehmer dynasty and the search for better factoring methods

Jeroen DEMEYER: The probability that a F_q-hypersurface is smooth

Mladen DIMITROV: Formes modulaires de Hilbert et représentations galoisiennes

Régis DUPONT: AGM and Borchardt's mean: applications to the computation of Riemann matrices and to the evaluation of modular forms

Ben GREEN: Primes in arithmetic progressions

Chandrashekhar KHARE: Transcendental p-adic Galois representations

Shinichi KOBAYASHI: The two variable generating function of Hecke L-values of CM elliptic curves

Christophe RITZENTHALER: AGM pour les courbes de genre 3 non hyperelliptiques

Fernando RODRIGUEZ-VILLEGAS: Algebraic hypergeometric functions

Damien STEHLE: Floating-Point LLL Revisited

Akshay VENKATESH: 3-torsion in the class groups of quadratic fields

Leonardo ZAPPONI: Invariants de Legendre supérieurs

(click on title for more information)

The computer algebra system PARI/GP -- September 13 - September 17, organizers: K. Belabas & X.-F. Roblot (description & schedule)

The computer algebra system MAGMA -- October 4 - October 8, organizer: J. Cannon (schedule)

Explicit algebraic number theory -- October 11 - October 15, organizers: H. Cohen & K. Belabas (schedule)

Explicit arithmetic geometry -- December 6 - December 10, organizer: J. Cremona (schedule .pdf)

• Housing information:
  Paris Tourism Office
  Cité universitaire
  Hotels


• The conference center address:
  Institut Henri Poincaré, Centre Emile Borel
  11, rue Pierre et Marie Curie
  F-75005 Paris (FRANCE)
  Tel: (33/0)1 44 27 67 75
  Fax: (33/0)1 44 07 09 37
  http://www.ihp.jussieu.fr/


• Download the trimester poster.