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ISBN 978-0-387-94609-2

Localisation : Colloque 1er étage (BOST)

algèbre de Hecke # anneau de déformation universelle # cohomologie galoisienne # conjecture de Serre # correspondance de Hecke # courbe elliptique # courbe modulaire # grand théorème de Fermat # intersection complète # représentation galoisienne # schéma en groupe # théorème de Wiles

11-03 ; 11D41 ; 11G18 ; 14Hxx

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Research talks;Number Theory

The assertions made by L. J. Mordell in his paper in Acta Mathematica 44(1952) are discussed. Mordell had been to a certain extent anticipated by E. Jacobsthal (1939).
backward induction - congruence - equation - non-zero coefficients - polynomials

11D09 ; 11D25 ; 11D41

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Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

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Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

... Lire [+]

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of this result. Third principle: The sought-after configurations which are always to be found in large sets are abundant.

* Furstenberg's Dynamical approach :
Partition Ramsey theory and topological dynamics Dynamical versions of van der Waerden's theorem, Hindman's theorem and Graham-Rothschild-Spencer's geometric Ramsey.
Density Ramsey theory and Furstenberg's correspondence principle Furstenberg's correspondence principle. Ergodic Szemeredi's theorem. Polynomial Szemeredi theorem. Density version of the Hales-Jewett theorem.

* Stone-Cech compactifications and Hindman's theorem :
Topological algebra in Stone-Cech compactifications. Proof of Hind-man's theorem via Poincare recurrence theorem for ultrafilters.

* IP sets and ergodic Ramsey theory :
Applications of IP sets and idempotent ultrafilters to ergodic-theoretical multiple recurrence and to density Ramsey theory. IP-polynomial Szemeredi theorem.

* Open problems and conjectures

If time permits:
* The nilpotent connection,
* Ergodic Ramsey theory and amenable groups
* The early results of Ramsey theory :
Hilbert's irreducibility theorem, Dickson-Schur work on Fermat's equation over finite fields, van der Waerden's theorem, Ramsey's theoremand its rediscovery by Erdos and Szekeres.

* Three main principles of Ramsey theory :
First principle: Complete disorder is impossible. Second principle: Behind every 'Partition' result there is a notion of largeness which is responsible for a 'Density' enhancement of ...

05D10 ; 37Axx ; 12D10 ; 11D41 ; 54D80 ; 37B20

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- 261 p.
ISBN 978-3-540-08489-1

Grundlehren der mathematischen wissenschaften , 0231

Localisation : Collection 1er étage

analyse diophantienne # analyse p-adique # approximation diophantienne # équation diophantienne # inégalité diophantienne # logarithme

10B45 ; 10B99 ; 11D41 ; 11D99 ; 11Dxx

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- xvi; 224 p.
ISBN 978-3-03719-183-5

IRMA lectures in mathematics and theoretical physics , 0028

Localisation : Ouvrage RdC (BUGE)

théorie de Baker # forme linéaire en logarithme # équation diophantienne # équation de Thue # conjecture abc # diviseur primaire # mesure d'irrationalité # analyse p-adique

11-02 ; 11J86 ; 11Dxx ; 11B37 ; 11D25 ; 11D41 ; 11D59 ; 11D61 ; 11D75 ; 11D88 ; 11J25 ; 11J81 ; 11J82

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- 341 p.

Localisation : Ouvrage RdC (LAND);Réserve

conjecture de Fermat # corps quadratique # nombres premiers réguliers # théorie des idéaux # théorie des nombres algébriques # théorème de Furtängler # théorème de Mirimanoff # théorème de Vandiver # théorème de Wieferich

11D41 ; 11R04 ; 11Rxx

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- 181 p.

Queen's Papers in Pure and Applied Mathematics , 0093

Localisation : Ouvrage RdC (JHA)

dernier théorème de Fermat # idéal de Stickelberger # nombre de Bernoulli # nombre de classes # somme de Jacobi # théorie de Kummer

11B68 ; 11D41 ; 11R29 ; 11Rxx

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- 152 p.
ISBN 978-0-8218-3124-3

American mathematical society translations series 2 , 0143

Localisation : Collection 1er étage

D-bloc de caractère # calcul de résolution # estimation de polynôme orthogonal # estimation en moyenne # groupe fini # géométrie diophantienne # logique modale # modèle de données et langage de description # obstruction complète au principe de Hasse # principe ergodique pour opérateur stochastique quadratique # problème du diviseur additif

03B45 ; 11D41 ; 11G10 ; 11G35 ; 11P99

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- 177 p.
ISBN 978-2-87647-144-3

Localisation : Ouvrage RdC (NOGU)

17 ème siècle # 18 ème siècle # 19 ème siècle # 1931 # 20 ème siècle # Kummer # Lamé # Legendre # Mirimanoff # histoire # théorème de Fermat # équation diophantienne

01A45 ; 01A55 ; 11-03 ; 11D41 ; 11Dxx

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- 196 p.
ISBN 978-0-8218-2670-6

Localisation : Monographie RdC (MOZZ)

dernier théorème de Fermat # histoire # théorie des nombres # équation de Fermat # équation de degré supérieur # équation diophantine

11D41

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- 77 p.
ISBN 978-90-6196-508-4

CWI tract , 0133

Localisation : Collection 1er étage

équation de Fermat # méthode de Chabauty # courbe elliptique # point rationnel # corps de nombre # restriction arithmétique # courbe hyperbolique # genre different de 1 sur un corps global

11D41 ; 11G30 ; 14G05

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- xviii; 457 p.
ISBN 978-1-107-09761-2

New mathematical monographs , 0032

Localisation : Ouvrage RdC (EVER)

équation discriminante # équation unitaire # ordre monogénique # algèbre étale # séparation des racines # conjecture de Shafarevich

11-02 ; 11D41 ; 11R04

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- 267 p.
ISBN 978-3-540-07855-5

Lecture notes in mathematics , 0536

Localisation : Collection 1er étage

analyse diophantienne # théorie des corps # corps modulaire # polynôme sur des corps finis # théorie arithmétique des anneaux de polynôme # équation diophantienne de degré supérieur # corps fini # groupe agélien fini # fonction zeta # fonction L # somme de Kloosterman

12-01 ; 11T06 ; 14G15 ; 11T55 ; 11D41

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