Zoé Chatzidakis


UMR 8553
Département de Mathématiques et Applications
Ecole Normale Supérieure
45 rue d'Ulm
75230 Paris Cedex 5
FRANCE
Bureau : T3, 4e étage (escalier B jusqu'au 3e, puis prendre le couloir et monter un étage. C'est près de la salle W.)
tél: (33) 1 44 32 20 56
fax: (33) 1 44 32 20 80
Adresse mail :

Bureau à Sophie Germain : bureau 6030, tél 01 57 27 92 06. Plan d'accès


Page de soutien à notre collègue lyonnais Tuna Altinel, qui était emprisonné en Turquie. (Il est maintenant en liberté provisoire, mais n'a toujours pas récupéré son passeport.)
Vous y trouverez toutes les informations. Signer la pétition
  


Cours avancé : Real closed fields and o-minimal structures

Room Henri Cartan. Mercredi 15h - 16h30; Jeudi 10h15 - 11h45.

Bibliographie :
Lou van den Dries, Tame topology and o-minimal structures
Alexander Prestel, Lectures on formally real fields
Et aussi Michel Coste, An introduction to o-minimal geometry, pdf
Yaacov Peterzil, A self-guide to o-minimality, Camerino tutorial June 2017. pdf

Papers I used around the Quantifier elimination of ℝ_{an} and ℝ_{an,exp}
J. Denef, L. van den Dries, $p$-adic and real subanalytic sets, J. Symbolic Logic 62 (1997), no. 4, 1481 - 1483. JSTOR
Lou van den Dries, Angus Macintyre and Dave Marker, The elementary theory of restricted analytic fields with exponentiation. Annals of Mathematics Vol. 140 No. 1 (1994), 183 - 205.
Notes de van den Dries sur l'élimination des quantificateurs de T_{an,^{-1}}: me demander.
L. van den Dries, C. Miller, On the real exponential field with restricted analytic functions, Isr. J. Math. 84 (1994), 19 - 56. (The first proof of o-minimality for ℝ_{an,exp}). Corrections in Isr. J. Math. 92 (1995), 427.
Y. Peterzil, S. Starchenko, Expansions of algebraically closed fields in o-minimal structures, Sel. Math., New Ser. 7 (2001), 409 - 445.
A. J. Wilkie, Lectures on the Model Theory of Real and Complex Exponentiation, in: Model Theory in Algebra, Analysis and Arithmetic: Cetraro 2012.

Around Pila-Wilkie
J. Pila, A. Wilkie, The rational points of a definable set, Duke Math. J. Vol 133, No. 3, 591 - 616.
Victoria Noquez, The Pila-Wilkie Theorem Louise Hay Logic Seminar, UIC. pdf

A few of the papers with applications (there are many others).
E. Bombieri, J. Pila, The number of integral points on arcs and ovals, Duke Math. J. Vol 59 No 2 (1989), 337 - 357.
J. Pila, Integer points on the dilation of a subanalytic surface, Quart. J. Math. 55 (2004), 207 - 223.
J. Pila, U. Zannier, Rational points in periodic analytic sets and the Manin-Mumford conjecture, Rend. Lincei Mat. Appl. 19 (2008), 149 - 162.
B. Klingler, A. Yafaev, The André-Oort conjecture, Annals of Math. 180 (2014), 1 - 59.
B. Klingler, E. Ullmo, A. Yafaev, The hyperbolic Ax-Lindemann-Weierstrass conjecture, Publ. Math. IHES 123 (2016), 333 - 360.
B. Bakker, B. Klingler, J. Tsimermanm Tame topology of arithmetic quotients and algebraicity of Hodge loci, pdf


Model Theory, Combinatorics and Valued Fields, A trimester at the Institut Henri Poincaré, 8 January - 6 April 2018


Articles et préprints

  1. Corrections de l'exemple 6.1 de l'article avec Hrushovski : The model theory of difference fields, (Trans. Amer. Math. Soc. 351 (1999), pp. 2997-3071) (Fév. 2000 - format dvi)
  2. Complément de l'article avec Hrushovski Asymptotic theories of differential fields (Illinois J. of Mathematics 47 Nr 3 (2003), 593 -- 618) : Exponential bounds for witnesses of diophantine definitions of $\Delta_0$-formulas (format dvi)
  3. Corrections de l'article Generic structures and simple theories (avec Anand Pillay), pdf
  4. A note on canonical bases and one-based types in supersimple theories, version publiée.
  5. (avec Charlotte Hardouin et Michael Singer) On the Definitions of Difference Galois Groups (pdf)
  6. (avec E. Hrushovski) Difference fields and descent in algebraic dynamics, I (pdf, ps) et II (pdf, ps).
  7. (avec E. Hrushovski) An invariant for difference field extensions, pdf.
  8. (avec E. Hrushovski) On subgroups of semi-abelian varieties defined by difference equations
  9. Model theory of difference fields and applications to algebraic dynamics, Proceedings of the Internal Congress of Mathematicians, Seoul 2014. Pages 1 -- 14.
  10. (avec D. Ghioca, D. Masser et G. Maurin) Unlikely, likely and impossible intersections without algebraic groups, version parue dans Rendiconti Lincei Matematica e Applicazione 24 (2013), 485 - 501. DOI 10.4171/RLM/663.
  11. Model theory of fields with operators -- a survey, dans: Logic without borders, Åsa Hirvonen et al. Ed., Ontos Mathematical Logic Vol. 5, De Gruyter 2015, 91 -- 113.
  12. (avec Matthew Harrison-Trainor et Rahim Moosa), Differential-algebraic jet spaces preserve internality to the constants. (Version parue au JSL)
  13. (avec Milan Perera), A criterion for p-henselianity in characteristic p, Bulletin of the Belgian Mathematical Society Simon Stevin, Vol. 24 (2017), No 1, 123 - 126.
  14. (avec Özlem Beyarslan), Geometric representation in the theory of pseudo-finite fields, J. Symb. Log. 82 (2017), no. 3, 1132 -- 1139.
  15. (avec E. Hrushovski) Revisiting virtual difference ideals, arXiv 2016.
  16. (avec Anand Pillay) Generalized Picard-Vessiot extension and diffential Galois cohomology, Arxiv 2017.
  17. Amalgamation of types in pseudo-algebraically closed fields and applications, arXiv 2017

Notes

  1. Cours de 3ème cycle: Théorie des modèles des corps finis et pseudo-finis (format postscript ou dvi)
  2. Exposés faits à l'Université de Tokay (Sept. 97): The model theory of difference fields (format postscript ou dvi)
  3. Cours de 3ème cycle (00-01): Théorie des Modèles : les outils classiques.(format dvi).
  4. Introduction to model theory (format dvi, pdf). These notes introduce very basic concepts of model theory. They contain some of the material of lectures given at Luminy (November 01). For those interested, I also wrote a model-theoretic treatment of limit groups, which you can obtain by clicking here (dvi).
  5. Model theory of difference fields, Notes d'un cours donné à l'Université de Notre Dame (South Bend, USA), en Septembre 2000 (format dvi et pdf). (Cette version n'est pas identique à la version publiée, en particulier, il faut ajouter 1 au numéro de section).
  6. Notes on the model theory of finite and pseudo-finite fields. Notes d'un mini-cours donné à l'Université Autonome de Madrid en novembre 2005 (format dvi ou ps).
  7. Slides (slightly expanded and corrected) of talk at ICMS, May 08.
  8. Cours de M2 : Théorie des Modèles des corps valués (printemps 2008).
  9. Notes de l'exposé Independence in (unbounded) PAC fields and imaginaries, Leeds, juin 08.
  10. Résumé détaillé de l'exposé Difference fields and descent of difference varieties, Leeds, mai 09. Version du 14/01/10.
  11. Notes on the model theory of finite and pseudo-finite fields. Notes d'un mini-cours donné à Helsinki en avril 2009 (similaire mais pas identique à celui donné à Madrid en 2005). Format dvi, ps ou pdf.
  12. Introductory notes on the model theory of valued fields. Notes d'un mini-cours donné à la Workshop Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry, mai 2008, (ICMS, Edinburg), format pdf.
  13. Preliminaries on Fields: une collection de résultats bien connus de théorie des modèles des corps provenant de sections préliminaires d'articles et mis ensemble. Version du 1er juillet 2011.
  14. Orsay workshop. Notes on lectures 1 - 4: Introduction to difference algebra and model theory; Groups definable in ACFA (version of 15 Dec 2011, final).
  15. Cours de logique, ENS, automne 2015.
  16. Notes on the model theory of finite and pseudo-finite fields. These notes arose from a 12 hour course given during the IMS 2018 Graduate Summer School in Logic, which was held at the National University of Singapore (18 June - 6 July 2018).


Liste de publications


This document was last modified on