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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 13 janvier 2017, 11h

Lieu : ENS, salle W

Wilkie's conjecture for restricted elementary functions

Gal Binyamini (Weizmann Institute of Science)

Let X be a set definable in some o-minimal structure. The Pila-Wilkie theorem (in its basic form) states that the number of rational points in the transcendental part of X grows sub-polynomially with the height of the points. The Wilkie conjecture stipulates that for sets definable in R_exp, one can sharpen this asymptotic to polylogarithmic. I will describe a complex-analytic approach to the proof of the Pila-Wilkie theorem for subanalytic sets. I will then discuss how this approach leads to a proof of the `restricted Wilkie conjecture', where we replace R_exp by the structure generated by the restrictions of exp and sin to the unit interval (both parts are joint work with Dmitry Novikov). If time permits I will discuss possible generalizations and applications.


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