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Tame geometry and diophantine approximation

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Tame geometry and diophantine approximation

Tame geometry is the study of structures where the definable sets admit finite complexity. Around 15 years ago Pila and Wilkie discovered a deep connection between tame geometry and diophantine approximation, in the form of asymptotic estimates on the number of rational points in a tame set (as a function of height). This later led to deep applications in diophantine geometry, functional transcendence and Hodge theory.I will describe some conjectures and a long-term project around a more effective form of tame geometry, suited for improving the quality of the diophantine approximation results and their applications. I will try to outline some of the pieces that are already available, and how they should conjecturally fit together. Finally I will survey some applications of the existing results around the Manin-Mumford conjecture, the Andre-Oort conjecture, Galois-orbit lower bounds in Shimura varieties, unlikely intersections in group schemes, and some other directions (time permitting).

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Gal Binayamini
Date : 16 octobre 2020
Horaire : 10h30 - 11h50
Lieu : Zoom