|Responsables :||Zoé Chatzidakis, Raf Cluckers, Silvain Rideau.|
|Email des responsables :||email@example.com|
Pour recevoir le programme par e-mail, écrivez à : zchatzid_at_dma.ens.fr.
|Orateur(s)||Hector Pasten - Pontificia Universidad Católica de Chile,|
|Titre||On non-Diophantine sets in rings of functions|
|Horaire||16:15 à 17:45|
For a ring R, a subset of a cartesian power of R is said to be Diophantine if it is positive existentially definable over R with parameters from R. In general, Diophantine sets over rings are not well-understood even in very natural situations; for instance, we do not know if the ring of integers Z is Diophantine in the field of rational numbers. To show that a set is Diophantine requires to produce a particular existential formula that defines it. However, to show that a set is not Diophantine is a more subtle task; in lack of a good description of Diophantine sets it requires to find at least a property shared by all of them. I will give an outline of some recent joint work with Garcia-Fritz and Pheidas on showing that several sets and relations over rings of polynomials and rational functions that are not Diophantine.
|Salle||Zoom, et salle 01|