Some problems arising from the Diophantine study of algebraic foliations
Seminar Room 1, Newton Institute
This survey talk will be devoted to various problems arising in the study of Diophantine properties of algebraic foliations.
Hopefully, I will explain (1) how algebraic foliations naturally enters into arithmetic geometry, (2) some known results established notably by means of Diophantine approximation techniques (concerning in particular the Grothendieck-Katz conjecture and its generalizations), and (3) discuss some Diophantine conjectures/problems, and some problems in (differential-)algebraic geometry arising from the use of Diophantine approximation techniques. This last part should present various issues where I expect model theory to be relevant.