Around the Dynamical Mordell–Lang conjecture (3/17)

par M. Quang-Khai Nguyen

lundi 2 nov. 2026, 10:30 → 11:30 Europe/Paris

Fokko du Cloux (Institut Camille Jordan)

The Dynamical Mordell-Lang conjecture is one of three important orbit conjectures in arithmetic dynamics. It predicts that, given an endomorphism f of a quasi-projective variety X over a field of characteristic 0, a point p in X, and a subvariety V of X, the return set of n such that f^n(p) is in V is a union of at most finitely many arithmetic progressions. This conjecture is inspired by the Mordell-Lang conjecture on subvarieties of semiabelian varieties, hence the name. It is also motivated by the Skolem-Mahler-Lech Theorem on linear recurrence sequences. This talk will present some examples, the methods used to study this problem, and some results. If time permits, we will discuss recent variants of this conjecture (positive characteristic, higher dimensional generalizations, etc.).