Dragos Ghioca

Given an abelian variety G defined over a field of characteristic 0, the intersection between a subvariety X of G with another subvariety Y of G for which dim(X) + dim(Y) dim(G) is generally expected to be empty. Rooted in this basic observation...

We present various results and conjectures regarding unlikely intersections of orbits for families of Drinfeld modules. Our questions are motivated by the groundbreaking result of Masser and Zannier (from 15 years ago) regarding torsion points in...

Starting from a classical result of Skolem, Mahler and Lech for linear recurrence sequences, we present an algebraic geometric generalization of it. Then we interpret our result from the point of view of dynamics, linking it with the Mordell-Lang...

Abstract: In early 1960's, Lang proved that if for a given polynomial G(X,Y) with complex coefficients, there exist infinitely many pairs (x,y) where both x and y are roots of unity such that G(x,y) = 0, then essentially G(X,Y) = X^mY^n - c, for some...