|Abstract:||Solving polynomial equations in integers or algebraic integers
x,y,... is far too hard, so one might try to solve for example with
x a power of 2, y a power of 3,... This problem when suitably
generalized is associated with the names of Mordell-Lang. Or one might try
to solve in roots of unity, a problem similarly associated with
Manin-Mumford. Both of these topics are fairly well understood.
Independently Zilber in 2002 and Pink in 2005 used a concept of unlikely
intersections to create a common generalization going far beyond the union
of both topics. In fact some related work started already in 1999 and
since then there has been enormous progress, particularly in the last two
years. We shall give a short introduction.