David Masser

University Basel
Title:Unlikely Intersections
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.