Effective integrality results in arithmetic dynamics

2:00pm, Wednesday, 11th October

Abstract

Through an analogy between torsion points on abelian varieties and preperiodic points of rational functions, problems in unlikely intersections motivated S. Ih to conjecture the finiteness of preperiodic points for a rational function, defined over a number field, which satisfy a certain integrality condition. This conjecture remains open, but equidistribution theorems, which provide a deep connection between geometry and dynamics, have led to partial results. Namely, the conjecture has been proved in the case of some special maps, and under certain local conditions. I will discuss how to make these results effective, and how they can be extended to the more general setting of a rational semigroup.