p-adic Values of G-functions and Unlikely Intersections

The Zilber-Pink conjecture is a far reaching and widely open conjecture in the area of "unlikely intersections" generalizing many previous results in the area, such as the recently established André-Oort conjecture. Recently the ``G-functions method'' of Y. André has been able to consistently establish the missing arithmetic result needed to establish cases of this conjecture for Shimura varieties. I will discuss how, using properties of the p-adic values of G-functions, we can get new insights on this conjecture in 2