Time: 10:00-11:00, Wednesday, June 24 2026
Venue: E14-212
Speaker: Francesco Tropeano
Title: Unlikely Intersections in Abelian Schemes
Abstract: Many natural questions in Diophantine Geometry can be phrased in terms of how special points occur on algebraic varieties. A guiding principle is that a variety should contain more special points than expected only if there is an underlying geometric reason. This philosophy is captured by the Zilber–Pink conjectures, which encompass classical results such as the Manin–Mumford and Mordell–Lang theorems. In this talk, I will introduce these ideas in the setting of families of abelian varieties and explain recent work establishing new cases of the conjecture for higher-dimensional subvarieties of abelian schemes. This is joint work with F. Barroero, L. Capuano, and T. Ge.
