NT seminar: Dynamics and small points in families of elliptic curves 

After describing Bogomolov's Conjecture (now a theorem following work of Zhang and Ullmo), I will give an analogous result in the setting of families of products of elliptic curves. Our work may be seen as a Bogomolov-type extension of theorems by Masser and Zannier in the theme of unlikely intersections. Key ingredients in our proof are Silverman's results on the variation of heights in elliptic families and an equidistribution theorem of Thuillier's along with complex-dynamical arguments. This is joint work with Laura DeMarco.