Title: Variation of canonical height and equidistribution
Speaker: Laura DeMarco
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:
In the 1990s, Ullmo and Zhang independently proved the Bogomolov Conjecture, about the geometry of points of small canonical height on abelian varieties; a key ingredient was an equidistribution statement for these points (that they proved jointly with Szpiro). Shortly after, Zhang posed a series of questions extending this conjecture to families of abelian varieties. In joint work with Myrto Mavraki, we solve this problem in the setting where A has dimension 2 and splits as a product of elliptic curves. There are three key ingredients: (1) Silverman's work on variation of canonical height, (2) an equidistribution theorem of Chambert-Loir, Thuillier, and Yuan, and (3) the work of Masser and Zannier treating the points of height 0.Date: Monday, September 26, 2016