Title: Periods of elliptic-elliptic surfaces

Abstract: We study the period map for elliptic surfaces with $p_g=q=1$. This class of elliptic surfaces is the last for which an infinitesimal Torelli statement was not known to hold at a generic member. Our main results are (1) that the period map is dominant, and (2) that its degree is > 1. Since the period domain in this context agrees with the period domain for self-mirror K3 surfaces, we obtain an interesting test case for the Hodge Conjecture. This is based on joint work with Philip Engel and Abigail Ward.