we will discuss recent work with z. zhang on torelli theorems for bidouble covers of a smooth quintic curve and 2 lines in the plane, and cubic 4-folds arising from a cubic 3-fold and a hyperplane intersecting transversely in $p^4$. the talk for graduate 2022年亚洲世界杯预选赛 will be, ``abelian varieties and the torelli theorem''. i will explain what an abelian variety is, and discuss the torelli theorem for curves.