Jacob Tsimerman of the Institute for Advanced Study presents a research talk given as part of the IAS workshop on Recent Developments in Hodge Theory and O-minimality. Starting from a family of varieties X over a base S, he builds the fiberwise quasi-period integrals and uses a flag variety to assemble a variation of mixed Hodge structures, producing a period map from S into a quotient D over Gamma. The talk addresses a precise technical question: can the original period integrals be recovered from the period map alone by taking derivatives? Tsimerman shows this recovery generally works, up to an algebraic closure, and characterizes the cases where it breaks down, with proofs relying on results from o-minimality. The work is joint with Bakker and Pila. This is a specialist seminar aimed at researchers in Hodge theory, algebraic geometry, and model theory, delivered at a blackboard level with no concessions to a general audience.