Watch a lecture series where Professor Phillip Griffiths explores the intricate relationship between Hodge theory and algebraic geometry, focusing on how Hodge-Riemann bilinear relations define metrics in vector bundles associated with polarized Hodge structures. Delve into the geometric and analytic properties of these metrics' curvatures, examining their crucial role in proving fundamental results about cohomology variation in algebraic variety families. Learn about these concepts through the lens of global differential geometry of period mappings, presented across two comprehensive sessions that illuminate the mathematical connections between these advanced theoretical frameworks.