Logarithmic Geometry and Hodge Theory -

Ben Bakker explained to us how to construct moduli spaces of polarized Hodge structures, and then produced period maps associated to families of smooth projective varieties. However, in practice one often encounters a family of smooth varieties degenerating to a singular variety -- what can be done in such situations? We will introduce some concepts from logarithmic geometry to help understand these situations, and then give an example of Kato-Usui's moduli of logarithmic Hodge structures, and period maps involving them.