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Explore logarithmic geometry concepts and their applications to Hodge theory in this mathematical seminar from the Institute for Advanced Study. Learn how logarithmic geometry provides tools for understanding families of smooth varieties that degenerate to singular varieties, extending beyond the classical case of smooth projective varieties. Discover Kato-Usui's construction of moduli spaces for logarithmic Hodge structures and examine period maps in this more general setting. Build upon foundational knowledge of moduli spaces of polarized Hodge structures and period maps for smooth families to tackle the challenging case of degenerating families. Gain insight into advanced techniques that bridge algebraic geometry and Hodge theory through the logarithmic framework.
