Period Mapping at Infinity

Explore a 54-minute lecture on Period Mapping at Infinity delivered by Philip Griffiths from the Institute for Advanced Study and University of Miami. Delve into the global study of period mapping in algebraic families of smooth varieties and its extension to singular varieties. Discover how the extension data associated with limiting mixed Hodge structures provides a powerful tool for studying families of singular varieties at the boundary of smooth variety families. Learn about new global invariants of limiting mixed Hodge structures, implications for moduli spaces, and a proposed construction of toroidal compactification for period mapping images. Gain insights into the rich geometric structure of extension data and its significance in understanding singular varieties. Follow the lecture's progression through introductory concepts, definitions, mixed Hodge structures, special structures, basic results, geometric cases, natural completions, and relevant references in this collaborative work with Mark Green and Colleen Robles.

Introduction
Outline
Definitions
Mixed Hodge Structures
Special Structures
Basic Results
Geometric Case
Natural Completions
References