Period Mappings at Infinity - Recent Developments I

Explore a comprehensive lecture on Period Mappings at Infinity and recent developments in the field. Delve into the intricate connections between Hodge theory, algebraic varieties, moduli spaces, algebraic groups, and period domains. Examine the classical nilpotent and sl2 orbit theorems as prototypical examples for understanding the asymptotic properties of period maps. Investigate how these theorems assign Hodge theoretic invariants to degenerations of smooth projective varieties and their applications in constructing and studying compactifications of moduli spaces. Learn about recent advancements in Hodge theory that extend beyond classical cases, particularly focusing on situations where the period domain is Hermitian and the infinitesimal period relation is trivial. Gain insights from the speaker's collaborative work with renowned mathematicians in expanding the applications of Hodge theory.