Period Mappings at Infinity - Recent Developments II

Explore recent developments in period mappings at infinity in this advanced mathematics lecture. Delve into Hodge theory's role in connecting algebraic varieties, moduli, algebraic groups, and associated representations. Examine the framework for understanding asymptotic properties of period maps, focusing on classical nilpotent and sl2 orbit theorems. 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 work expanding Hodge theory beyond classical cases, covering joint research with prominent mathematicians in the field. Gain insights into the challenges and progress made in applying these concepts beyond the traditional settings of principally polarized abelian varieties (ppav) and K3 surfaces.