Log Symplectic Pairs and Mixed Hodge Structures

Explore a 54-minute lecture on log symplectic pairs and mixed Hodge structures presented by Andrew Harder from Lehigh University. Delve into the relationship between log symplectic pairs and degenerations of hyperkaehler varieties, focusing on a specific class called "pure weight" log symplectic pairs. Examine how the classification of these pairs relates to log Calabi-Yau surfaces. Investigate topics such as degenerations of K3 surfaces, mixed Hodge structures, and their generalization to higher dimensions. Learn about good degenerations, cohomology of log symplectic pairs, and the extension to LMHS. Discover new examples derived from existing ones, including those obtained by blowing up toric varieties.

Intro
Outline
Degenerations of K3 surfaces
Distinguishing features
Log Calabi-Yau surfaces
Mixed Hodge structure
Generalization to higher dimensions
Goals
Good degenerations
Consequences
Cohomology of log symplectic pairs of pure weight 2
Definition
Extension to LMHS
New examples from old examples
Blowing up toric varieties