Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds

Explore Hodge Theory and Lagrangian Fibrations in this comprehensive mathematics colloquium talk by Christian Schnell. Delve into the intricacies of holomorphic symplectic manifolds and their Lagrangian fibrations, examining the conjectures proposed by Junliang Shen, Qizheng Yin, and Davesh Maulik. Learn about Kähler manifolds, holomorphic 2-forms, and the properties of smooth fibers in n-dimensional abelian varieties. Investigate topics such as hard Lefschetz theorems, isomorphisms, symmetries, and decomposition theorems. Gain insights into the non-compact case, symplectic forms, complexes of sheaves, and chromology. Understand the borderline case and its implications for the field of algebraic geometry.

Introduction
My topic
Hodge theory
Hard left sheds
Isomorphism
Symmetries
Lagrangian vibrations
Schnells proof
Noncompact case
Smooth fibers
Decomposition theorem
symplectic form
complexes of sheaves
chromology
borderline case
Symmetry Explanation