Phillip Griffiths is one of the foremost figures in Complex and Algebraic Geometry, with over 900 mathematical descendants and 150 influential books and articles. He is notably at the origin of Hodge Theory, a topic that has blossomed into one of the major currents of thought across many domains of modern mathematics and physics.Ludmil Katzarkov is a world leader in Mirror Symmetry, Symplectic Geometry, Mathematical Physics and Algebraic Geometry. He initiated higher-dimensional factorization theory, gave the first significant advance on the Shafarevich holomorphic convexity conjecture, and introduced the most modern generalized viewpoint on Homological Mirror Symmetry relating Algebraic and Symplectic Geometry.Carlos Simpson is a pioneer and main proponent of Nonabelian Hodge Theory, generalizing Griffiths’ theory to character varieties and nonabelian cohomology following Hitchin’s notion of Higgs bundle. He has also contributed to the theory of Higher Categories, and to the computer formalization of mathematical proofs.

• Preface.- Introduction.- The Coble-Mukai lattice from Q-Gorenstein deformations.- Hyperbolic geometry of moduli spaces of algebraic varieties via Hodge theory, and beyond.- Semistable reduction over thick log points.- Degeneration of Hodge structures on I-surfaces.- Foliations and stable maps.- Pseudoconvexity at infinity in Hodge theory: a codimension one example.- The model theory of canonical models of Shimura curves.- Moduli spaces on Kuznetsov components are irreducible symplectic varieties.- Mapping class groups of simply connected Kahler manifolds.- Hodge theory of degenerations, (II): vanishing cohomology and geometric applications.

Phillip Griffiths is one of the foremost figures in Complex and Algebraic Geometry, with over 900 mathematical descendants and 150 influential books and articles. He is notably at the origin of Hodge Theory, a topic that has blossomed into one of the major currents of thought across many domains of modern mathematics and physics.Ludmil Katzarkov is a world leader in Mirror Symmetry, Symplectic Geometry, Mathematical Physics and Algebraic Geometry. He initiated higher-dimensional factorization theory, gave the first significant advance on the Shafarevich holomorphic convexity conjecture, and introduced the most modern generalized viewpoint on Homological Mirror Symmetry relating Algebraic and Symplectic Geometry.Carlos Simpson is a pioneer and main proponent of Nonabelian Hodge Theory, generalizing Griffiths’ theory to character varieties and nonabelian cohomology following Hitchin’s notion of Higgs bundle. He has also contributed to the theory of Higher Categories, and to the computer formalization of mathematical proofs.

• Preface.- Introduction.- The Coble-Mukai lattice from Q-Gorenstein deformations.- Hyperbolic geometry of moduli spaces of algebraic varieties via Hodge theory, and beyond.- Semistable reduction over thick log points.- Degeneration of Hodge structures on I-surfaces.- Foliations and stable maps.- Pseudoconvexity at infinity in Hodge theory: a codimension one example.- The model theory of canonical models of Shimura curves.- Moduli spaces on Kuznetsov components are irreducible symplectic varieties.- Mapping class groups of simply connected Kahler manifolds.- Hodge theory of degenerations, (II): vanishing cohomology and geometric applications.

Phillip Griffiths is one of the foremost figures in Complex and Algebraic Geometry, with over 900 mathematical descendants and 150 influential books and articles. He is notably at the origin of Hodge Theory, a topic that has blossomed into one of the major currents of thought across many domains of modern mathematics and physics.Ludmil Katzarkov is a world leader in Mirror Symmetry, Symplectic Geometry, Mathematical Physics and Algebraic Geometry. He initiated higher-dimensional factorization theory, gave the first significant advance on the Shafarevich holomorphic convexity conjecture, and introduced the most modern generalized viewpoint on Homological Mirror Symmetry relating Algebraic and Symplectic Geometry.Carlos Simpson is a pioneer and main proponent of Nonabelian Hodge Theory, generalizing Griffiths’ theory to character varieties and nonabelian cohomology following Hitchin’s notion of Higgs bundle. He has also contributed to the theory of Higher Categories, and to the computer formalization of mathematical proofs.

• Preface.- Introduction.- The Coble-Mukai lattice from Q-Gorenstein deformations.- Hyperbolic geometry of moduli spaces of algebraic varieties via Hodge theory, and beyond.- Semistable reduction over thick log points.- Degeneration of Hodge structures on I-surfaces.- Foliations and stable maps.- Pseudoconvexity at infinity in Hodge theory: a codimension one example.- The model theory of canonical models of Shimura curves.- Moduli spaces on Kuznetsov components are irreducible symplectic varieties.- Mapping class groups of simply connected Kahler manifolds.- Hodge theory of degenerations, (II): vanishing cohomology and geometric applications.