Log Symplectic Pairs and Mixed Hodge Structures
Explores log symplectic pairs, their connection to hyperkaehler variety degenerations, and classification of pure weight pairs. Discusses analogies with log Calabi-Yau surfaces and implications for mixed Hodge structures.
Mixed Period Maps: Definability and Algebraicity
Explore definable analytic spaces and their applications in algebraic geometry, focusing on period maps and mixed Hodge structures. Learn about o-minimal geometry and its role in proving key conjectures.
Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure
Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.
Period Mapping at Infinity
Explore Hodge theory's global study of period mapping at infinity, including new invariants, moduli space implications, and geometric insights for singular varieties.
Differential Equations and Mixed Hodge Structures
Explore the interplay between differential equations and mixed Hodge structures, focusing on periods, kappa series, and motific gamma in number theory and algebraic geometry.
Hecke Actions on Loops and Periods of Iterated Shimura Integrals
Exploration of Hecke actions on loops and periods of iterated Shimura integrals, focusing on SL_2(Z) and modular curves, with insights into mixed modular motives and Galois action.
Mixed Hodge Structures on Cohomology Jump Ideals
Explore mixed Hodge structures on cohomology jump ideals in representation varieties, extending Goldman and Millson's work to non-compact Kähler manifolds and variations of mixed Hodge structures.
L2 Invariants of Hodge Modules and Shafarevich Morphisms
Explore L2 invariants of Hodge Modules and Shafarevich morphisms, including L2 constructible cohomology and Mixed Hodge structures, with potential topological implications of linear Shafarevich conjecture.
Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture
Extension data analysis in mixed Hodge structures: capturing global family invariants and proving Shafarevich's Conjecture in the nilpotent case through monodromy and level 1-2 extensions.
A Guide to Variations of Mixed Hodge Structure - Generalities and Examples
Explore mixed Hodge structures, their variations, and computational methods using global monodromy and iterated integrals. Illustrates concepts with the elliptic KZB variation over the universal elliptic curve.
Extensions of Hodge Structure and Completions of Fundamental Groups
Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.
Hodge-Theoretic Aspects of Mirror Symmetry
Explores mirror symmetry for Fano varieties through Hodge theory, discussing Hodge diamond rotation, Katzarkov--Kontsevich--Pantev conjectures, and the mirror P=W conjecture in relation to mixed Hodge structures.
Archimedean Height Pairings for Higher Cycles
Explore archimedean height pairings for higher cycles, their interpretation as mixed Hodge structure invariants, and asymptotic behavior in Hodge-Tate variations.
Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models
Explores mixed Hodge structures in Landau-Ginzburg models, focusing on functorial behavior and a new spectral sequence relating decomposed functions, with applications in mirror symmetry.
Hodge Theory for Poisson Varieties and Nonperturbative Quantization
Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.
Hodge Theory for Non-Archimedean Analytic Spaces
Explore Hodge theory for non-Archimedean analytic spaces, extending Deligne's work and generalizing complex analytic constructions. Gain insights into K-analytic spaces and their cohomology groups.