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#Mixed Hodge Structures

Showing: 16 courses
IMSA

Log Symplectic Pairs and Mixed Hodge Structures

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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.
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15 Lesons
54 minutes
On-Demand
Free-Video
IMSA

Mixed Period Maps: Definability and Algebraicity

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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.
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14 Lesons
56 minutes
On-Demand
Free-Video
IMSA

Holomorphic Bisectional Curvature and Applications to Deformations and Rigidity of Mixed Hodge Structure

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Explore holomorphic bisectional curvature in Hodge theory, focusing on mixed Hodge metrics, rigidity results, and applications to geometric examples.
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15 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Period Mapping at Infinity

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Explore Hodge theory's global study of period mapping at infinity, including new invariants, moduli space implications, and geometric insights for singular varieties.
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9 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Differential Equations and Mixed Hodge Structures

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Explore the interplay between differential equations and mixed Hodge structures, focusing on periods, kappa series, and motific gamma in number theory and algebraic geometry.
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10 Lesons
1 hour
On-Demand
Free-Video
IMSA

Hecke Actions on Loops and Periods of Iterated Shimura Integrals

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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.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Mixed Hodge Structures on Cohomology Jump Ideals

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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.
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1 Lesons
57 minutes
On-Demand
Free-Video
IMSA

L2 Invariants of Hodge Modules and Shafarevich Morphisms

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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.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
IMSA

Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture

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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.
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1 Lesons
33 minutes
On-Demand
Free-Video
IMSA

A Guide to Variations of Mixed Hodge Structure - Generalities and Examples

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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.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
IMSA

Extensions of Hodge Structure and Completions of Fundamental Groups

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Explore extensions of mixed Hodge structures, unipotent and relative completions of fundamental groups, and their geometric interpretations in L-functions and motives theory.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Hodge-Theoretic Aspects of Mirror Symmetry

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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.
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1 Lesons
55 minutes
On-Demand
Free-Video
IMSA

Archimedean Height Pairings for Higher Cycles

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Explore archimedean height pairings for higher cycles, their interpretation as mixed Hodge structure invariants, and asymptotic behavior in Hodge-Tate variations.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Mixed Hodge Structures Attached to Hybrid Landau–Ginzburg Models

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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.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
IMSA

Hodge Theory for Poisson Varieties and Nonperturbative Quantization

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Explore Hodge theory for Poisson varieties and nonperturbative quantization, focusing on K-theory and mixed Hodge structures to simplify complex calculations in deformation quantization.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institute for Advanced Study

Hodge Theory for Non-Archimedean Analytic Spaces

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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.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video