Mixed Hodge Structures Courses and Certifications

IMSA

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.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 54 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 57 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 33 minutes
• On-Demand
• Free Video

Fields Institute

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.

• YouTube
• 1 hour
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Galois Group of the Category of Mixed Hodge Tate Structures

Explore the Galois group of mixed Hodge-Tate structures, focusing on Tannakian formalism and the canonical description of the Hopf algebra in relation to graded comodules.

• YouTube
• 59 minutes
• On-Demand
• Free Video

IMSA

Differential Equations and Mixed Hodge Structures

Explores asymptotic Hodge theory, focusing on period-theoretic aspects through examples. Discusses motivic Gamma functions and their role in encoding invariants of variations of Hodge structures on P^1.

• YouTube
• 59 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

The Galois Group of the Category of Mixed Hodge-Tate Structures

Explore the Galois group of mixed Hodge-Tate structures, examining its Hopf algebra structure, derived category models, and applications to period theory in complex and p-adic settings.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Institute for Advanced Study

Cohomologically Tropical Varieties and Mixed Hodge Structures

Delve into advanced geometric concepts exploring tropicalizations of torus subvarieties, focusing on Poincaré duality and mixed Hodge structures in relation to hyperplane arrangements.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Nonabelian Mixed Hodge Structures

Explore nonabelian mixed Hodge structures, their relation to rational homotopy, and applications to character varieties and schematic homotopy types. Examine weights from noncompact bases and parabolic structures.

• YouTube
• 1 hour 38 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

IMSA

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.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video