Hodge Theory Courses and Certifications

IMSA

Period Mappings at Infinity - Recent Developments II

Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases of ppav and K3s.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

IMSA

Period Mappings at Infinity - Recent Developments I

Explores recent advancements in Hodge theory, focusing on asymptotic properties of period maps and their applications to moduli spaces beyond classical cases like ppav and K3s.

• YouTube
• 59 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

IMSA

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.

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

IMSA

Unitary Representations of Reductive Lie Groups

Explore unitary representations of reductive Lie groups using Hodge theory, including progress on a conjecture. Joint work with Kari Vilonen presented by Harvard's Wilfried Schmid.

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

IMSA

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.

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

IMSA

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.

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

IMSA

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.

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

Hausdorff Center for Mathematics

Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry

Explore p-adic geometry through Riemann-Hilbert correspondence, covering local systems, Galois representations, Hodge theory, and cohomology in this advanced mathematics lecture.

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

IMSA

A Parallel Reality Look at Generalized Geometry

Explore generalized geometries and related "Hodge theory" through a fresh perspective, building on classical works by Donaldson and Simpson in this advanced mathematics seminar.

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

Institut des Hautes Etudes Scientifiques (IHES)

Vanishing Theorems for the Irregular Hodge Filtration

Explore recent advances in irregular Hodge filtration, focusing on Kodaira vanishing theorems similar to Saito's for mixed Hodge modules.

• YouTube
• 1 hour 9 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

IMSA

Introduction to Variations of Hodge Structures

Explore the foundational concepts of variations of Hodge structures, preparing you for advanced mathematical understanding in this specialized field of study.

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

Institute for Advanced Study

Non-abelian Rees Construction and Motives

Explore non-abelian generalizations of the Rees construction in algebraic geometry, connecting prehomogeneous spaces to monoidal categories with applications to motives.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Harvard CMSA

Degrees of Hodge Loci

Explore the geometric properties and computational aspects of Hodge loci through advanced mathematical analysis in this specialized geometry and physics seminar.

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