Hodge Theory Courses and Certifications

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

Explore Hodge theory and curvature properties with the University of Miami. Learn about Hodge metrics, rigidity results, and geometric classes in under an hour.

• YouTube
• 58 minutes
• On-Demand
• Free Online Course

Period Mapping at Infinity

Explore the global study of period mapping at infinity with the University of Miami. Learn about Hodge theory, mixed Hodge structures, and their applications in algebraic varieties.

• YouTube
• 54 minutes
• On-Demand
• Free Online Course

Unitary Representations of Reductive Lie Groups

Explore unitary representations of reductive Lie groups using Hodge theory in this less than 1-hour material from University of Miami.

• YouTube
• 48 minutes
• On-Demand
• Free Online Course

Minimal Exponents of Singularities

Explore the concept of minimal exponents of singularities with Harvard's Mihnea Popa in this 1-2 hour program offered by the University of Miami. Delve into D-modules, Hodge theory, and birational geometry.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Online Course

Fixed Points in Toroidal Compactifications and Essential Dimension of Covers

Explore algebraic object complexity with the University of Miami. Learn about essential dimensions, congruence covers of Shimura varieties, and new fixed point theorems in under an hour.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

A Non-Archimedean Definable Chow Theorem

Explore algebraization theorems and their applications in Diophantine geometry and Hodge theory in this less than 1-hour material from the University of Miami.

• YouTube
• 45 minutes
• On-Demand
• Free Online Course

Log Symplectic Pairs and Mixed Hodge Structures

Explore the relationship between log symplectic pairs and hyperkaehler varieties in this less than 1-hour material from the University of Miami. Dive into degenerations, cohomology, and more.

• YouTube
• 54 minutes
• On-Demand
• Free Online Course

O-Minimality and Hodge Theory - Definable GAGA + Griffiths Conjecture

Explore o-minimal geometry and Hodge theory in this series of lectures by the University of Miami. Learn about definable GAGA statements, Griffiths Conjecture, and more in just 1-2 hours.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Online Course

Mixed Period Maps: Definability and Algebraicity

Explore o-minimal geometry and its applications in proving Griffiths' conjecture in this short lecture series by the University of Miami.

• YouTube
• 56 minutes
• On-Demand
• Free Online Course

A Parallel Reality Look at Generalized Geometry

Explore generalized geometries and Hodge theory in a seminar by Ludmil Katzarkov from the University of Miami. Less than 1 hour workload.

• YouTube
• 55 minutes
• On-Demand
• Free Online Course

Hodge Theory, Higgs Bundles on Moduli Spaces of Manifolds and Hyperbolicity II

Explore Hodge Theory and Higgs Bundles in this under 1-hour material from the University of Miami. Delve into the geometry of log spaces, variation of Hodge structures, and Griffiths' curvature formula.

• YouTube
• 59 minutes
• On-Demand
• Free Online Course

Period Mappings at Infinity - Recent Developments II

Explore Hodge theory's link between algebraic varieties, groups, and period domains with Duke University's Colleen Robles in this 1-2 hour University of Miami offering.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Online Course

Comparing Geometric and Hodge-Theoretic Compactifications I

Explore geometric and Hodge-theoretic compactifications with the University of Miami. Delve into classical period domains, moduli spaces, and stable K3 surfaces in this 1-2 hour study.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Online Course

Volumes of Definable Sets in O Minimal Expansions and Affine GAGA Theorems

Explore the affine GAGA theorem and o-minimal methods with the University of Miami. Learn about their applications in Hodge theory in this 1-2 hour study.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Online Course

Periods and Moduli of Elliptic Surfaces I

Explore the derivative of the period map and the $j$-invariant of a Kaehler elliptic surface in this 1-2 hour study from the University of Miami.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Online Course