Hodge Theory Courses and Certifications

International Centre for Theoretical Sciences

Topics in Hodge Theory - 2023

Explore advanced mathematical concepts connecting differential geometry, algebraic dynamics, and transcendental methods through expert lectures on Torelli maps, Arakelov theory, and holomorphic forms.

• YouTube
• 20 hours 11 minutes
• On-Demand
• Free Video

Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 6

Explore advanced concepts in o-minimality and their applications to Hodge Theory in this graduate-level lecture by Jacob Tsimerman from the University of Toronto.

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

Fields Institute

Applications of O-minimality to Hodge Theory - Lecture 1

Explore o-minimality's applications in Hodge Theory, delving into advanced mathematical concepts and their interconnections in this graduate-level lecture by Jacob Tsimerman.

• YouTube
• 1 hour 41 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Hodge Theory for the Conservativity Conjecture

Explore Hodge theory's application to the conservativity conjecture in algebraic geometry and number theory with Joseph Ayoub's insightful lecture.

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

Fields Institute

Hodge Theory and Some Questions About 2x2 Matrices

Explore Hodge theory and intriguing questions about 2x2 matrices in this advanced mathematical lecture by Daniel Litt from the University of Toronto.

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

IMSA

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

Explores Hodge theory, Higgs bundles, and their applications to moduli spaces and hyperbolicity, focusing on complex geometry and variation of Hodge structures.

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

IMSA

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

Explores connections between Hodge theory, Higgs bundles, and moduli spaces, focusing on geometric properties of log spaces and variations of Hodge structures in complex manifolds.

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

IMSA

Tame Geometry and Hodge Theory II

Explores applications of tame geometry in Hodge theory, covering algebraization results, tameness of period maps, functional transcendence, and atypical intersection conjectures in complex algebraic geometry.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

International Mathematical Union

Hodge Theory, Between Algebraicity and Transcendence

Explore recent advances in Hodge theory, comparing algebraic structures and bounding transcendence using o-minimal geometry. Gain insights into complex algebraic varieties and their applications.

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

IMSA

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

Explore o-minimal geometry, definable GAGA, and Griffiths Conjecture in algebraic geometry. Learn about definable analytic spaces, Oka coherence, and their applications to period maps and variations of mixed Hodge structures.

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

IMSA

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.

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

Institut des Hautes Etudes Scientifiques (IHES)

Birational and Singularity Invariants from Non-Commutative Hodge Theory

Explore new additive invariants of smooth projective varieties called Hodge atoms, their applications to birational equivalence, and novel singularity invariants in algebraic geometry.

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

Institute for Advanced Study

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.

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

BunG Seminar

Moduli Spaces in p-adic Non-abelian Hodge Theory

Delve into p-adic non-abelian Hodge theory through geometric moduli spaces, exploring Higgs bundles, pro-étale vector bundles, and their relationships to Simpson correspondence.

• YouTube
• 2 hours 11 minutes
• On-Demand
• Free Video

Stony Brook Mathematics

Hodge Theory and Lagrangian Fibrations in Holomorphic Symplectic Manifolds

Explore Hodge theory and Lagrangian fibrations in holomorphic symplectic manifolds. Delve into conjectures, isomorphisms, and decomposition theorems in this advanced mathematical discourse.

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