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Mathematics
Hodge Theory

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Explore the foundations of Hodge theory, including its connections to moduli spaces, Higgs bundles, and algebraic geometry. Learn from leading mathematicians through accessible YouTube lectures, ideal for beginners interested in advanced mathematical concepts and their modern applications.

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IMSA
Positivity in Hodge Theory and Algebraic Geometry - Lecture 2

Delve into advanced concepts of Hodge theory, exploring bilinear relations, metrics in vector bundles, and their applications to period mappings in algebraic geometry through expert mathematical discourse.
- YouTube
- 1 hour
- On-Demand
- Free Video
IMSA
Positivity in Hodge Theory and Algebraic Geometry - Part 1

Delve into advanced concepts of Hodge theory, exploring bilinear relations, metrics in vector bundles, and their applications to period mappings in algebraic geometry through expert mathematical discourse.
- YouTube
- 1 hour 2 minutes
- On-Demand
- Free Video
IMSA
Infinitesimal Methods in Mixed Hodge Theory

Delve into advanced mathematical concepts exploring infinitesimal variations in mixed Hodge theory, with applications to Fano 3-folds and anticanonical surfaces.
- YouTube
- 57 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Introduction to Hodge Theory

Discover how Hodge structures encode integrals of algebraic differential forms over topological cycles, bridging transcendental operations with algebraic structures.
- YouTube
- 1 hour 10 minutes
- On-Demand
- Free Video
BIMSA
Nonlinear Hodge Theory in Positive Characteristic

Explore advanced nonlinear Hodge theory techniques and their applications in positive characteristic algebraic geometry through expert mathematical analysis.
- YouTube
- 1 hour 1 minute
- On-Demand
- Free Video
BIMSA
Hodge Theory of Kloosterman Connections

Explore advanced Hodge theory applications to Kloosterman connections in this specialized mathematical lecture by Javier Fresán.
- YouTube
- 1 hour 8 minutes
- On-Demand
- Free Video
BIMSA
Hodge Theory of p-adic Varieties

Explore advanced Hodge theory applied to p-adic varieties through expert mathematical analysis and theoretical frameworks.
- YouTube
- 1 hour
- On-Demand
- Free Video
BIMSA
Some Applications of Non-Abelian Hodge Theory

Explore advanced applications of non-abelian Hodge theory through expert mathematical insights and theoretical developments in this specialized lecture.
- YouTube
- 59 minutes
- On-Demand
- Free Video
IMSA
Lefschetz Devissage and Hodge Theory

Delve into Lefschetz devissage and Hodge theory, exploring complex algebraic varieties, hyperplane sections, monodromy representations, and variations of Hodge structure with Carlos Simpson.
- YouTube
- 1 hour 2 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Introduction to Non-abelian Hodge Theory

Discover Simpson's correspondence between complex local systems and semistable Higgs bundles, generalizing classical Hodge theory for smooth projective varieties.
- YouTube
- 1 hour 15 minutes
- On-Demand
- Free Video
Harvard CMSA
Tame Geometry and Hodge Theory

Discover applications of o-minimality in complex geometry and Hodge theory through an expert introduction to tame geometric structures and their mathematical foundations.
- YouTube
- 1 hour 40 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Introduction to Non-abelian Hodge Theory

Discover Simpson's correspondence between complex local systems and semistable Higgs bundles, generalizing classical Hodge theory for smooth projective varieties.
- YouTube
- 1 hour 11 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Introduction to Hodge Theory II

Explore Hodge structures and their role in algebraic geometry, focusing on cohomology groups, parameter spaces, and o-minimal definability in algebraic families.
- YouTube
- 1 hour 11 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Logarithmic Geometry and Hodge Theory

Explore logarithmic geometry concepts to understand degenerating families of varieties and Kato-Usui's moduli of logarithmic Hodge structures with period maps.
- YouTube
- 1 hour 8 minutes
- On-Demand
- Free Video
Institute for Advanced Study
Hodge Theory and Representations of Real Groups

Explore how Hodge structures from geometry solve complex problems in representation theory of real reductive groups, covering K-types, unitarity, and the Orbit Method.
- YouTube
- 1 hour 13 minutes
- On-Demand
- Free Video

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