Galois Representations Courses and Certifications

Fields Institute

Abelian Arboreal Galois Representations

Explore abelian arboreal Galois representations in algebraic dynamics through advanced mathematical theory and applications in this specialized workshop presentation.

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

BIMSA

Modularity of Galois Representations

Explore advanced connections between Galois representations and modular forms in this specialized mathematics lecture by James Newton at ICBS2025.

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

Institut des Hautes Etudes Scientifiques (IHES)

On the Bloch-Kato Conjecture for Four-Dimensional Symplectic Galois Representations from Siegel Modular Forms

Explore the Bloch-Kato Conjecture for 4D symplectic Galois representations from Siegel modular forms, covering Selmer ranks, L-functions, and ramified cohomology classes.

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

Centre International de Rencontres Mathématiques

Galois Representations and Statistics - Lecture 1

Explore Galois representations and statistics in arithmetic through an advanced mathematical lecture by René Schoof.

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

BIMSA

Multivariable (φ, Γ)-Modules and Local-Global Compatibility

Explore multivariable $(\varphi, \Gamma)$-modules, extending Colmez's construction to $\mathrm{GL}_2(K)$ representations and comparing with Galois representations in mod $p$ cohomology of Shimura curves.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Aspects of the p-adic Locally Analytic Langlands Program

Explore geometric aspects of p-adic Langlands program, focusing on locally analytic representations as sheaves on variants of Fargues-Scholze's stack of G-bundles.

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

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Aspects of the p-adic Locally Analytic Langlands Correspondence III

Explore geometric aspects of p-adic Langlands correspondence, focusing on moduli stacks of Galois representations and their geometric properties in this advanced mathematical lecture.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Geometric Aspects of the p-adic Locally Analytic Langlands Program

Explore geometric aspects of p-adic Langlands program, focusing on locally analytic representations as sheaves on variants of Fargues-Scholze's stack of G-bundles.

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

Centre International de Rencontres Mathématiques

A Geometric Realization of Affine Hecke Algebras - Lecture 1

Explore geometric realization of affine Hecke algebras through equivariant K-theory of Steinberg varieties, covering Springer resolution and Deligne-Langlands classification.

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

Centre International de Rencontres Mathématiques

A Geometric Realization of Affine Hecke Algebras - Lecture 3

Explore geometric realization of affine Hecke algebras through equivariant K-theory of Steinberg varieties, covering Springer resolution and Deligne-Langlands classification.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Geometric Sen Theory, Locally Analytic Representations and the Completed Cohomology of Shimura Varieties - Lecture 3

Explore advanced methods for analyzing locally analytic vectors in completed cohomology of Shimura varieties through geometric Sen theory and recent mathematical developments.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Geometric Sen Theory, Locally Analytic Representations and the Completed Cohomology of Shimura Varieties - Lecture 2

Explore advanced methods for analyzing locally analytic vectors in completed cohomology of Shimura varieties through geometric Sen theory and recent mathematical developments.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Deformations of Reducible Galois Representations with Large Selmer p-Rank

Explore advanced deformations of reducible Galois representations and their connection to large Selmer p-rank in this specialized number theory lecture by Eknath Ghate.

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

Fields Institute

Hypergeometric Functions, Galois Representations, and Modular Forms

Explore connections between hypergeometric functions, Galois representations, and modular forms in advanced number theory and algebraic geometry.

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

Simons Foundation

On the Bloch–Kato Conjecture for Some Four-Dimensional Symplectic Galois Representations - March 14, 2025

Delve into Naomi Sweeting's exploration of the Bloch-Kato Conjecture for four-dimensional symplectic Galois representations, examining the relationship between Selmer ranks and L-function vanishing orders through ramified Galois cohomology classes.

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