Galois Groups Courses and Certifications

Institute for Advanced Study

Introduction to Differential Galois Theory

Explore algebraic groups describing symmetries of differential equation systems using differentially closed fields and fundamental theorems.

• YouTube
• 1 hour 9 minutes
• On-Demand
• Free Video

NPTEL-NOC IITM

Solvable Groups: Polynomial Solvability and Galois Theory - Part 1

Explore solvable groups, their connection to polynomial solvability, and their applications in Galois theory and field theory.

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

NPTEL-NOC IITM

Galois Extensions and Galois Groups - Lecture 14

Explore Galois extensions and groups, delving into fundamental concepts and initial examples in algebraic theory.

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

Instituto de Matemática Pura e Aplicada

Galois Groups of D-finite Series Modulo Primes

Explore Galois groups of D-finite series modulo primes in this advanced mathematical presentation connecting differential equations with number theory concepts.

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

Fields Institute

The Charm and Mystery of Absolute Galois Groups

Explore the fascinating world of absolute Galois groups in this mathematical seminar by Ján Mináč, examining their charm and mysterious properties.

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

UC Berkeley

Mathematics: the Language of Nature

2 reviews

Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics.

• World Science U
• On-Demand
• Free Online Course

Fields Institute

Galois Groups of Lacunary Sparse Polynomial Systems

Explore Galois groups in lacunary sparse polynomial systems, examining their properties and applications in algebraic geometry and number theory.

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

Fields Institute

The Period-Index Problem for Higher Degree Galois Cohomology Groups Over Hensel Semi-Global Fields

Delve into advanced Galois cohomology theory, exploring period-index relationships over Hensel semi-global fields and their implications for higher degree groups.

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

Hausdorff Center for Mathematics

Computability Questions About Infinite Galois Groups

Explore computability theory applied to infinite Galois groups through tree representations, examining decidability properties and complexity differences between finite fields and ℚ.

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

Hausdorff Center for Mathematics

Computability Questions About Infinite Galois Groups

Explore computability theory applied to infinite Galois groups through tree representations, examining decidability properties and complexity measures for algebraic field extensions.

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

Chennai Mathematical Institute;  NPTEL

Introduction to Galois Theory

Explore algebraic structures, field extensions, and Galois groups. Delve into fundamental theorems and applications like insolvability of quintics and cyclotomic extensions.

• Swayam
• 8 weeks
• On-Demand
• Free Online Course

Mathemaniac

Why You Can't Solve Quintic Equations - Galois Theory Approach

Explore the fascinating world of Galois theory and discover why quintic equations can't be solved using a formula, with insights accessible to math enthusiasts of all levels.

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

Institut des Hautes Etudes Scientifiques (IHES)

Weil Anima - 2/4

Explore advanced refinements of the Weil group through homotopy-theoretic methods, connecting Galois representations to automorphic forms and the Langlands program.

• YouTube
• 2 hours 3 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Weil Anima - 1/4

Explore homotopy-theoretic refinements of the Weil group in number theory, addressing deficiencies in Galois representations and their connections to automorphic forms and Langlands program.

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

Hausdorff Center for Mathematics

The Galois Group of the Category of Mixed Hodge Tate Structures

Explore the Galois group of mixed Hodge-Tate structures, focusing on Tannakian formalism and the canonical description of the Hopf algebra in relation to graded comodules.

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