Fundamental theorem of Galois theory

FIT4.3. Galois Correspondence 1 - Examples

Field Theory: We define Galois extensions and state the Fundamental Theorem of Galois Theory. Proofs are given in the next part; we give examples to illustrate the main ideas.

From playlist Abstract Algebra

Galois theory: Fundamental theorem of algebra

This lecture is part of an online graduate course on Galois theory. We use Galois theory to give a (mostly) algebraic proof that the complex numbers form an algebraically closed field.

From playlist Galois theory

Visual Group Theory, Lecture 6.6: The fundamental theorem of Galois theory

Visual Group Theory, Lecture 6.6: The fundamental theorem of Galois theory The fundamental theorem of Galois theory guarantees a remarkable correspondence between the subfield lattice of a polynomial and the subgroup lattice of its Galois group. After illustrating this with a detailed exa

From playlist Visual Group Theory

Galois theory: Introduction

This lecture is part of an online course on Galois theory. This is an introductory lecture, giving an informal overview of Galois theory. We discuss some historical examples of problems that it was used to solve, such as the Abel-Ruffini theorem that degree 5 polynomials cannot in genera

From playlist Galois theory

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Galois theory: Main theorem

This lecture is part of an online graduate course on Galois theory. We prove the main theorem of Galois theory, given a bijection between subgroups of a Galois group and subextensions of a Galois extension. We illustrate it with the example of the splitting field of 4th roots of 2.

From playlist Galois theory

Galois theory II | Math History | NJ Wildberger

We continue our historical introduction to the ideas of Galois and others on the fundamental problem of how to solve polynomial equations. In this video we focus on Galois' insights into how extending our field of coefficients, typically by introducing some radicals, the symmetries of the

From playlist MathHistory: A course in the History of Mathematics

FIT4.1. Galois Group of a Polynomial

EDIT: There was an in-video annotation that was erased in 2018. My source (Herstein) assumes characteristic 0 for the initial Galois theory section, so separability is an automatic property. Let's assume that unless noted. In general, Galois = separable plus normal. Field Theory: We

From playlist Abstract Algebra

Galois theory I | Math History | NJ Wildberger

Galois theory gives a beautiful insight into the classical problem of when a given polynomial equation in one variable, such as x^5-3x^2+4=0 has solutions which can be expressed using radicals. Historically the problem of solving algebraic equations is one of the great drivers of algebra,

From playlist MathHistory: A course in the History of Mathematics

Kevin Buzzard (lecture 2/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

Aaron Silberstein - Plane Curve Singularities and the Absolute Galois Group of Q

Plane Curve Singularities and the Absolute Galois Group of Q

From playlist Center of Math Research: the Worldwide Lecture Seminar Series

Richard Taylor "Reciprocity Laws" [2012]

Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu

From playlist Number Theory

Francis Brown - 4/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)

In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of

From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)

Kevin Buzzard (lecture 4/20) Automorphic Forms And The Langlands Program [2017]

Full course playlist: https://www.youtube.com/playlist?list=PLhsb6tmzSpiysoRR0bZozub-MM0k3mdFR http://wwwf.imperial.ac.uk/~buzzard/MSRI/ Summer Graduate School Automorphic Forms and the Langlands Program July 24, 2017 - August 04, 2017 Kevin Buzzard (Imperial College, London) https://w

From playlist MSRI Summer School: Automorphic Forms And The Langlands Program, by Kevin Buzzard [2017]

Introduction to p-adic Hodge theory (Lecture 1) by Denis Benois

PERFECTOID SPACES ORGANIZERS : Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri and Narasimha Kumar Cheraku DATE & TIME : 09 September 2019 to 20 September 2019 VENUE : Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknat

From playlist Perfectoid Spaces 2019

Francis Brown - 1/4 Mixed Modular Motives and Modular Forms for SL_2 (\Z)

In the `Esquisse d'un programme', Grothendieck proposed studying the action of the absolute Galois group upon the system of profinite fundamental groups of moduli spaces of curves of genus g with n marked points. Around 1990, Ihara, Drinfeld and Deligne independently initiated the study of

From playlist Francis Brown - Mixed Modular Motives and Modular Forms for SL_2 (\Z)

Winnie Li: Unramified graph covers of finite degree

Abstract: Given a finite connected undirected graph X, its fundamental group plays the role of the absolute Galois group of X. The familiar Galois theory holds in this setting. In this talk we shall discuss graph theoretical counter parts of several important theorems for number fields. T

From playlist Women at CIRM

The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg

In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t

From playlist Algebraic Calculus One