Galois geometry

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

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

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 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

Galois theory: Algebraic closure

This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically

From playlist Galois theory

Jochen Koenigsmann : Galois codes for arithmetic and geometry via the power of valuation theory

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Algebra

Galois theory: Field extensions

This lecture is part of an online course on Galois theory. We review some basic results about field extensions and algebraic numbers. We define the degree of a field extension and show that a number is algebraic over a field if and only if it is contained in a finite extension. We use thi

From playlist Galois theory

Galois theory: Infinite Galois extensions

This lecture is part of an online graduate course on Galois theory. We show how to extend Galois theory to infinite Galois extensions. The main difference is that the Galois group has a topology, and intermediate field extensions now correspond to closed subgroups of the Galois group. We

From playlist Galois theory

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

Counting Galois representations - Frank Calegari

Members' Seminar Topic:Counting Galois representations Speaker: Frank Calegari Affiliation: University of Chicago Date: November 4, 2016 For more video, visit http://video.ias.edu

From playlist Mathematics

11/08/18 Frank Sottile

Galois Groups for Systems of Equations

From playlist Fall 2018 Symbolic-Numeric Computing

SummerSchool 20060724 1130 Starr - Tsen-Lang theorem

From playlist Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"

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

John Voight, Belyi maps in number theory: a survey

VaNTAGe Seminar, August 17, 2021 License CC-BY-NC-SA

From playlist Belyi maps and Hurwitz spaces

Victoria Hoskins: Group actions on quiver moduli spaces and applications

Abstract: We study two types of actions on King’s moduli spaces of quiver representations over a field k, and we decompose their fixed loci using group cohomology in order to give modular interpretations of the components. The first type of action arises by considering finite groups of qui

From playlist Algebraic and Complex Geometry

John Thompson and Jacques Tits - The Abel Prize interview 2008

0:21 Interest in and contributions to mathematics in childhood / early youth 3:56 Group theory and Niels Henrik Abel 5:46 Why simple groups are important for classification for finite groups in general - Decomposition theorem 6:52 Group theory: Peter Ludwig Mejdell Sylow and Sophus Lie 7:2

From playlist John Griggs Thompson

Jean-Pierre Serre: How to prove that Galois groups are "large"

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Number Theory

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

SummerSchool 20060726 1000 Darmon - Faltings' Theorem II

From playlist Clay Mathematics Institute Summer School 2006 on "Arithmetic geometry"