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
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
15 - Algorithmic aspects of the Galois theory in recent times
Orateur(s) : M. Singer Public : Tous Date : vendredi 28 octobre Lieu : Institut Henri Poincaré
From playlist Colloque Evariste Galois
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
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
Title: Consistent Systems of Linear Differential and Difference Equations April 2016 Kolchin Seminar Workshop
From playlist April 2016 Kolchin Seminar Workshop
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
Michael Singer - Walks, Difference Equations and Elliptic Curves [2017]
Slides for this talk: http://www.birs.ca//workshops//2017/17w5090/files/Singer.pdf Michael Singer, North Carolina State University Thursday, September 21, 2017 09:00 - 10:03 Walks, Difference Equations and Elliptic Curves Video taken from: http://www.birs.ca/events/2017/5-day-workshops/1
From playlist Mathematics
Finiteness theorems for Kolchin's constrained cohomology
By Anand Pillay, University of Notre Dame Finiteness theorems for Kolchin's constrained cohomology Kolchin Seminar, CUNY Graduate Center, October 4, 2019
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Reid Dale Talk 1 9/16/16 Part 2
Title: An Introduction to Pillay's Differential Galois Theory (Part 1)
From playlist Fall 2016
11/22/2019, Thomas Dreyfus, Université de Strasbourg
Thomas Dreyfus, Université de Strasbourg Differential transcendence of solutions of difference equations (remote presentation) A function is said to be differentially algebraic if it satisfies a non trivial algebraic differential equation. It is said to be differentially transcendent oth
From playlist Fall 2019 Kolchin Seminar in Differential Algebra
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
Introduction to p-adic Hodge theory (Lecture 3) 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) Eknath
From playlist Perfectoid Spaces 2019
John Coates: (1/4) Classical algebraic Iwasawa theory [AWS 2018]
slides for this lecture: http://swc-alpha.math.arizona.edu/video/2018/2018CoatesLecture1Slides.pdf lecture notes: http://swc.math.arizona.edu/aws/2018/2018CoatesNotes.pdf CLASSICAL ALGEBRAIC IWASAWA THEORY. JOHN COATES If one wants to learn Iwasawa theory, the starting point has to be t
From playlist Number Theory
Michael Harris "Shimura varieties and the search for a Langlands transform" [2012]
Michael Harris, Institut de mathématiques de Jussieu "Shimura varieties and the search for a Langlands transform" The Langlands reciprocity conjectures predict the existence of a correspondence between certain classes of representations of Galois groups of number fields and automorphic re
From playlist Number Theory
This lecture is part of an online graduate course on Galois theory. We define the discriminant of a finite field extension, ans show that it is essentially the same as the discriminant of a minimal polynomial of a generator. We then give some applications to algebraic number fields. Corr
From playlist Galois theory
Umberto Zannier - Ambients for the Betti map and the question of its rank
November 16, 2017 - This is the final talk of a series of three Fall 2017 Minerva Lectures In this last lecture we shall further consider some of the mentioned contexts involving the Betti map. We shall also discuss in short some recent work with Yves André and Pietro Corvaja, where we obt
From playlist Minerva Lectures Umberto Zannier