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 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
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: 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
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
Galois theory: Splitting fields
This lecture is part of an online course on Galois theory. We define the splitting field of a polynomial p over a field K (a field that is generated by roots of p and such that p splits into linear factors). We give a few examples, and show that it exists and is unique up to isomorphism
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
CTNT 2020 - CM Points on Modular Curves: Volcanoes and Reality - Pete Clark
The Connecticut Summer School in Number Theory (CTNT) is a summer school in number theory for advanced undergraduate and beginning graduate students, to be followed by a research conference. For more information and resources please visit: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2020 - Conference Videos
Modern Algebra - Chapter 18: Subgroups
Redfield Chapter 18: Subgroups
From playlist Modern Algebra - Chapter 18
Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai
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
Padma Srinivasan, Computing exceptions primes for Galois representations of abelian surfaces
VaNTAGe Seminar on Dec 8, 2020 License CC-BY-NC-SA
From playlist ICERM/AGNTC workshop updates
Perfectoid spaces (Lecture 1) by Kiran Kedlaya
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
Barry Mazur - Logic, Elliptic curves, and Diophantine stability
This is the third lecture of the 2014 Minerva Lecture series at the Princeton University Mathematics Department. October 17, 2014 An introduction to aspects of mathematical logic and the arithmetic of elliptic curves that make these branches of mathematics inspiring to each other. Speci
From playlist Minerva Lectures - Barry Mazur
Models for Galois deformation rings - Brandon Levin
Workshop on Motives, Galois Representations and Cohomology Around the Langlands Program Topic: Models for Galois deformation rings Speaker: Brandon Levin Affiliation: University of Chicago Date: November 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Pete Clark, The torsion subgroup of a CM elliptic curve over a number field
VaNTAGe seminar, June 22, 2021 License CC-BY-NC-SA
From playlist Modular curves and Galois representations
Jeremy Rouse, l-adic images of Galois for elliptic curves over Q
VaNTAGe seminar, June 22, 2021 License: CC-BY-NC-SA
From playlist Modular curves and Galois representations
Visual Group Theory, Lecture 6.4: Galois groups
Visual Group Theory, Lecture 6.4: Galois groups The Galois group Gal(f(x)) of a polynomial f(x) is the automorphism group of its splitting field. The degree of a chain of field extensions satisfies a "tower law", analogous to the tower law for the index of a chain of subgroups. This hints
From playlist Visual Group Theory