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
This lecture is part of an online graduate course on Lie groups. This lecture is about Lie's theorem, which implies that a complex solvable Lie algebra is isomorphic to a subalgebra of the upper triangular matrices. . For the other lectures in the course see https://www.youtube.com/playl
From playlist Lie groups
We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at
From playlist Abstract algebra
David Zureick-Brown, Moduli spaces and arithmetic statistics
VaNTAGe seminar on March 3, 2020 License: CC-BY-NC-SA Closed captions provided by Andrew Sutherland.
From playlist Class groups of number fields
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
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
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
Differential Isomorphism and Equivalence of Algebraic Varieties Board at 49:35 Sum_i=1^N 2/(x-phi_i(y,t))^2
From playlist Fall 2017
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
Theorem 1.10 - part 10.1 - Serre Tate's Neron-Ogg-Shafarevich
This video is the first of four videos about the Neron-Ogg-Shafarevich Theorem regarding good reduction at p of Abelian Varieties and its relation to the ramification of the l-adic Tate module.
From playlist Theorem 1.10
Bjorn Poonen, Heuristics for the arithmetic of elliptic curves
VaNTAGe seminar on Sep 1, 2020. License: CC-BY-NC-SA. Closed captions provided by Brian Reinhart.
From playlist Rational points on elliptic curves
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
Theorem 1.10 - part 10.5 - Neron-Ogg-Shafarevich - Structure of m-Torsion of A mod p
Here we use the theory of Neron Models, Chevalley-Rosenlicht, and a handful of other things to determine the structure of the torsion of an Abelian variety with bad reduction modulo p. This is used in proving the hard part of the Neron-Ogg-Shafarevich criterion: if an abelian variety has a
From playlist Theorem 1.10
Order of Cosets Equals Order of Subgroup | Abstract Algebra
We prove that for a group G and a subgroup H, every coset Ha of H has the same order as H, and thus all the cosets of the subgroup H have the same order as each other. This is our final step to prove Lagrange's Theorem, which states for a finite group G and subgroup H, the order of G is a
From playlist Abstract Algebra
Galois Groups Revisited - Chapter 25
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
From playlist Modern Algebra - Chapter 25
Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory
Lagrange's theorem is another very important theorem in group theory, and is very intuitive once you see it the right way, like what is presented here. This video also discusses the idea of subgroups and cosets, which are crucial in the development of the Lagrange's theorem. Other than c
From playlist Essence of Group Theory
Ignat Soroko: Intersections and joins of subgroups in free groups
Abstract : The famous Hanna Neumann Conjecture (now the Friedman--Mineyev theorem) gives an upper bound for the ranks of the intersection of arbitrary subgroups H and K of a non-abelian free group. It is an interesting question to `quantify' this bound with respect to the rank of the join
From playlist Virtual Conference
Why you can't solve quintic equations (Galois theory approach) #SoME2
An entry to #SoME2. It is a famous theorem (called Abel-Ruffini theorem) that there is no quintic formula, or quintic equations are not solvable; but very likely you are not told the exact reason why. Here is how traditionally we knew that such a formula cannot exist, using Galois theory.
From playlist Traditional topics, explained in a new way